## Selected Excogitations and General Exegesis

a certain impression I had of mathematicians was ... that they spent immoderate amounts of time declaring each other's work trivial.''
(Richard Preston)

From his prize winning article The Mountains of Pi, New Yorker, March 9, 1992

It's about as interesting as going to the beach and counting sand. I wouldn't be caught dead doing that kind of work.''

The universe contains at most two to the power fifty' grains of sand.''
(Archimedes)

Americans are broad-minded people. They'll accept the fact that a person can be alcoholic, a dope fiend or a wife-beater, but if a man doesn't drive a car, everybody thinks that something is wrong with him.''
(Art Buchwald, local newspaper, March 1996)

Caution, skepticism, scorn, distrust and entitlement seem to be intrinsic to many of us because of our training as scientists... . These qualities hinder your job search and career change.''

Former astrophysicist Stephen Rosen, now director, Scientific Career Transitions Program, New York City, giving job-hunting advice in an on-line career counseling session.

(Quoted in Science, 4 August 1995, page 637)

Consider a precise number that is well known to generations of parents and doctors: the normal human body temperature of 98.6 Farenheit. Recent investigations involving millions of measurements reveal that this number is wrong; normal human body temperature is actually 98.2 Farenheit. The fault, however, lies not iwth Dr. Wunderlich's original measurements - they were averaged and sensibly rounded to the nearest degree: 37 Celsius. When this temperature was converted to Farenheit, however, the rounding was forgotten and 98.6 was taken to be accurate to the nearest tenth of a degree. Had the original interval between 36.5 and 37.5 Celsius been translated, the equivalent Farenheit temperatures would have ranged from 97.7 to 99.5. Apparently, discalculia can even cause fevers.''

John Allen Paulus, in A Mathematician Reads the Newspaper' (Basic Books)

(Quoted in Science, August 18, 1995, page 992)

When Gladstone was British Prime Minister he visited Michael Faraday's laboratory and asked if some esoteric substance called Electricity' would ever have practical significance.

"One day, sir, you will tax it."

(Quoted in Science, 1994). As Michael Saunders points out, this can not be correct because Faraday died in 1867 and Gladstone became PM in 1868. A more plausible PM would be Peel as electricity was discovered in 1831. Equally well it may be an urbane legend'.

 "the proof is left as an exercise" occurred in De Triangulis Omnimodis' by Regiomontanus, written 1464 and published 1533. He is quoted as saying "This is seen to be the converse of the preceding. Moreover, it has a straightforward proof, as did the preceding. Whereupon I leave it to you for homework." ''
(Quoted in Science, 1994)

As the fading light of a dying day filtered through the window blinds, Roger stood over his victim with a smoking .45, surprised at the serenity that filled him after pumping six slugs into the bloodless tyrant that had mocked him day after day, and then he shuffled out of the office with one last look back at the shattered computer terminal lying there like a silicon armidillo left to rot on the information highway.''

• From the winner of the 1994 Bulwer-Lytton Fiction contest for lousy literature

Named for the author of It was a dark and stormy night.' in the novel Paul Clifford', 1830. (Later winners are quoted below.)

• I imagine most of that stuff on the information highway is roadkill anyway.''
(John Updike, 1994)

It's going to be about bad news. It's going to be about the future of this country, about foreign policy, about defense policy. There are a lot of issues left. I'm certain something will pop up in November. So we'll be able to put it together.''

Robert Dole on what is the key issue?' in the '96 Presidential election.

(Quoted in the Economist, March 16, 1996, page 23)

My dearest Miss Dorothea Sankey

My affectionate & most excellent wife is as you are aware still living - and I am proud to say her health is good. Nevertheless it is always well to take time by the forelock and be prepared for all events. Should anything happen to her, will you supply in her place - as soon as the proper period for decent mourning is over.

Till then I am your devoted servant
Anthony Trollope.''

Anthony Trollope taking precautions in 1861.

• Sotheby's at auction in 1942 described this letter as "one of the most extraordinary letters ever offered for sale".
• (Quoted from The Oxford Book of Letters in the Economist, March 23, 1996, page 90)

I believe that the motion picture is destined to revolutionize our educational system and that in a few years it will supplant largely, if not entirely, the use of textbooks.''

(Thomas Alva Edison, 1922)

Keynes distrusted intellectual rigour of the Ricardian type as likely to get in the way of original thinking and saw that it was not uncommon to hit on a valid conclusion before finding a logical path to it.

I don't really start', he said, until I get my proofs back from the printer. Then I can begin serious writing.' ''

two excerpts from Keynes the man written on the 50th Anniverary of Keynes' death.

(Sir Alec Cairncross, in the Economist, April 20, 1996)

One major barrier to entry into new markets is the requirement to see the future with clarity. It has been said that to so fortell the future, one has to invent it. To be able to invent the future is the dividend that basic research pays.''

An econonomic case for basic research, by Eugen Wong, Hong Kong University of Science and Technology

(In Nature, May 16, 1996, pages 178-9)

 'Ace, watch your head!' hissed Wanda urgently, yet somehow provocatively, through red, full, sensuous lips, but he couldn't, you know, since nobody can actually watch more than part of his nose or a little cheek or lips if he really tries, but he appreciated her warning.''

• Janice Estey of Aspen 1996 Bulwer-Lytton Grand Prize Winner

• Because the Indians of the high Andes were believed to have little sense of humor, Professor Juan Lyner was amazed to hear this knee-slapper that apparently had been around for centuries at all of the Inca spots: Llama ask you this. Guanaco on a picnic? Alpaca lunch.' ''

• John Ashman of Houston 1995 Bulwer-Lytton Grand Prize Winner

• We know [smoking is] not good for kids. But a lot of other things aren't good. Drinking's not good. Some would say milk's not good.''

Robert Dole echoing the tobacco companies on smoking?

( Page 27 in the Economist, July 6, 1996)

I feel so strongly about the wrongness of reading a lecture that my language may seem immoderate .... The spoken word and the written word are quite different arts .... I feel that to collect an audience and then read one's material is like inviting a friend to go for a walk and asking him not to mind if you go alongside him in your car.''

( Page 76 in Science, July 5, 1996)

I know, it's hard to believe that Microsoft would release a product before it was ready, but there you have it. A Seattle cyberwag says, "At Microsoft, quality is job 1.1." We had him killed. ''

from Welcome to Stale

A take-off of Microsoft's webzine'', Slate, Stale, August 1996.

No presidential candidate in the future will be so inept that four of his major speeches can be boiled down to these four historic sentences: Agriculture is important. Our rivers are full of fish. You cannot have freedom with out liberty. The future lies ahead.''

the (no doubt partisan) Louisville Courier-Journal on Thomas Dewey in 1948, quoted in Jack Beatty's review of James Patterson's Grand Expectations, The United States, 1945-1974. Beatty goes on to say:

Tom Dewey, make room for Bob (like everyone else in this room I was born'') Dole.

and lists many other fine quotes from Patterson's book.

(From pp. 107-112 in the Atlantic Monthly, September 1996)

Writers often thank their colleagues for their help. Mine have given none. .. Writers often thank their typists. I thank mine. Mrs George Cook is not a particularly good typist, but her spelling and grammar are good. The responsibility for any mistakes is mine, but the fault is hers. Finally, writers too often thank their wives. I have no wife.''

Acknowledgement by Edward Ingram in The Beginning of the Great Game in Asia, 1828-1834.

(From p. 83 in the Economist, September 7th 1996)

I see some parallels between the shifts of fashion in mathematics and in music. In music, the popular new styles of jazz and rock became fashionable a little earlier than the new mathematical styles of chaos and complexity theory. Jazz and rock were long despised by classical musicians, but have emerged as art-forms more accessible than classical music to a wide section of the public. Jazz and rock are no longer to be despised as passing fads. Neither are chaos and complexity theory. But still, classical music and classical mathematics are not dead. Mozart lives, and so does Euler. When the wheel of fashion turns once more, quantum mechanics and hard analysis will once again be in style.''

Freeman Dyson's review of Nature's Numbers by Ian Stewart (Basic Books, 1995).

(From p. 612 in the American Mathematical Monthly, August-September 1996)

I was sitting by Dr. Franklin, who perceived that I was not insensible to these mutilations. I have made a rule, said he, whenever in my power, to avoid becoming the draughtsman of papers to be reviewed by a public body.''

Jefferson writing in 1818 of the drafting of the Declaration of Independence.

(From p. 74 of Conor Cruise O'Brien's disturbing article Thomas Jefferson: Radical and Racist, in the Atlantic Monthly, October 1996)
["The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants."
(Jefferson quoted on Oklahoma bomb suspect McVeigh's T-shirt.)]

My morale has never been higher than since I stopped asking for grants to keep my lab going.''

Robert Pollack, Columbia Professor of biology. Speaking on "the crisis in scientific morale", September 19, 1996 at GWU's symposium Science in Crisis at the Millennium.

(Quoted from p. 1805 in the September 27, 1996 Science)

smugness, brutality, unctuous rectitude and tact"

Cecil Rhodes own sardonic paraphrase of the criteria for a Rhodes Scholarship:

• 30% for "literary and scholarly attainments";
• 20% for "fondness of and success in manly outdoor sports";
• 30% for "qualities of manhood, truth, courage, devotion to duty...";
• 20% for "moral force of character and instincts to lead and to take an interest in his school-mates".

(Quoted from Cecil Rhodes Traduced, pp. 80-81 in the October 5, 1996 Economist)

The dictum that everything that people do is 'cultural' ... licenses the idea that every cultural critic can meaningfully analyze even the most intricate accomplishments of art and science. ... It is distinctly weird to listen to pronouncements on the nature of mathematics from the lips of someone who cannot tell you what a complex number is!''

Norman Levitt, from "The flight From Science and Reason," New York Academy of Science.

(Quoted from p. 183 in the October 11, 1996 Science)

Church discipline is also somewhat of a remove from the time when the Emperor Henry IV was made to stand in the snow for three days outside the Pope's castle at Canossa, awaiting forgiveness. A French Bishop, Jacques Gaillot, because of his ultra-liberal views was recently transferred from his position at Evreux, in Normandy, and given charge instead of the defunct dioscese of Partenia, in Southern Algeria, which has been covered by sand since the Middle Ages. Gaillot has retaliated by creating a virtual dioscese on the Internet, which can be reached at http://www.partenia.fr ''

Cullen Murphy, "Broken Covenant?"

(Quoted from p. 24 in the November, 1996 Atlantic Monthly)

We were a polite society and I expected to lead a quiet life teaching mechanics and listening to my senior colleagues gently but obliquely poking fun at one another. This dream of somnolent peace vanished very quickly when Rutherford came to Cambridge. Rutherford was the only person I have met who immediately impressed me as a great man. He was a big man and made a big noise and he seemed to enjoy every minute of his life. I remember that when transatlantic broadcasting first came in, Rutherford told us at a dinner in Hall how he had spoken into a microphone to America and had been heard all over the continent. One of the bolder of our Fellows said "Surely you did not need to use apparatus for that." ''

Geoffrey Fellows, 1952, as quoted by George Batchelor in The Life and Legacy of G.I. Taylor (Cambridge University Press).

(Quoted in "Vignettes: Yesteryear in Oxbridge" p. 733 in Science November 1, 1996)

Then, owls and bats,
Cowls and twats,
Monks and nuns, in a cloister's moods,

From Robert Browning's (1841) Pippa Passes, which also contains "God's in his Heaven, all's right with the world."

(Quoted on page 56-66 of Bill Byerson, Mother Tongue: The English Language, Penguin, 1990.)

He goes on to say about "this disconcerting quote" that

Browning had apparently somewhere come across the word twat - which meant precisely the same as it does now - but somehow took it to mean a piece of head gear for nuns. The verse became a source of twittering amusement for generations of schoolboys and a perennial embarrassment to their elders, but the word was never altered and Browning was allowed to live out his life in wholesome ignorance because no one could think of a suitably delicate way of explaining his mistake to him.''

Two major advances are responsible for both the recent progress and current optimism. First, recombinant DNA technology has made it possible to identify every gene and protein in an organism and to manipulate them in order to explore their functions. Second, it has been discovered that the molecular mechanisms of development have been conserved during animal evolution to a far greater extent than had been imagined. This conservation means that discoveries about the development of worms and files, which come from the kind of powerful genetic studies that are not possible in mammals, greatly accelerate the rate at which we can discover the mechanisms and molecules that operate during our own development.
... ...
It is tempting to think that the main principles of neural development will have been discovered by the end of the century and that the cellular and molecular basis of the mind will be the main challenge for the next. An alternative view is that this feeling that understanding is just a few steps away is a recurring and necessary delusion that keeps scientists from dwelling on the complexity the face and how much more remains to be discovered.''

(Editorial on page 1063 of Science November 15, 1996)

Neural Development: Mysterious No More? written by Martin Raff (University College, London).

[It is hard to imagine a better case for basic science'' than that afforded by this conservation principle -- if worms were good enough for Darwin ... !]

3. SPACE SYMPOSIUM: THEOLOGIANS JOIN SCIENTISTS AT WHITE HOUSE.

Vice President Gore, who was clearly on top of the technical issues, met on Wednesday with a group of tough-minded scientists, clergy and fuzzy romantics to discuss the questions raised by evidence of extraterrestrial life. For physicist/astronomer John Bahcall, the remarkable thing was not that such questions were being asked, but that we have the tools to answer them.''

(From WHAT'S NEW by Robert L. Park -- Friday, 13 Dec 96)

WHAT'S NEW is published every Friday by the AMERICAN PHYSICAL SOCIETY.

As the test beds begin to prove WDM (wavelength division multiplexing') networks feasible, telephone company executives will have to judge whether they are wise. If a single glass fiber can carry all the voice, fax, video and data traffic for a large corporation yet costs little more than today's high-speed Internet connections, how much will they be able to charge for telephone service? Peter Cochrane of BT Laboratories in Ipswich, England, predicts that "photonics will transform the telecoms industry by effectively making bandwidth free and distance irrelevant." Joel Birnbaum, director of Hewlett-Packard Laboratories, expects that this will relegate telephone companies to the role of digital utilities. "You will buy computing like you now buy water or power," he says.

Others, such as industry analyst Francis McInerney, believe the double-time march of technology has already doomed them to fall behind. AT&T and its ilk, he claims, "are already dead. When individuals have [megabits per second of bandwidth], telephone service should cost about three cents a month." Having discovered how to offer high-bandwidth service, telephone companies may now need to invent useful things to do with it, just to stay in business. ''

(From BANDWIDTH, UNLIMITED by W. Wayt Gibbs)

In the January 1997 on-line Scientific American.

Before Canada jeopardizes its scientific future and compromises its scientific community to achieve short-term budgetary solutions, it must recognize that the funding of university sicence is both a government responsibility and a long-range investment. Without government support, Canada's university science infrastructure will erode, and along with it, the country's competitiveness in a world economy increasingly based on knowledge.''
(Editorial on page 139 of Science January 10, 1997)

Canada's Crisis: Can Business Rescue Science? written by Albert Aguyo and Richard A. Murphy (McGill, Montreal Neurological).

1. SENATOR GRAMM EMERGES AS THE CHAMPION OF BASIC RESEARCH

178 new bills were introduced in the Senate on Tuesday -- one, S.124, is a thing of beauty: "The National Research Investment Act of 1997." It calls for doubling the federal investment in basic science and medical research over a 10-year period (WN 17 Jan 97). Funds must be allocated by a peer review system and can not be used for the commercialization of technologies. A dozen non-defense agencies and programs are covered by the bill, which is the work of Phil Gramm (R-TX). Gramm pointed out that in 1965, 5.7% of the federal budget went for non-defense R&D -- 32 years later, that has dropped to only 1.9%, and real spending on research has declined for four straight years. Ten-year doubling requires an annual increase of 7% -- just what leaders of the science community have been calling for (WN 10 Jan 97)."

(From WHAT'S NEW by Robert L. Park -- Friday, 24 January, 1997)

WHAT'S NEW is published every Friday by the AMERICAN PHYSICAL SOCIETY. It is interesting to contrast a conservative US senator (an ex-academic) from a liberal Canadian government.

a British officer told a sergeant to post four lookouts to watch for the German army which was advancing through Belgium. Later, the officer discovered that the sergeant had posted only three. Asked to explain his lapse, the soldier said he had judged the fourth guard unnecessary. 'The enemy would hardly come from that direction,' he explained, 'it's private property.' ''

(Quoted from Back to the Front by Stephen O'Shea)

From page 59 in MACLEANS Magazine of February 10, 1997.

Admirers of Thomas Jefferson have long quoted his statement about black men and women that is inscribed on the Jefferson Memorial: 'Nothing is more certainly written in the book of fate than that these people are to be free.' But they and the inscription, as Conor Cruise O'Brien pointed out in 'Thomas Jefferson: Radical and Racist' (October, 1996, Atlantic), omit Jefferson's subsequent clause: 'Nor is it less certain that the two races, equally free, cannot live in the same government.'"

(Quoted from What Jefferson Helps to Explain by Benjamin Schwarz)

From page 60 in the Atlantic Monthly of March, 1997. [There are well established copyright notions of "paternity" and "integrity" in the use of material -- the later which this clearly violates!]

A centre of excellence is, by definition, a place where second class people may perform first class work.''

A truly popular lecture cannot teach, and a lecture that truly teaches cannot be popular.''

The most prominent requisite to a lecturer, though perhaps not really the most important, is a good delivery; for though to all true philosophers science and nature will have charms innumerably in every dress, yet I am sorry to say that the generality of mankind cannot accompany us one short hour unless the path is strewed with flowers.''

Excerpted from "Michael Faraday -- and the Royal Institution, the genius of man and place", by J.M. Thomas, Adam Hilger, Bristol, 1991.

The body of mathematics to which the calculus gives rise embodies a certain swashbuckling style of thinking, at once bold and dramatic, given over to large intellectual gestures and indifferent, in large measure, to any very detailed description of the world. It is a style that has shaped the physical but not the biological sciences, and its success in Newtonian mechanics, general relativity and quantum mechanics is among the miracles of mankind. But the era in thought that the calculus made possible is coming to an end. Everyone feels this is so and everyone is right.''
(From Vignettes: Changing Times in Science, 28 February 1997, page 1276)

From David Berlinski's "A Tour of the Calculus" (Pantheon Books, 1995)

[8] 94m:94015 Beutelspacher, Albrecht Cryptology. An introduction to the art and science of enciphering, encrypting, concealing, hiding and safeguarding described without any arcane skullduggery but not without cunning waggery for the delectation and instruction of the general public. Transformation from German into English succored and abetted by J. Chris Fisher. MAA Spectrum. Mathematical Association of America, Washington, DC, 1994. xvi+156 pp. ISBN: 0-88385-504-6 94A60 (94-01)''
(From Math Reviews)

A serious "best title" candidate...

It's generally the way with progress that it looks much greater than it really is.''
(From The Wittgenstein Controversy, by Evelyn Toynton in the Atlantic Monthly June 1997, pp. 28-41.)

The epigraph that Ludwig Wittgenstein (1889-1951) ("whereof one cannot speak, thereof one must be silent") had wished for an unrealized joint publication of Tractatus Logico-Philosophicus (1922) and Philosophical Investigations (1953): suggesting the two volumes are not irreconcilable.

Compare the following for which I have no good source:

"The world will change. It will probably change for the better. It won't seem better to me."

(J. B. Priestly)

In 1965 the Russian mathematician Alexander Konrod said "Chess is the Drosophila of artificial intelligence." However, computer chess has developed as genetics might have if the geneticists had concentrated their efforts starting in 1910 on breeding racing Drosophila. We would have some science, but mainly we would have very fast fruit flies.''
(From John McCarthy's review of Kasparov versus Deep Blue by Monty Newborn (Springer, 1996) in Science, 6 June 1997, page 1518)

He goes on to point out that of three features of human chess play two were used in early programs (forward pruning, identifying parallel moves, and partitioning (never used)). None survives in present programs. Material on Making computer chess scientific is available from John McCarthy's web site

A research policy does not consist of programs, but of hiring high-quality scientists. When you hire someone good, you've made your research policy for the next 20 years.''
Chief CNRS advisor Vincent Courtillot quoted in New CNRS Chief Gets Marching Orders, Science, 18 July, 1997, page 308)

Mathematicians are like pilots who maneuver their great lumbering planes into the sky without ever asking how the damn things stay aloft.
...
The computer has in turn changed the very nature of mathematical experience, suggesting for the first time that mathematics, like physics, may yet become an empirical discipline, a place where things are discovered because they are seen.
...
The existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself.''
(From David Berlinski's somewhat negative review of The Pleasures of Counting by T. W. Korner (Cambridge, 1996)
in The Sciences, July/August 1997, pages 37-41)

Korner is a careful and stimulating writer/teacher.

If I can give an abstract proof of something, I'm reasonably happy. But if I can get a concrete, computational proof and actually produce numbers I'm much happier. I'm rather an addict of doing things on the computer, because that gives you an explicit criterion of what's going on. I have a visual way of thinking, and I'm happy if I can see a picture of what I'm working with.''
(John Milnor)

Page 78 of Who got Einstein's Office? by Ed Regis, Addison-Wesley, 1986. A history of the Institute for Advanced Study. The answer is Arnie Beurling.

The term "reviewed publication" has an appealing ring for the naive rather than the realistic... Let's face it: (1) in this day and age of specialization, you may not find competent reviewers for certain contributions; (2) older scientists may agree that over the past two decades, the relative decline in research funds has been accompanied by an increasing number of meaningless, often unfair reviews; (3) some people are so desperate to get published that they will comply with the demands of reviewers, no matter how asinine they are.''
(August Epple)

From Organizing Scientific Meetings quoted on page 400 of Science October 17, 1997.

The NYT also has a stunning revelation about the way the Ivy League used to do business. Last Friday, the President of Darmouth used the occasion of dedicating a campus Jewish student center to haul out a 1934 letter between an alumnus of the school and the director of admissions. The alum complained that "the campus seems more Jewish each time I arrive in Hanover. And unfortunately many of them (on quick judgment) seem to be the 'kike' type." And the Dartmouth admissions man wrote back, "I am glad to have your comments on the Jewish problem, and I shall appreciate your help along this line in the future. If we go beyond the 5 percent or 6 percent in the Class of 1938, I shall be grieved beyond words." In reacting to the revelation, Elie Wiesel summons a simple fact that suggests how much times have changed: the current presidents of Harvard, Yale, and Princeton are Jewish.''

(SLATE, Tuesday November 11, 1997)

This is the essence of science. Even though I do not understand quantum mechanics or the nerve cell membrane, I trust those who do. Most scientists are quite ignorant about most sciences but all use a shared grammar that allows them to recognize their craft when they see it. The motto of the Royal Society of London is 'Nullius in verba' : trust not in words. Observation and experiment are what count, not opinion and introspection. Few working scientists have much respect for those who try to interpret nature in metaphysical terms. For most wearers of white coats, philosophy is to science as pornography is to sex: it is cheaper, easier, and some people seem, bafflingly, to prefer it. Outside of psychology it plays almost no part in the functions of the research machine.''
(Steve Jones, University College, London)

From his review of How the Mind Works (by Steve Pinker) in The New York Review of Books (pages 13-14) November 6, 1997. [Two solitudes indeed! See below]

If you have a great idea, solid science, and earthshaking discoveries, you are still only 10% of the way there,''
(David Tomei, LXR Biotechnology Inc.)

Quoted in Science page 1039, November 7, 1997. [On the vicissitudes of startup companies.]

There he received his hardest job of the war - a rush request to convert typewriters to twenty-one different languages of Asia and the South Pacific.
...
The implications of the work and its difficulty brought him to near collapse, but he completed it with only one mistake: on the Burmese typewriter he put a letter upside down. Years later, after he had discovered his error, he told the language professor he had worked with that he would fix that letter on the professor's Burmese typewriter. The professor said not to bother; in the intervening years, as a result of typewriters copied from Martin's original, that upside-down letter had been accepted in Burma as proper typewriter style.''
(Ian Frazier)

Page 88 in Typewriter Man, the Atlantic Monthly, November 1997: "For Martin Tytell, the machinery of writing has been a life's work." [A fine example of convergence.]

The T-bone terror proves that ministers have no grasp of science or maths - let alone our liberties

The giant finger whooshes out of the night sky and points at the dumbstruck face in the window. "It could be you," says a voice. This week the Agriculture Minister Jack Cunningham impersonated the National Lottery advertiser. As the nation's fork was poised with a T-bone steak on its way to the nation's mouth, Dr Cunningham screamed: "Don't touch it." According to the great god science, new variant Creutzfeldt-Jakob disease (nvCJD) could be lurking in that mouthful. There is a small risk, and where there is risk, a government must ban.

Perhaps only mathematicians are aware of the enormity of what the Government did this week. It took a risk that is statistically negligible and exploited it as an act of insufferable nannying. Beef ribs, T-bones and oxtails present a public health risk publicised as "very small" and "a chance of one case per year" (though none of Britain's 22 nvCJD cases has been positively linked to beef). Most newspapers cluelessly converted "a chance" into a certainty, and ridiculed the risk as a tiny one in 56 million. But that is not what the scientists said. They suggested the chance was "5 per cent", so the risk is nearer to one in 1.1 billion, or one in 560 million among the half of the population that eats beef. There can have been no more tenuous basis for an infringement of personal liberty.''

(Simon Jenkins)

Simon Jenkins on Boneless Wonders in the Times of London, Dec 6, 1997

The common situation is this: An experimentalist performs a resolution analysis and finds a limited-range power law with a value of D smaller than the embedding dimension. Without necessarily resorting to special underlying mechanistic arguments, the experimentalist then often chooses to label the object for which she or he finds this power law a ''fractal''. This is the fractal geometry of nature.''

(David Avnir et al, Hebrew University)

From Is the geometry of nature fractal? in Science January 2, 1998, 39-40. Their review of all articles from 1990 to 1996 in Physical Reviews suggests very little substance for claims of fractility.

Most nonscientists who like to think of themselves as knowledgeable about modern science really know only about technologies - and specifically those technologies likely to bring economic profits in the short term.''

(Takashi Tachibana, Japanese Journalist)

From Closing the Knowledge Gap Between Scientist and Nonscientist in Science August 7, 1998, 778-779.

Another thing I must point out is that you cannot prove a vague theory wrong. ... Also, if the process of computing the consequences is indefinite, then with a little skill any experimental result can be made to look like the expected consequences.''

(Richard Feynman, 1964)

Quoted by Gary Taubes in The (Political) Science of Salt, Science August 14, 1998, 898-907.

Renyi would become one of Erdos's most important collaborators. ... Their long collaborative sessions were often fueled by endless cups of strong coffee. Caffeine is the drug of choice for most of the world's mathematicians and coffee is the preferred delivery system. Renyi, undoubtedly wired on espresso, summed this up in a famous remark almost always attributed to Erdos: "A mathematician is a machine for turning coffee into theorems." ... Turan, after scornfully drinking a cup of American coffee, invented the corollary: "Weak coffee is only fit for lemmas." ''

(Bruce Schechter, 1998)

On page 155 of My Brain is Open, Schechter's 1998 Simon and Schuster biography of Erdos. Schechter's Erdos is recognisable. The book contains interesting material on the Erdos-Selberg controversy (pp. 144-151). For more about the coffee see Dick Askey's recollection.

Once the opening ceremonies were over, the real meat of the Congress was then served up in the form of about 1400 individual talks and posters. I estimated that with luck I might be able to comprehend 2% of them. For two successive weeks in the halls of a single University, ICM'98 perpetuated the myth of the unity of mathematics; which myth is supposedly validated by the repetition of that most weaselly of rhetorical phrases: "Well, in principle, you could understand all the talks." ''

(Philip Davis, 1998)

Describing the Berlin International Congress of Mathematicians in the October 1998 SIAM News.

Looking over the past 150 years -- at the tiny garden at Brno, the filthy fly room at Columbia, the labs of the New York Botanical Garden, the basement lab at Stanford, and the sun-drenched early gatherings at Cold Spring Harbor -- it seems that the fringes, not the mainstream, are the most promising places to discover revolutionary advances.''

(Paul Berg and Maxine Singer, 1998)

In Inspired Choices, Science October 30, 1998, 873-874s, on the past 150 years of biological research.

Should we teach mathematical proofs in the high school? In my opinion, the answer is yes...Rigorous proofs are the hallmark of mathematics, they are an essential part of mathematics' contribution to general culture.''
George Polya (1981). Mathematical discovery: On understanding, learning, and teaching problem solving (Combined Edition), New York, Wiley & Sons (p. 2-126)
A mathematical deduction appears to Descartes as a chain of conclusions, a sequence of successive steps. What is needed for the validity of deduction is intuitive insight at each step which shows that the conclusion attained by that step evidently flows and necessarily follows from formerly acquired knowledge (acquired directly by intuition or indirectly by previous steps) ... I think that in teaching high school age youngsters we should emphasize intuitive insight more than, and long before, deductive reasoning.'' (ibid, p. 2-128)
This "quasi-experimental" approach to proof can help to de-emphasis a focus on rigor and formality for its own sake, and to instead support the view expressed by Hadamard when he stated "The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it" (J. Hadamard, in E. Borel, Lecons sur la theorie des fonctions, 3rd ed. 1928, quoted in Polya, (1981), (p. 2/127).
intuition comes to us much earlier and with much less outside influence than formal arguments which we cannot really understand unless we have reached a relatively high level of logical experience and sophistication. Therefore, I think that in teaching high school age youngsters we should emphasize intuitive insight more than, and long before, deductive reasoning.'' (ibid, p. 2-128)

In the first place, the beginner must be convinced that proofs deserve to be studied, that they have a purpose, that they are interesting.'' (ibid, p. 2-128)

The purpose of a legal proof is to remove a doubt, but this is also the most obvious and natural purpose of a mathematical proof. We are in doubt about a clearly stated mathematical assertion, we do not know whether it is true or false. Then we have a problem: to remove the doubt, we should either prove that assertion or disprove it.'' (ibid, p. 2-129)

(Polya quotes are thanks to Laurie Edwards)

The basic difference between playing a human and playing a supermatch against Deep Blue is the eerie and almost empty sensation of not having a human sitting opposite you. With humans, you automatically know a lot about their nationality, gender, mannerisms, and such minor things as a persistent cough or bad breath. Years ago we had to endure chain-smokers who blew smoke our way. But Deep Blue wasn't obnoxious, it was simply nothing at all, an empty chair not an opponent but something empty and relentless.''
(Garry Kasparov, 1998)

Kasparov writing on TechMate in Forbes (22/2/98) - a collection on super computing.

All professions look bad in the movies ... why should scientists expect to be treated differently?''
(Michael Crichton, 1999)

Addressing the 1999 AAAS Meetings, and quoted in Science February 19, 1999, page 1111.

the academy was a sort of club for retired Parisian scientists, happy to be able to come together once a week to talk about science for 2 hours after lunch and a little nap.''
(Guy Ourison, January 1999)

Inaugural speech as President to the French Academy of Science quoted in Science April 23, 1999, page 580.

User-interface criticism is a genre to watch. It will probably be more influential and beneficial to the next century than film criticism was to the twentieth century. The twenty-first century will be filled with surprises, but one can safely count on it to bring more complexity to almost everything. Bearing the full brunt of that complexity, the great user-interface designers of the future will provide people with the means to understand and enrich their own humanity, and to stay human.''
(Jaron Lanier, June 1999)

From page 43 of Interface-off in The Sciences May/June 1999, pages 38-43.

A real number complexity model appropriate for this context is given in the recent landmark work of Blum, Cucker, Shub and Smale . In discussing their motivation for seeking a suitable theoretical foundation for modern scientific computing, where most of the algorithms are real number algorithms' the authors of this work quote the following illuminating remarks of John von Neumann, made in 1948: There exists today a very elaborate system of formal logic, and specifically, of logic applied to mathematics. This is a discipline with many good sides but also serious weaknesses.... Everybody who has worked in formal logic will confirm that it is one of the technically most refactory parts of mathematics. The reason for this is that it deals with rigid, all-or-none concepts, and has very little contact with the continuous concept of the real or the complex number, that is with mathematical analysis. Yet analysis is the technically most successful and best-elaborated part of mathematics. Thus formal logic, by the nature of its approach, is cut off from the best cultivated portions of mathematics, and forced onto the most difficult mathematical terrain, into combinatorics.

The theory of automata, of the digital, all-or-none type as discussed up to now, is certainly a chapter in formal logic. It would, therefore, seem that it will have to share this unattractive property of formal logic. It will have to be, from the mathematical point of view, combinatorial rather than analytical.''

( l. Blum, P. Cucker, M. Shub and S. Smale (1998), Complexity and Real Computation, Springer-Verlag, New York)

Commentary thanks to Larry Nazareth

Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.''
(Augustus De Morgan)

Adrian Rice (What Makes a Great Mathematics Teacher?) from page 540 of The American Mathematical Monthly, June-July 1999

In 1831, Fourier's posthumous work on equations showed 33 figures of solution, got with enormous labour. Thinking this is a good opportunity to illustrate the superiority of the method of W. G. Horner, not yet known in France, and not much known in England, I proposed to one of my classes, in 1841, to beat Fourier on this point, as a Christmas exercise. I received several answers, agreeing with each other, to 50 places of decimals. In 1848, I repeated the proposal, requesting that 50 places might be exceeded: I obtained answers of 75, 65, 63, 58, 57, and 52 places.''
(Augustus De Morgan)

Adrian Rice from page 542 of The American Mathematical Monthly, June-July 1999

I think we need more institutes, but then you run into the question, Is it better to spend $2 million and have another institute or to fund another twenty-five or so researchers each year? It's a question of trying to keep the discipline alive and thriving. There's no doubt the really big ideas in mathematics come from maybe 5 percent of the people, but you need a broad base to nourish the 5 percent and to work out all the details as they move on to more adventuresome things. Look at, say, mathematicians at Group III universities. It's a rarity when they get funding. How do you keep them in the system? ... We're under terrific pressure to increase the size of our grants. If we did what the [National Science] board wants us to do, we would fund 800 people instead of 1,400. It's a question of whether DMS did the right thing when they pulled so many people down to one month of summer support. This took some of the pressure off the Foundation to put more money in mathematics. Suppose we funded 800 people. How much noise would it create? Would there be a march on Washington? I often think that's the way to go. See whether mathematicians would stand up for themselves or whether they'd just meekly accept. In chemistry, people get declined, and in two months they turn around with another proposal. Mathematicians --- they get declined twice, and they fold. I think mathematicians have such a personal investment in their problems that if you turn down their proposals, they take it as if you're judging them as mathematicians. They're not as flexible and often don't seem to be able to move to another class of problems. We fund proposals, not individuals.'' (D. J. Lewis) Interview with Allyn Jackson from page 669 of The Notices of The AMS, June-July 1999 Notices: After your time at the NSF, do you have any advice for the math community about what they should be doing to try to improve the funding for mathematics? Lewis: I don't think that up to this date they've made a very good case for why they should be funded. The bottom line is, What are you doing for the citizens of the country? Notices: When you say make the case,'' what do you mean concretely? Do groups of mathematicians have to descend on Capitol Hill? Lewis: They've got to do some demonstrations of what mathematics has accomplished for the good of society. One of the things mathematicians have done is education. For example, if mathematicians took seriously the job of training elementary and middle school teachers, they could make some claim that they really improve things. Also, science is getting so complicated, it can be done only with the help of mathematics. Is the math community willing to step up and participate? If so, they will have nonmathematicians making the case for greater funding of mathematics. It is always best to have outsiders make your case for you. Once upon a time I thought going to Capitol Hill would be effective. I don't think it will get very far if mathematicians go to Capitol Hill without the support of others. These days information technology and biology and medicine are the themes that echo well with the president and Congress.'' (D. J. Lewis) Interview with Allyn Jackson from page 672 of The Notices of The AMS, June-July 1999 The work then proceeds in a manner unique to science. Because practitioners publish their work electronically, through the e-print archives at the Los Alamos National Laboratory in New Mexico, the entire community can read a paper hours after its authors finish typing the last footnote. As a result, no one theorist or even a collaboration does definitive work. Instead, the field progresses like a jazz performance: A few theorists develop a theme, which others quickly take up and elaborate. By the time it's fully developed, a few dozen physicists, working anywhere from Princeton to Bombay to the beaches of Santa Barbara, may have played important parts.'' (Gary Taubes) From String Theorists Find a Rosetta Stone on page 513 of Science, 23rd July, 1999 'where almost one quarter hour was spent, each beholding the other with admiration before one word was spoken: at last Mr. Briggs began "My Lord, I have undertaken this long journey purposely to see your person, and to know by what wit or ingenuity you first came to think of this most excellent help unto Astronomy, viz. the Logarithms: but my Lord, being by you found out, I wonder nobody else found it out before, when now being known it appears so easy." ' (Henry Briggs, 1617) Briggs, later the first Savelian Professor of Geometry in Oxford, is describing his first meeting with Napier whom he had traveled from London to Edinburgh to meet. From H.W. Turnbull's The Great Mathematicians, Methuen, 1929. Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise.'' (J. W. Tuckey, 1962) From the Annals of Mathematical Statistics , Volume 33. Compare the 1964 Feynman quote above!  One of the beauties of learning is that it admits its provisionality, its imperfections. This scholarly scrupulousness, this willingness to admit that even the best-supported of theories is still a theory, is now being exploited by the unscrupulous. But that we do not know everything does not mean we know nothing. Not all theories are of equal weight. The moon, even the moon over Kansas, is not made of green cheese. Genesis, as a theory, is bunk. If the overabundant new knowledge of the modern age is, let's say, a tornado, then Oz is the extraordinary, Technicolored new world in which it has landed us, the world from which --- life not being a movie --- there is no way home. In the immortal words of Dorothy Gale, Toto, something tells me we're not in Kansas any more.' To which one can only add: Thank goodness, baby, and amen.'' (Salman Rushdie) From his article "Locking out that disruptive Darwin fellow" in the Globe and Mail , September 2, 1999 The mental maps, gave rise to industries that could not have been predicted, and created a new class of technological workers whom wise societies took pains to nurture. Are we about to go through this process again? A renowned social analyst and management philosopher looks to history for insights.'' (Peter Drucker) Beyond the Information Revolution in The Atlantic Monthly Online November 3, 1999 When the facts change, I change my mind. What do you do, sir?'' (John Maynard Keynes) Quoted in The Economist, December 18 1999, page 47 Look miss, if I disagree with Darwin, he's not going to send me to hell.'' (An anonymous student's "Pascal wager-style" rationale) Quoted in The Globe and Mail, January 1, 2000, page D22 by Laura Penny describing a first year University class in Buffalo in which one third of the students were creationists.  Most working scientists may be naive about the history of their discipline and therefore overly susceptible to the lure of objectivist mythology. But I have never met a pure scientific realist who views social context as entirely irrelevant, or only as an enemy to be expunged by the twin lights of universal reason and incontrovertible observation. And surely, no working scientist can espouse pure relativism at the other pole of the dichotomy. (The public, I suspect, misunderstands the basic reason for such exceptionless denial. In numerous letters and queries, sympathetic and interested nonprofessionals have told me that scientists cannot be relativists because their commitment to such a grand and glorious goal as the explanation of our vast and mysterious universe must presuppose a genuine reality "out there" to discover. In fact, as all working scientists know in their bones, the incoherence of relativism arises from virtually opposite and much more quotidian motives. Most daily activity in science can only be described as tedious and boring, not to mention expensive and frustrating. Thomas Edison was just about right in his famous formula for invention as 1% inspiration mixed with 99% perspiration. How could scientists ever muster the energy and stamina to clean cages, run gels, calibrate instruments, and replicate experiments, if they did not believe that such exacting, mindless, and repetitious activities can reveal truthful information about a real world? If all science arises as pure social construction, one might as well reside in an armchair and think great thoughts.) Similarly, and ignoring some self-promoting and cynical rhetoricians, I have never met a serious social critic or historian of science who espoused anything close to a doctrine of pure relativism. The true, insightful, and fundamental statement that science, as a quintessentially human activity, must reflect a surrounding social context does not imply either that no accessible external reality exists, or that science, as a socially embedded and constructed institution, cannot achieve progressively more adequate understanding of nature's facts and mechanisms. '' (Stephen J. Gould) From the article: 'Deconstructing the "Science Wars" by Reconstructing an Old Mold' in Science, Jan 14, 2000: 253-261.  caused Thorstein Veblen to comment acerbically in 1908 that "business principles" were transforming higher education into "a merchantable commodity, to be produced on a piece-rate plan, rated, bought, and sold by standard units, measured, counted and reduced to staple equivalence by impersonal, mechanical tests. '' ... New products and new processes do not appear full-grown," Vannevar Bush, President Franklin Roosevelt's chief science adviser, declared in 1944. "They are founded on new principles and new conceptions, which in turn are painstakingly developed by research in the purest realms of science." '' (Eyal Press and Jennifer Washburn) From The Kept University in The Atlantic Monthly Online, March 2000. Which quote better reflects Science in 2001? Most important to Fox was a young instructor who had arrived at Cornell two years before from Williams and Mary. William Lloyd Garrison Williams had written his Ph.D thesis under Leonard Dickson at Chicago in 1920. Born in Friendship, Kansas, Williams, who was named for the famous abolitionist William LLoyd Garrison, attended a small Quaker school in Indiana, taught school briefly in North Dakota and then attended Haverford College where he earned a B.A. degree. From 1910-13 he attended Oxford University as a Rhodes Scholar, and after receving a B.A. and M.A., he took a faculty position at Miami University of Ohio. His Ph.D. work at Chicago was done during the summers. He also taught briefly at Gettysburg College and William and Mary before coming to Cornell. In 1924, Williams moved to McGill University, where he helped develop the graduate program. He was the founder and organizer of the Canadian Mathematical Congress, the first meeting of which was in Montreal in 1945. Nearly all of the support the Congress was able to acquire was due to William's efforts (see W.L.G. Williams, 1888-1976, G. De B. Robinson, Proc. Royal Society of Canada, 1976). A man of remarkable ability and compassion, Williams took a strong personal interest in his fellowman. A lifelong member of the Society of Friends, he was a tireless worker for Quaker causes.'' (James A. Donaldson and Richard J. Fleming) From "Elbert F. Fox: An Early Pioneer", American Math Monthly 107 (2000) 105-128. Gravity Turntable Sets New Record LONG BEACH, CALIFORNIA--Scientists have been scrutinizing gravity since the time of Newton, but they've had difficulty measuring the power of its pull. Now, thanks to a clever device, physicists have the most precise measurement yet. .... "[It] should have been obvious" that previous measures of big G were off, says physicist Randy Newman of the University of California, Irvine. The new result, announced this week at the American Physical Society meeting, sets big G tentatively at 6.67423 0.00009 x 10-11 m3/(kg s2). "It's one of the fundamental constants," Gundlach says. "Mankind should just know it. It's a philosophical thing."' From ScienceNow May 5, 2000. Imagine Dostoyevsky. There are some incidents like this, two boys killing other children, in his famous diary. Imagine what Dostoyevsky would do with that. He would deal with the transcendentally important question of evil in the child. Today the editor would say, "Fyodor, tomorrow, please, your piece. Don't tell me you need ten months for thinking. Fyodor, tomorrow!" " (George Steiner) Quoted in James Gleick's Faster (Pantheon 1999), pages 97-88, on instant opinion -- sound bites and 'hurry sickness'. So my reaction surprises me. I tell Natalie that math is important and relevant and that I wished I'd made the effort to understand. I wish somebody had found a way of making sense of it all. This revelation comes from reading a stack of magazines about the future, about computers and artificial intelligence, cars and planes, food production and global warming. And I have come to the conclusion that Mr. Kool was right. Math has something to do with calculations, formulas, theories and right angles. And everything to do with real life. Mathematicians not only have the language of the future (they didn't send Taming of the Shrew into space, just binary blips) but they can use it to predict when Andromeda will perform a cosmic dance with the Milky Way. It's mathematicians who are designing the intelligent car that knows when you're falling asleep at the wheel or brakes to avoid an accident. It can predict social chaos and the probability of feeding billions. It even explains the stock market and oil prices.'' ... Paulette Bourgeois lives in Toronto where she is calculating the probability of ever balancing her chequebook. She is the author of the Franklin the Turtle books for children. (Paulette Bourgeois) Quoted from "The Numbers Game," The Globe and Mail July 13, 2000, page A14.  Mathematics is the language of high technology. Indeed it is, but I think it is also becoming the eyes of science.'' (Tom Brzustowski, NSERC President) Addressing the MITACS NCE annual general meeting June 6, 2000. This is fundamentally wrong. We are not entering a time when copyright is more threatened than it is in real space. We are instead entering a time when copyright is more effectively protected than at any time since Gutenberg. The power to regulate access to and use of copyrighted material is about to be perfected. Whatever the mavens of the mid-1990s may have thought, cyberspace is about to give the holders of copyrighted property the biggest gift of protection they have ever known. In such an age -- in a time when the protections are being perfected -- the real question for law is not, how can law aid in that protection? but rather, is that protection too great? The mavens were right when they predicted that cyberspace will teach us that everything we thought about copyright was wrong. But the lesson in the future will be that copyright is protected far too well. The problem will center not on copy-right but on copy-duty -- the duty of owners of protected property to make that property available.'' (Lawrence Lessig) Quoted from page 127 of his book: "Code and other laws of Cyberspace", Basic Books, 1999. An informed list of the most profound scientific developments of the 20th century is likely to include general relativity, quantum mechanics, big bang cosmology, the unraveling of the genetic code, evolutionary biology, and perhaps a few other topics of the reader's choice. Among these, quantum mechanics is unique because of its profoundly radical quality. Quantum mechanics forced physicists to reshape their ideas of reality, to rethink the nature of things at the deepest level, and to revise their concepts of position and speed, as well as their notions of cause and effect. '' (Daniel Kleppner and Roman Jackiw) Quoted from the article "One Hundred Years of Quantum Physics" in Science August 11, pages 893-898. http://www.sciencemag.org/cgi/content/full/289/5481/893 A wealthy (15th Century) German merchant, seeking to provide his son with a good business education, consulted a learned man as to which European institution offered the best training. "If you only want him to be able to cope with addition and subtraction," the expert replied, "then any French or German university will do. But if you are intent on your son going on to multiplication and division -- assuming that he has sufficient gifts -- then you will have to send him to Italy.'' (Georges Ifrah) From page 577 of "The Universal History of Numbers: From Prehistory to the Invention of the Computer", translated from French, John Wiley, 2000. (Emphasizing quite how great an advance positional notation was!) 2000 was a banner year for scientists deciphering the "book of life"; this year saw the completion of the genome sequences of complex organisms ranging from the fruit fly to the human. Genomes carry the torch of life from one generation to the next for every organism on Earth. Each genome--physically just molecules of DNA--is a script written in a four-letter alphabet. Not too long ago, determining the precise sequence of those letters was such a slow, tedious process that only the most dedicated geneticist would attempt to read any one "paragraph"--a single gene. But today, genome sequencing is a billion-dollar, worldwide enterprise. Terabytes of sequence data generated through a melding of biology, chemistry, physics, mathematics, computer science, and engineering are changing the way biologists work and think. Science marks the production of this torrent of genome data as the Breakthrough of 2000; it might well be the breakthrough of the decade, perhaps even the century, for all its potential to alter our view of the world we live in.'' (Elizabeth Pennisi) From ''BREAKTHROUGH OF THE YEAR: Genomics Comes of Age.'' Cover story in Science of December 22, 2000. "Not until the creation and maintenance of decent conditions of life for all people are recognized and accepted as a common obligation of all people and all countries - not until then shall we, with a certain degree of justification, be able to speak of humankind as civilized." (Albert Einstein, 1945) "Capitalism is the extraordinary belief that the nastiest of men, for the nastiest of reasons, will somehow work for the benefit of us all." (John Maynard Keynes) "When we have before us a fine map, in which the line of the coast, now rocky, now sandy, is clearly indicated, together with the winding of the rivers, the elevations of the land, and the distribution of the population, we have the simultaneous suggestion of so many facts, the sense of mastery over so much reality, that we gaze at it with delight, and need no practical motive to keep us studying it, perhaps for hours altogether. A map is not naturally thought of as an aesthetic object... And yet, let the tints of it be a little subtle, let the lines be a little delicate, and the masses of the land and sea somewhat balanced, and we really have a beautiful thing; a thing the charm of which consists almost entirely in its meaning, but which nevertheless pleases us in the same way as a picture or a graphic symbol might please. Give the symbol a little intrinsic worth of form, line and color, and it attracts like a magnet all the values of things it is known to symbolize. It becomes beautiful in its expressiveness." (George Santayana) From "The Sense of Beauty", 1896. "If my teachers had begun by telling me that mathematics was pure play with presuppositions, and wholly in the air, I might have become a good mathematician, because I am happy enough in the realm of essence. But they were overworked drudges, and I was largely inattentive, and inclined lazily to attribute to incapacity in myself or to a literary temperament that dullness which perhaps was due simply to lack of initiation." (George Santayana} From pp. 238-9 "Persons and Places", 1945. "He designed and built chess-playing, maze-solving, juggling and mind-reading machines. These activities bear out Shannon's claim that he was more motivated by curiosity than usefulness. In his words I just wondered how things were put together.' " (Claude Shannon) From Claude Shannon's (1916-2001) obituary. "The price of metaphor is eternal vigilance" (Arturo Rosenblueth and Norbert Wiener) Quoted by R. C. Leowontin, in Science page 1264, Feb 16, 2001 (The Human Genome Issue). "What is particularly ironic about this is that it follows from the empirical study of numbers as a product of mind that it is natural for people to believe that numbers are not a product of mind!" (George Lakoff and Rafael E. Nunez) On page 81 of Where Mathematics Comes From, Basic Books, 2000. Recent Discoveries about the Nature of Mind. In recent years, there have been revolutionary advances in cognitive science ---- advances that have a profound bearing on our understanding of mathematics. Perhaps the most profound of these new insights are the following: 1. The embodiment of mind. The detailed nature of our bodies, our brains and our everyday functioning in the world structures human concepts and human reason. This includes mathematical concepts and mathematical reason. 2. The cognitive unconscious. Most thought is unconscious --- not repressed in the Freudian sense but simply inaccessible to direct conscious introspection. We cannot look directly at our conceptual systems and at our low-level thought processes. This includes most mathematical thought. 3. Metaphorical thought. For the most part, human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in sensory-motor systems. The mechanism by which the abstract is comprehended in terms of the concept is called conceptual metaphor. Mathematical thought also makes use of line." (George Lakoff and Rafael E. Nunez) On page 5 of Where Mathematics Comes From, Basic Books, 2000. "The early study of Euclid made me a hater of geometry." (James Joseph Sylvester, 1814-97, Second LMS President) quoted in D. MacHale, "Comic Sections" (Dublin 1993). "a thrill which is indistinguishable from the thrill I feel when I enter the Sagrestia Nuovo of the Capella Medici and see before me the austere beauty of the four statues representing 'Day', 'Night', 'Evening', and 'Dawn' which Michelangelo has set over the tomb of Guiliano de'Medici and Lorenzo de'Medici." (G. N. Watson, 1886-1965) "All physicists and a good many quite respectable mathematicians are contemptuous about proof." (G. H. Hardy, 1877-1947) A century after biology started to think physically: "The idea that we could make biology mathematical, I think, perhaps is not working, but what is happening, strangely enough, is that maybe mathematics will become biological,!" (Greg Chaitin, Interview, 2000.) "The waves of the sea, the little ripples on the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology, and all of them the physicist can more or less easily read and adequately solve." (D'Arcy Thompson, On Growth and Form'' 1917) In Philip Ball's "The Self-Made Tapestry: Pattern Formation in Nature,'' "A doctorate compels most of us to be detailed and narrow, and to carve out our own specialities, and tenure commitees rarely like boldness. Later, when our jobs are safe we can be synthetic, and generalize." (Paul Kennedy) Writing critically about A.J.P. Taylor (The Nonconformist') in the Atlantic Monthly April 2001, page 114. ... it is no doubt important to attend to the eternally beautiful and true. But it is more important not to be eaten." (Jerry Fodor) Distinguishing effortless early learning of language and social customs from later labourious general purpose concept acquisition, Egan writes: "The bad news is that our evolution equipped us to live in small, stable, hunter-gatherer societies. We are Pleistocene people, but our languaged brains have created massive, multicultural, technologically sophisticated and rapidly changing societies for us to live in." --- "The cement like learning of our early years can accomodate almost anything, then it fixes and becomes almost unmovable." --- "we can, as a result, change our earlier beliefs and commitments. We also know this is difficult for most people." (Kieran Egan) In Kieran Egan's, Getting it Wrong from the Beginning -- Major Mistakes in the Project to Educate Everybody (in press). "EINSTEIN ON SCIENTIFIC TRUTH & ITS TRIUMPH" This is what Albert Einstein said quoting Max Planck "...a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents die and a new generation grows up that's familiar with it." or ... "A new scientific truth usually does not make its way in the sense that its opponents are persuaded and declare themselves enlightened, but rather that the opponents become extinct and the rising generation was made familiar with the truth from the very beginning". Max Planck, in THE QUANTUM BEAT by F.G.Major, Springer (1998). "And Max Planck, surveying his own career in his Scientific Autobiography, sadly remarked that 'a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.'" (Thomas Kuhn) On page 151 of T.S. Kuhn, The Structure of Scientific Revolutions, 3rd ed., Univ. of Chicago Press, 1996. (Quoting: Max Planck, Scientific Autobiography and Other Papers, trans. F. Gaynor (New York, 1949), pp. 33-34. See also "Conversations with a Mathematician" by Greg Chaitin.) the idea that we could make biology mathematical, I think, perhaps is not working, but what is happening, strangely enough, is that maybe mathematics will become biological, not that biology will become mathematical, mathematics may go in that direction!" (Interview with Gregory Chaitin by Hans-Ulrich Obrist (Musee d'Art Moderne de la Ville de Paris), Paris/CDG Airport, October 2000.) In "THE CREATIVE LIFE: SCIENCE VS ART,'' "The message is that mathematics is quasi-empirical, that mathematics is not the same as physics, not an empirical science, but I think it's more akin to an empirical science than mathematicians would like to admit." "Mathematicians normally think that they possess absolute truth. They read God's thoughts. They have absolute certainty and all the rest of us have doubts. Even the best physics is uncertain, it is tentative. Newtonian science was replaced by relativity theory, and then---wrong!---quantum mechanics showed that relativity theory is incorrect. But mathematicians like to think that mathematics is forever, that it is eternal. Well, there is an element of that. Certainly a mathematical proof gives more certainty than an argument in physics or than experimental evidence, but mathematics is not certain. This is the real message of Godel's famous incompleteness theorem and of Turing's work on uncomputability." "You see, with Godel and Turing the notion that mathematics has limitations seems very shocking and surprising. But my theory just measures mathematical information. Once you measure mathematical information you see that any mathematical theory can only have a finite amount of information. But the world of mathematics has an infinite amount of information. Therefore it is natural that any given mathematical theory is limited, the same way that as physics progresses you need new laws of physics." "Mathematicians like to think that they know all the laws. My work suggests that mathematicians also have to add new axioms, simply because there is an infinite amount of mathematical information. This is very controversial. I think mathematicians, in general, hate my ideas. Physicists love my ideas because I am saying that mathematics has some of the uncertainties and some of the characteristics of physics. Another aspect of my work is that I found randomness in the foundations of mathematics. Mathematicians either don't understand that assertion or else it is a nightmare for them... ": "This skyhook-skyscraper construction of science from the roof down to the yet unconstructed foundations was possible because the behaviour of the system at each level depended only on a very approximate, simplified, abstracted characterization at the level beneath1. This is lucky, else the safety of bridges and airplanes might depend on the correctness of the "Eightfold Way" of looking at elementary particles. 1 ... More than fifty years ago Bertrand Russell made the same point about the architecture of mathematics. See the "Preface" to Principia Mathematica "... the chief reason in favour of any theory on the principles of mathematics must always be inductive, i.e., it must lie in the fact that the theory in question allows us to deduce ordinary mathematics. In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; hence the early deductions, until they reach this point, give reason rather for believing the premises because true consequences follow from them, than for believing the consequences because they follow from the premises." Contemporary preferences for deductive formalisms frequently blind us to this important fact, which is no less true today than it was in 1910." (Herbert A. Simon) On page 16 of The Sciences of the Artificial," MIT Press, 1996. " Hardy asked What's your father doing these days. How about that esthetic measure of his?' I replied that my father's book was out. He said, 'Good, now he can get back to real mathematics'." (Garret Birkoff) Quoted in Towering Figures, 1890-1950, by David E. Zitarelli on page 618 of MAA Monthly Aug-Sept, Vol 108, (2001), 606-635 : regarding G. D. Birkhoff's Aesthetic Measures (1933). "I DO CONSIDER it appropriate to pay one's tribute to Prof. Subramanyan Chandrasekhar at the outset, before taking a plunge into the aesthetics of macro-causality, based on his book Truth and Beauty: Aesthetics and Motivations in Science. Brought up on the refined diet of music, mathematics and aesthetics, Chandrasekhar's own writing is probably the most appropriate mirror of his personality. I quote: "When Michelson was asked towards the end of his life, why he had devoted such a large fraction of his time to the measurement of the velocity of light, he is said to have replied 'It was so much fun'." Prof. Chandrasekhar goes on to some length to explain the term quoting even the Oxford Dictionary -- "fun" means "drollery", what Michelson really meant, Chandrasekhar asserts is "pleasure" and "enjoyment" - evidently "fun" in the colloquial sense, a concept, so familiar in our so called ordinary life has no place in Chandrasekhar's dictionary..." (Bikash Sinha) " His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his preeminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary---"so happy in his conjectures", said de Morgan, "as to seem to know more than he could possibly have any means of proving."'-- J. M. Keynes 1956 ... If Edison, Fineman, Gauss, and Newton had all been intensely tutored from the age of three by brilliant parents, as J.S. Mill was, then I might at least consider the possibility that my own mental muscles might have been stronger if my own parents had been more demanding. But they were not and I will not. When you see [Edison's] mind at play in his notebooks, the sheer multitude and richness of his ideas makes you recognize that there is something that can't be understood easily---that we may never be able to understand.' (historian Paul Israel, quoted in McAuliffe 1995). I think what lies at the heart of these mysteries is genetic, probably emergenic. The configuration of traits of intellect, mental energy, and temperament with which, during the plague years of 1665--6, Isaac Newton revolutionized the world of science were, I believe, the consequence of a genetic lottery that occurred about nine months prior to his birth, on Christmas day, in 1642. ... Gauss's second son, Eugene, emigrated to the United States in 1830, enlisted in the army, and later went into business in Missouri. Eugene is said to have had some of his father's gift for languages and the ability to perform prodigious arithmetic calculations, which he did for recreation after his sight failed him in old age. " (David T. Lykken) For Poincare, ignoring the emotional sensibility, even in mathematical demonstrations "would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility" (p. 2047).' (Nathalie Sinclair) Quoting Henri Poincare's "Mathematical creation" (1956). In J. Newman (Ed.), The World of Mathematics ( pp. 2041-2050). Simon and Schuster. "The controversy between those who think mathematics is discovered and those who think it is invented may run and run, like many perennial problems of philosophy. Controversies such as those between idealists and realists, and between dogmatists and sceptics, have already lasted more than two and a half thousand years. I do not expect to be able to convert those committed to the discovery view of mathematics to the inventionist view. However what I have shown is that a better case can be put for mathematics being invented than our critics sometimes allow. Just as realists often caricature the relativist views of social constructivists in science, so too the strengths of the fallibilist views are not given enough credit. For although fallibilists believe that mathematics has a contingent, fallible and historically shifting character, they also argue that mathematical knowledge is to a large extent necessary, stable and autonomous. Once humans have invented something by laying down the rules for its existence, like chess, the theory of numbers, or the Mandelbrot set, the implications and patterns that emerge from the underlying constellation of rules may continue to surprise us. But this does not change the fact that we invented the game in the first place. It just shows what a rich invention it was. As the great eighteenth century philosopher Giambattista Vico said, the only truths we can know for certain are those we have invented ourselves. Mathematics is surely the greatest of such inventions." (Paul Ernst) From Is Mathematics Discovered or Invented? (THES, 1996 and after). " Who owns the Internet? Until recently, nobody. That's because, although the Internet was "Made in the U.S.A.," its unique design transformed it into a resource for innovation that anyone in the world could use. Today, however, courts and corporations are attempting to wall off portions of cyberspace. In so doing, they are destroying the Internet's potential to foster democracy and economic growth worldwide. " (Lawrence Lessig) From Who Owns The Internet? Foreign Policy, November-December 2001. "Predicting the future is an activity fraught with error. Wilbur Wright, co-inventor of the motorized airplane that successfully completed the first manned flight in 1903, seems to have learned this lesson when he noted: "In 1901, I said to my brother Orville that man would not fly for 50 years. Ever since I have ... avoided predictions." Despite the admonition of Wright, faulty future forecasting seems a favored human pastime, especially among those who would presumably avoid opportunities to so easily put their feet in their mouths. What follows are some of the more striking exemplars of expert error in forecasting the future of technological innovations. "Louis Pasteur's theory of germs is ridiculous fiction." -- Piem Pachet, Professor of Physiology, 1872 "The abdomen, the chest, and the brain will forever be shut from the intrusion of the wise and humane surgeon." -- Sir John Eric Erickren, British surgeon to Queen Victoria, 1873 "Radio has no future. Heavier than air flying machines are impossible. X-rays will prove to be a hoax." -- William Thomson (Lord Kelvin), English physicist and inventor, 1899 "There is not the slightest indication that nuclear energy will ever be obtainable. It would mean that the atom would have to be shattered at will." -- Albert Einstein, 1932 "Man will never reach the moon, regardless of all future scientific advances." -- Lee De Forest, Radio pioneer, 1957 Computers and information technologies seem to hold a special place in the forecasters' hall of humiliation, be they predictions from the media, business, politicians, scientists, or technologists. Here are some examples: "This 'telephone' has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us." -- Western Union internal memo, 1876 "I think there is a world market for maybe five computers." -- Thomas Watson, chair of IBM, 1943 "The problem with television is that people must sit and keep their eyes glued on a screen; the average American family hasn't time for it." -- New York Times, 1949 "Where ... the ENIAC is equipped with 18,000 vacuum tubes and weights 30 tons, computers in the future may have only 1,000 vacuum tubes and weigh only 1.5 tons." -- Popular Mechanics, 1949 "Folks, the Mac platform is through -- totally." -- John C. Dvorak, PC Magazine, 1998 "There is no reason anyone would want a computer in their home." -- Ken Olson, president, chairman and founder, Digital Equipment Corp, 1977 "640K ought to be enough for anybody." -- Attributed to Bill Gates, Microsoft chair, 1981 "By the turn of this century, we will live in a paperless society." -- Roger Smith, chair of General Motors, 1986 "I predict the Internet ... will go spectacularly supernova and in 1996 catastrophically collapse." -- Bob Metcalfe, 3Com founder and inventor, 1995 "Credit reports are particularly vulnerable ... [as] are billing, payroll, accounting, pension and profit-sharing programs." -- Leon A Kappelman [author of this article] on likely Y2K problems, 1999 " (Leon A Kappelman) From "The Future is Ours," Communications of the ACM, March 2001, pg. 46. " Computation with Roman numerals is certainly algorithmic - it's just that the algorithms are complicated. In 1953, I had a summer job at Bell Labs in New Jersey (now Lucent), and my supervisor was Claude Shannon (who has died only very recently). On his desk was a mechanical calculator that worked with Roman numerals. Shannon had designed it and had it built in the little shop Bell Labs had put at his disposal. On a name plate, one could read that the machine was to be called: Throback I. Martin from a foggy morning in Berkeley" (Martin Davis) Martin Davis, Visiting Scholar UC Berkeley, Professor Emeritus, NYU. Following up on queries on the Historia Mathematica list, Jan 12, 2002. " [1] If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of everyone, and the receiver cannot dispossess himself of it. [2] Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lites his taper at mine, receives light without darkening me. [3] That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density at any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement, or exclusive appropriation. [4] Inventions then cannot, in nature, be a subject of property. " (Thomas Jefferson) Letter from Thomas Jefferson to Issac McPherson (August 13, 1813), in The Writings of Thomas Jefferson 6 quoted from page 94 of the future of ideas by Lawrence Lessig, Random House, 2001. The question of the ultimate foundations and the ultimate meaning of mathematics remains open: we do not know in what direction it will find its final solution or even whether a final objective answer can be expected at all. 'Mathematizing' may well be a creative activity of man, like language or music, of primary originality, whose Historical decisions defy complete objective rationalisation." (Hermann Weyl) In "Obituary: David Hilbert 1862 - 1943", RSBIOS, 4, 1944, pp. 547 - 553; and American Philosophical Society Year Book, 1944, pp. 387 - 395, p. 392. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate." Bertrand Russell) From "Recent Work on the Principles of Mathematics in International Monthly, 4 (July, 1901), 83-101. (Collected Papers, v3, p.366; revised version in Newman's World of Mathematics, v3, p. 1577.) "The problems of mathematics are not problems in a vacuum. There pulses in them the life of ideas which realize themselves in concreto through our [or throught] human endeavors in our historical existence, but forming an indissoluble whole transcending any particular science." (Hermann Weyl) In "David Hilbert and his mathematical work," Bull. Am. Math. Soc., 50 (1944), p. 615. THE FUTURE OF E-PUBLISHING. Although e-publishing has suffered a series of setbacks this year, Wired magazine still found plenty of optimism about the future of e-books. Michael S. Hart of Project Guttenberg, which offers books in electronic form, says: "The number of e-books available for free download on the Net will pass 20,000. The number of Net users will start heading towards 1 billion." Librarian Cynthia Orr, a co-founder of BookBrowser.com, thinks e-publishers should pay more attention to libraries, and says that if the major publishers worked with librarians or distributors "to figure out how to let libraries purchase or license their e-books, and let readers 'check them out' for free," that would help build "a market that otherwise threatens to just collapse for lack of interest. Librarians have been careful defenders of copyright over the years ... and our budgets are far higher than they realize." And Mark Gross, president of Data Conversion Laboratory, thinks that the e-publishing has already won a stealth war: ""What people forget is e-books were going strong before they were called e-books and they went on to sweep into many aspects of business and publishing. Most of this has gone unnoticed by the media. Probably because it has been a kind of backdoor revolution. To cite one example: Print law books are just about gone. People don't use them in law firms anymore. It's all electronic books or online. A revolution has occurred, but no one's noticed." (Wired Magazine) Wired, December 25, 2001. "Dear brother; I have often been surprised that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause; viz. that though Reason is feasted, Imagination is starved; while Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert. To assist Reason by the stimulus of Imagination is the design of the following production." Samuel Taylor Coleridge then launches into an ode on mathematics, the first verses of which are as follows: " On a given finite line Which must no way incline; To describe an equi - - lateral tri - A -N -G -L -E. Now let AB Be the given line Which must no way incline; The great Mathematician Makes this requisition, That we describe an Equi - - lateral Tri - - angle on it; Aid us, Reason - aid us, Wit! From the centre A at the distance AB, Describe the circle BCD At the distance BA from B the centre The round ACE to describe boldly venture. (Third postulate see) And from the point C In which the circles make a pother cutting and slashing one another Bid the straight lines a journeying go. CACB those lines will show To the points, which by AB are reckoned And postulate the second For authority you know ABC Triumphant shall be An equilateral Triangle No Peter Pindar carp, nor Zoilus can wrangle." (Samuel Coleridge) In a letter to his brother the Reverend George Coleridge. "There is a story, no doubt exaggerated, that the Pope once remarked that two types of proposals exist for peace in the Middle East: The realistic and the miraculous. The realistic solution is divine intervention. The miraculous involves a voluntary agreement between the two sides." (Paul Adams) From his article "Israel, Palestinians now further apart than two years ago" in the The Globe and Mail, Monday, April 15,2002 "Moreover a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock our efforts. It should be to us a guidepost on the mazy path to hidden truths, and ultimately a reminder of our pleasure in the successful solution. ... Besides it is an error to believe that rigor in the proof is the enemy of simplicity." (David Hilbert) In his 23' Mathematische Probleme lecture to the Paris International Congress, 1900 (see Yandell's, fine account in The Honors Class, A.K. Peters, 2002). ... waved his manuscript and confessed his publishing woes. ... "I said, 'I'm afraid no one's going to get to read these words. And I love these words.'" Ann Sparanese, a librarian in the audience, sent an SOS over the Internet to fellow librarians. Within hours, they inundated HarperCollins with angry e-mails - and orders for Stupid White Men. Some also threatened a boycott. "Those librarians," says Moore, ... "That's one terrorist group you don't want to mess with." HarperCollins caved. ... (Jan Wong) Quoted from "Lunch with Michael Moore - A smart white guy with attitude," The Globe and Mail May 18, 2002, page F2.  Old ideas give way slowly; for they are more than abstract logical forms and categories. They are habits, predispositions, deeply engrained attitudes of aversion and preference. Moreover, the conviction persists-though history shows it to be a hallucination that all the questions that the human mind has asked are questions that can be answered in terms of the alternatives that the questions themselves present. But in fact intellectual progress usually occurs through sheer abandonment of questions together with both of the alternatives they assume an abandonment that results from their decreasing vitality and a change of urgent interest. We do not solve them: we get over them. Old questions are solved by disappearing, evaporating, while new questions corresponding to the changed attitude of endeavor and preference take their place. Doubtless the greatest dissolvent in contemporary thought of old questions, the greatest precipitant of new methods, new intentions, new problems, is the one effected by the scientific revolution that found its climax in the " Origin of Species."  (John Dewey) Quoted from The Influence of Darwin on Philosophy, 1910. The first [axiom] said that when one wrote to the other (they often preferred to exchange thoughts in writing instead of orally), it was completely indifferent whether what they said was right or wrong. As Hardy put it, otherwise they could not write completely as they pleased, but would have to feel a certain responsibility thereby. The second axiom was to the effect that, when one received a letter from the other, he was under no obligation whatsoever to read it, let alone answer it, - because, as they said, it might be that the recipient of the letter would prefer not to work at that particular time, or perhaps that he was just then interested in other problems.... The third axiom was to the effect that, although it did not really matter if they both thought about the same detail, still, it was preferable that they should not do so. And, finally, the fourth, and perhaps most important axiom, stated that it was quite indifferent if one of them had not contributed the least bit to the contents of a paper under their common name; otherwise there would constantly arise quarrels and difficulties in that now one, and now the other, would oppose being named co-author.'' (Harald Bohr) Hardy and Littlewood's Four Axioms for Collaboration quoted from the preface of Bella Bollobas' 1988 edition of Littlewood's Miscellany. (Other quotes from the Miscellany.) "I got into a research project which can be very simply described as concerned with the realization of the "Nash program" (making use of words made conventional by others that refer to suggestions I had originally made in my early works in game theory). In this project a considerable quantity of work in the form of calculations has been done up to now. Much of the value of this work is in developing the methods by which tools like Mathematica can be used with suitable special programs for the solution of problems by successive approximation methods." (John Nash) On page 241 of "The Essential John Nash", edited by Harold W. Kuhn and Sylvia Nasar, Princeton Univ. Press, 2001. "A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven." (Jean Chretien) The Canadian Prime Minister explaining Canada's conditions for determining if Iraq has complied, September 5, 2002. Sounds a lot like Bertrand Russell! "No man can worthely praise Ptolemye ... yet muste ye and all men take heed, that both in him and in all mennes workes, you be not abused by their autoritye, but evermore attend to their reasons, and examine them well, ever regarding more what is saide, and how it is proved, than who saieth it, for autorite often times deceaveth many menne." (Robert Record) The great textbook writer in his cosmology text The castle of knowledge' (1556) quoted on page 47 of Oxford Figures, Oxford University Press, 2000. "The future has arrived; it's just not evenly distributed." (Douglas Gibson) On his Vancouver home page. "The plural of 'anecdote' is not 'evidence'." (Alan L. Leshner) Science's publisher speaking at the Federal S&T Forum, Oct 2, 2002. " ... Several years ago I was invited to contemplate being marooned on the proverbial desert island. What book would I most wish to have there, in addition to the Bible and the complete works of Shakespeare? My immediate answer was: Abramowitz and Stegun's Handbook of Mathematical Functions. If I could substitute for the Bible, I would choose Gradsteyn and Ryzhik's Table of Integrals, Series and Products. Compounding the impiety, I would give up Shakespeare in favor of Prudnikov, Brychkov And Marichev's of Integrals and Series ... On the island, there would be much time to think about waves on the water that carve ridges on the sand beneath and focus sunlight there; shapes of clouds; subtle tints in the sky... With the arrogance that keeps us theorists going, I harbor the delusion that it would be not too difficult to guess the underlying physics and formulate the governing equations. It is when contemplating how to solve these equations - to convert formulations into explanations - that humility sets in. Then, compendia of formulas become indispensable." (Michael Berry) "Why are special functions special?" Physics Today, April 2001. "I will be glad if I have succeeded in impressing the idea that it is not only pleasant to read at times the works of the old mathematical authors , but this may occasionally be of use for the actual advancement of science." (Constantin Caratheodory) Speaking to an MAA meeting in 1936. "I have myself always thought of a mathematician as in the first instance an observer, a man who gazes at a distant range of mountains and notes down his observations. His object is simply to distinguish clearly and notify to others as many different peaks as he can. There are some peaks which he can distinguish easily, while others are less clear. He sees A sharply, while of B he can obtain only transitory glimpses. At last he makes out a ridge which leads from A, and following it to its end he discovers that it culminates in B. B is now fixed in his vision, and from this point he can proceed to further discoveries. In other cases perhaps he can distinguish a ridge which vanishes in the distance, and conjectures that it leads to a peak in the clouds or below the horizon. But when he sees a peak he believes that it is there simply because he sees it. If he wishes someone else to see it, he points to it, either directly or through the chain of summits which led him to recognize it himself. When his pupil also sees it, the research, the argument, the proof is finished. The analogy is a rough one, but I am sure that it is not altogether misleading. If we were to push it to its extreme we should be led to a rather paradoxical conclusion; that we can, in the last analysis, do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lecture, devices to stimulate the imagination of pupils. This is plainly not the whole truth, but there is a good deal in it. The image gives us a genuine approximation to the processes of mathematical pedagogy on the one hand and of mathematical discovery on the other; it is only the very unsophisticated outsider who imagines that mathematicians make discoveries by turning the handle of some miraculous machine. Finally the image gives us at any rate a crude picture of Hilbert's metamathematical proof, the sort of proof which is a ground for its conclusion and whose object is to convince ." (G.H. Hardy) From the Preface to David Broussoud's recent book "Proofs and Confirmation: The Story of the Alternating Sign Matrix Conjecture," MAA, 1999. Broussoud cites Hardy's "Rouse Ball Lecture of 1928". "[T]o suggest that the normal processes of scholarship work well on the whole and in the long run is in no way contradictory to the view that the processes of selection and sifting which are essential to the scholarly process are filled with error and sometimes prejudice." (Kenneth Arrow) From E. Roy Weintraub and Ted Gayer, "Equilibrium Proofmaking," Journal of the History of Economic Thought, 23 (Dec. 2001), 421-442. "Mathematical proofs like diamonds should be hard and clear, and will be touched with nothing but strict reasoning." (John Locke) From The Mathematical Universe by William Dunham, John Wiley, 1994. In his review of Winchester's previous book, The Map That Changed the World (3), Stephen Jay Gould wrote: I don't mean to sound like an academic sourpuss, but I just don't understand the priorities of publishers who spare no expense to produce an elegantly illustrated and beautifully designed book and then permit the text to wallow in simple, straight-out factual errors, all easily corrected for the minimal cost of one scrutiny of the galleys by a reader with professional expertise... (4) With Krakatoa, the publisher clearly spared considerable expense, and this new book also wallows in errors. Perhaps, given our popular culture's appetite for sensationalized disasters, a modern publisher would rather not see all those pesky details corrected.'' (Tom Simkin and Richard S. Fiske) Review entitled "Clouded Picture of a Big Bang" from Science, July 4, 2003, page 50-51) "Again, I have to repeat the dictum of Harvard's president, Larry Summers: "In the history of the world, no one has ever washed a rented car." Most Iraqis still feel they are renting their own country --- first from Saddam and now from us. They have to be given ownership. If the Bush team is ready to put in the time, energy and money to make that happen --- great. But if not, it's going to have to make the necessary compromises to bring in the U.N. and the international community to help. '' (Thomas Freedman) New York Times August 26, 2003. "The paomnnehil pweor of the hmuan mnid. Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe." Psased on by Kevin Hare, Spetmber 2003. " "The great tragedy of science," the biologist Thomas Henry Huxley lamented, is "the slaying of a beautiful hypothesis by an ugly fact." By that standard, political science is going through a homely phase. It's not even three weeks since the Iowa caucuses, and voters have wiped out several decades' worth of conventional wisdom about presidential primaries." Some columnist in February 2004. "By 1948, the Marxist-Leninist ideas about the proletariat and its political capacity seemed more and more to me to disagree with reality ... I pondered my doubts, and for several years the study of mathematics was all that allowed me to preserve my inner equilibrium. Bolshevik ideology was, for me, in ruins. I had to build another life." (Jean Van Heijenoort, 1913-1986) From his autobiography With Trotsky in Exile, quoted in Anita Feferman's From Trotsky to Godel "Numbers are not the only thing that computers are good at processing. Indeed, only a cursory familiarity with fractal geometry is needed to see that computers are good at creating and manipulating visual representations of data. There is a story told of the mathematician Claude Chevalley, who, as a true Bourbaki, was extremely opposed to the use of images in geometric reasoning. He is said to have been giving a very abstract and algebraic lecture when he got stuck. After a moment of pondering, he turned to the blackboard, and, trying to hide what he was doing, drew a little diagram, looked at it for a moment, then quickly erased it, and turned back to the audience and proceeded with the lecture. It is perhaps an apocryphal story, but it illustrates the necessary role of images and diagrams in mathematical reasoning-even for the most diehard anti-imagers. The computer offers those less expert, and less stubborn than Chevalley, access to the kinds of images that could only be imagined in the heads of the most gifted mathematicians, images that can be coloured, moved and otherwise manipulated in all sorts of ways. " (Nathalie Sinclair, 2004) From Making the Connection: Research and Practice in Undergraduate Mathematics, M. Carlson and C. Rasmussen (Eds), MAA Notes, in press. Greenwood: It was quite a popular course. There used to be a saying that if Wedderburn says something is true, accept it but don't try to prove it because you won't be able to. If Eisenhart says something is true, get out his book and by using cross references 20 to 30 times you can work up a proof for it. And if Lefschetz says something is true ... Tucker: It is probably false. Greenwood: ... my apologies to Professor Lefschetz, look for a proof and for a counterexample at the same time. Aspray: Since you both had close associations with Church, I was wondering if you could tell me something about him. What was his wider mathematical training and interests? What were his research habits? I understood he kept rather unusual working hours. How was he as a lecturer? As a thesis director? Rosser: In his lectures he was painstakingly careful. There was a story that went the rounds. If Church said it's obvious, then everybody saw it a half hour ago. If Weyl says it's obvious, von Neumann can prove it. If Lefschetz says it's obvious, it's false. From the Princeton Oral History Project Excerpts from Google's filing with the SEC -- Google is not a conventional company. We do not intend to become one. -- A management team distracted by a series of short-term targets is as pointless as a dieter stepping on the scale every half hour. -- We will not hesitate to place major bets on promising new opportunities. -- For example, we would fund projects that have a 10 percent chance of earning a billion dollars over the long term. Do not be surprised if we place smaller bets in areas that seem very speculative or even strange. -- Our employees, who have named themselves Googlers, are everything. -- We provide many unusual benefits for our employees, including meals free of charge, doctors and washing machines. -- Don't be evil. We believe strongly that in the long term, we will be better served -- as shareholders and in all other ways -- by a company that does good things for the world even if we forgo some short-term gains." (John Shinal) From San Francisco Chronicle, Friday, April 30, 2004 "The discussion was going beautifully until I discovered that he was talking about the Peloponnesian War while I was discussing WW II." (Nicholas Katzenbach) Katzenbach writing in the The American Oxonian, describing his first meeting with his tutor Lord Lindsay in Balliol around 1948. The subject was the effect of war upon morals. "A coded message, for example, might represent gibberish to one person and valuable information to another. Consider the number 14159265... Depending on your prior knowledge, or lack thereof, it is either a meaningless random sequence of digits, or else the fractional part of pi, an important piece of scientific information." (Hans Christian von Baeyer) On page 11 of his recent book Information The New Language of Science, Weidenfeld and Nicolson, 2003. The metaphor of shooting naturally became a familiar one in writings about his photography. Cartier-Bresson himself used it often: "approach tenderly, gently . . . on tiptoe even if the subject is a still life," he said. "A velvet hand, a hawk's eye these we should all have." He also said: "I adore shooting photographs. It's like being a hunter. But some hunters are vegetarians which is my relationship to photography." And later, explaining his dislike of the automatic camera, he said, "It's like shooting partridges with a machine gun." With a Brownie that he had received as a gift, he began to snap photographs in Africa, but they ended up ruined. Contracting blackwater fever, he nearly died. The way he told the story, a witch doctor got him out of a coma. While still feverish, he wrote a postcard to his grandfather asking that he be buried in Normandy, at the edge of the Eawy forest, with Debussy's string quartet to be played at the funeral. An uncle wrote back: "Your grandfather finds all that too expensive. It would be preferable that you return first." (New York Times) From Henri Cartier-Bresson's New York Times Obituary of August 4, 2004. "Despite the narrative force that the concept of entropy appears to evoke in everyday writing, in scientific writing entropy remains a thermodynamic quantity and a mathematical formula that numerically quantifies disorder. When the American scientist Claude Shannon found that the mathematical formula of Boltzmann defined a useful quantity in information theory, he hesitated to name this newly discovered quantity entropy because of its philosophical baggage. The mathematician John Von Neumann encouraged Shannon to go ahead with the name entropy, however, since "no one knows what entropy is, so in a debate you will always have the advantage." From The American Heritage Book of English Usage, p. 158. "The connections between chemical science and technology in the new synthetic-dye industry that began to develop after William Henry Perkin's synthesis of mauve in 1856 are complex. But one contribution of the science of carbon chemistry to the synthetic-dye industry was clearly crucial: chemical theory embodied in chemical formulae. Linear chemical formulae, like H2O for water, had been introduced by the Swedish chemist Jacob Berzelius (1779-1848) in 1813. They presented the composition of chemical compounds according to a theory of definite quantitative units or portions of substances. With atomism, this new quantitative theory shared the assumption of discontinuous composition of substances. But the algebraic form of Berzelian formulae avoided narrow definitions in terms of "atoms," which many chemists rejected as metaphysical entities. Letters, numbers, and additivity were sufficient to represent quantitative units of elements and discontinuous composition of compounds. Different arrangements of letters visually showed how units of elements were combined with each other. The structural formulae of the 1860s displayed chemical and spatial arrangements in an even more pictorial form. Beginning in the late 1820s, chemists used chemical formulae as tools on paper to model the constitution of organic compounds. Using chemical formulae as paper tools, chemists reduced the complexity in the "jungle of organic chemistry" (F. Wehler). Chemical formulae enabled them, for example, to order organic chemical reactions by formula equations that distinguished between a main reaction, side reactions, and successive reactions. In the 1860s, chemical formulae had become an emblem not only of academic chemistry but also of the synthetic-dye industry. Quantitative chemical theory was implemented in the new alliance between carbon chemistry and the synthetic-dye industry in the form of paper tools that were subordinated to chemists' experimental and technological goals (6). Compared with the connections between academic chemistry and the arts and crafts in the 18th (Ursala Klein) In "Not a Pure Science: Chemistry in the 18th and 19th Centuries" Science, 5 November 2004 "Whether we scientists are inspired, bored, or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute embarrassment to many researchers, and it is therefore not often acknowledged. Such fundamental notions as reality, space, time, and causality--notions found at the core of the scientific enterprise--all rely on particular metaphysical assumptions about the world." (Christof Koch) In Thinking About the Conscious Mind," a review of John R. Searle's Mind. A Brief Introduction, OUP 2004. "And it is one of the ironies of this entire field that were you to write a history of ideas in the whole of DNA, simply from the documented information as it exists in the literature - that is, a kind of Hegelian history of ideas - you would certainly say that Watson and Crick depended on Von Neumann, because von Neumann essentially tells you how it's done. But of course no one knew anything about the other. It's a great paradox to me that this connection was not seen. Of course, all this leads to a real distrust about what historians of science say, especially those of the history of ideas." (Sidney Brenner) 2002 Nobelist Sidney Brenner talking about von Neumann's essay on The General and Logical Theory of Automata on pages 35--36 of My life in Science as told to Lewis Wolpert. "Sometime in the 1970s Paul Turan spent part of a summer in Edmonton. I wanted to meet him so went there. He was a few days late so I had arrived a couple of days earlier. A group went to the airport to meet him, and stopped at a coffee shop before going to the university. It was very hot so I offered to stay in the car and keep the windows down. I said I did not drink coffee. Turan then told the joke about mathematicians being machines which turn coffee into theorems, and then added: "You prove good theorems. Just think how much better they would be if you drank coffee". I have heard the statement attributed to Renyi by more than one Hungarian, but this was somewhat later. Turan just stated it." (Richard Askey) The definitive version of "Erdos and Coffee"? As told to the historia mathematica list on Feb 3, 2005. Elsewhere Kronecker said "In mathematics, I recognize true scientific value only in concrete mathematical truths, or to put it more pointedly, only in mathematical formulas." ... I would rather say "computations" than "formulas", but my view is essentially the same. (Harold M. Edwards) On page 1 of Essays on Constructive Mathematics, Springer 2005. Edwards comments elswhere that his own preference for constructivism was forged by experience of computing in the fifties---"trivial by today's standards". "One little know piece of Mayr's history, Rubinoff said, was his service on a National Research Council committee, which formed in the late 1960's, to examine the consequences of building a sea-level canal through the Isthmus of Panama. Mayr was accused by one of the committee engineers of "having an elastic collision with reality." But, said Rubinoff, if it weren't for Mayr's tenacity, the proposed canal would have destroyed 3 million years of isolated evolution. Frank Sulloway, author and former Mayr student, said that his career was influenced by meeting two minds: Darwin's and Mayr's. "The minute you meet one, you sooner or later meet the other," he said. Both were famously persistent. Quoting 19th-century novelist Anthony Trollope, "Darwin once wrote: "It's dogged as does it... I have often and often thought that this is the motto for every scientific worker." "The only person I know who's about as dogged is Ernst Mayr," said Sulloway." (The Scientist) February 3, 2005 obituary of Ernst Meyr. (See www.biomedcentral.com/news/20050204/01.) "Dear Friend Wollstein, By the time you receive these lines, we three will have solved the problem in another way - in the way which you have continually attempted to dissuade us. ... What has been done against the Jews in recent months arouses well-founded anxiety that we will no longer be allowed to experience a bearable situation. ... Forgive us, that we still cause you trouble beyond death; I am convinced that you will do what you are able to do (and which perhaps is not very much). Forgive us also our desertion! We wish you and all our friends will experience better times. Yours faithfully, Felix Hausdorff" (Felix Hausdorff) MacTutor gives more of Felix Hausdorff's last letter written on the eve of suicide (January 25, 1942). About H.E. Smith: In the book "Elementary Number Theory" (Chelsea, New York, 1958. An English translation of vol. 1 of the German book Vorlesungen ueber Zahlentheorie), p.31, the author, Edmund Landau, mentions the question whether the infinite series$\sum \mu(n)/n$converges (TEX notation; \mu is the Moebius function). After giving a reference to the answer in Part 7 of the same V.u.Z, and without saying what the answer is, Landau writes: "Gordan used to say something to the effect that 'Number Theory is useful since one can, after all, use it to get a doctorate with.' In 1899 I received my doctorate by answering this question." He was a brilliant talker and wit. Working in the purely speculative region of the theory of numbers, it was perhaps natural that he should take an anti-utilitarian view of mathematical science, and that he should express it in exaggerated terms as a defiance to the grossly utilitarian views then popular. It is reported that once in a lecture after explaining a new solution of an old problem he said, "It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstances can it be of the smallest possible utility." I believe that it was at a banquet of the Red Lions that he proposed the toast "Pure mathematics; may it never be of any use to anyone." This is taken from Alexander Macfarlane, _Ten British Mathematicians of the Nineteenth Century_ (1916), 63-4. The text is that of lectures he gave in 1903-1904, and the editors in their introduction say that "His personal acquaintance with British mathematicians of the nineteenth century imparts to many of these lectures a personal touch which greatly adds to their general interest." A copy of the book is available on the Project Gutenberg website: "By its own count, Wal-Mart has 460 terabytes of data stored on Teradata mainframes, made by NCR, at its Bentonville headquarters. To put that in perspective, the Internet has less than half as much data, according to experts." (Constance Hays) In "What Wal-Mart Knows About Customers' Habits", NYT November 14, 2004. Just what does it mean to prove something? Although the Annals will publish Dr Hales's paper, Peter Annals, an editor of the Annals, whose own work does not involve the use of computers, says that the paper will be accompanied by an unusual disclaimer, stating that the computer programs accompanying the paper have not undergone peer review. There is a simple reason for that, Dr Sarnak says-it is impossible to find peers who are willing to review the computer code. However, there is a flip-side to the disclaimer as well-Dr Sarnak says that the editors of the Annals expect to receive, and publish, more papers of this type-for things, he believes, will change over the next 20-50 years. Dr Sarnak points out that maths may become "a bit like experimental physics" where certain results are taken on trust, and independent duplication of experiments replaces examination of a colleague's paper. Why should the non-mathematician care about things of this nature? The foremost reason is that mathematics is beautiful, even if it is, sadly, more inaccessible than other forms of art. The second is that it is useful, and that its utility depends in part on its certainty, and that that certainty cannot come without a notion of proof. Dr Gonthier, for instance, and his sponsors at Microsoft, hope that the techniques he and his colleagues have developed to formally prove mathematical theorems can be used to "prove" that a computer program is free of bugs-and that would certainly be a useful proposition in today's software society if it does, indeed, turn out to be true. In Proof and beauty, the Economist, March 31, 2005 Writers we admire and re-read are absorbed into the fine print of our consciousness, into the white noise of our thoughts, and in this sense, they can never die. Saul Bellow started publishing in the 1940's, and his work spreads across the century he helped to define. He also redefined the novel, broadened it, liberated it, made it warm with human sense and wit and grand purpose. Henry James once proposed an obvious but helpful truth: "the deepest quality of a work of art will always be the quality of the mind of the producer." We are saying farewell to a mind of unrivalled quality. He opened our universe a little more. We owe him everything. (Ian McEwan) Master of the Universe, an obituary for Saul Bellow (1915-2005) NYT April 7, 2005. Why should I refuse a good dinner simply because I don't understand the digestive processes involved? (Oliver Heaviside) Heaviside (1850-1925) when criticized for his daring use of operators before they could be justified formally. Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes. [Mathematicians are a kind of Frenchman: whatever you say to them they translate into their own language, and right away it is something entirely different.] (Johann Wolfgang von Goethe) Maximen und Reflexionen, no. 1279, on page 160 of the Penguin classic edition. Ask Dr. Edward Witten of the Institute for Advanced Study in Princeton, New Jersey what he does all day, and it's difficult to get a straight answer. "There isn't a clear task," Witten told CNN. "If you are a researcher you are trying to figure out what the question is as well as what the answer is. "You want to find the question that is sufficiently easy that you might be able to answer it, and sufficiently hard that the answer is interesting. You spend a lot of time thinking and you spend a lot of time floundering around." " (Ed Witten) CNN June 27, 2005. "I don't think biochemists are going to be the least bit interested in what philosophers think about genes," Jones replies. "As I've said in the past, philosophy is to science as pornography is to sex: It's cheaper, easier, and some people prefer it.", Moving swiftly along, Jones and Stangroom ponder racial differences in IQ, the debate over genetically modified crops, health insurance, and the future of the human race. In the next chapter, Harvard evolutionary psychologist Steven Pinker is probed on "Evolutionary Psychology and the Blank Slate." The conversation moves from the structure of the brain to adaptive explanations for music, creationism, and beyond. Stangroom asks Pinker about the accusations that biological explanations of behavior are determinist and reduce human beings to the status of automatons. " "Most people have no idea what they mean when they level the accusation of determinism," "Pinker answers. "It's a nonspecific "boo" word, intended to make something seem bad without any content." (Jeremy Stangroom's interviews) The Scientist describing What (some) scientists say (Routledge Press). June 20th, 2005. [For earlier quote See above] Harald Bohr is reported to have remarked "Most analysts spend half their time hunting through the literature for inequalities they want to use, but cannot prove." (D.J.H. Garling) On page 575 of his very positive review of Michael Steele's The Cauchy Schwarz Master Class in the MAA Monthly, June-July 2005, 575-579. "How ridiculous to make evolution the enemy of God. What could be more elegant, more simple, more brilliant, more economical, more creative, indeed more divine than a planet with millions of life forms, distinct and yet interactive, all ultimately derived from accumulated variations in a single double-stranded molecule, pliable and fecund enough to give us mollusks and mice, Newton and Einstein? Even if it did give us the Kansas State Board of Education, too." (Charles Krauthammer) In "Phony Theory, False Conflict. 'Intelligent Design' Foolishly Pits Evolution Against Faith." The Washington Post 18/11/2005 "The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics. " (Johannes Kepler) Johannes Kepler (1571 - 1630) "[Maxwell asked whether he would like to see an experimental demonstration of conical refraction] No. I have been teaching it all my life, and I do not want to have my ideas upset." (Isaac Todhunter) Isaac Todhunter (1820 - 1884) "Rigour is the affair of philosophy, not of mathematics." (Bonaventura Cavalieri) Bonaventura Cavalieri (1598 - 1647) "How dreadful are the curses which Mohammedanism lays on its votaries! Besides the fanatical frenzy, which is as dangerous in a man as hydrophobia in a dog, there is this fearful fatalistic apathy. The effects are apparent in many countries. Improvident habits, slovenly systems of agriculture, sluggish methods of commerce, and insecurity of property exist wherever the followers of the Prophet rule or live. A degraded sensualism deprives this life of its grace and refinement; the next of its dignity and sanctity. The fact that in Mohammedan law every woman must belong to some man as his absolute property, either as a child, a wife, or a concubine, must delay the final extinction of slavery until the faith of Islam has ceased to be a great power among men. Individual Moslems may show splendid qualities, but the influence of the religion paralyses the social development of those who follow it. No stronger retrograde force exists in the world. Far from being moribund, Mohammedanism is a militant and proselytizing faith. It has already spread throughout Central Africa, raising fearless warriors at every step; and were it not that Christianity is sheltered in the strong arms of science, the science against which it had vainly struggled, the civilization of modern Europe might fall, as fell the civilization of ancient Rome." " (Winston Churchill) Speech by Churchill in The River War, ed 1, Vol. II, pages 248-50 (London: Longmans, Green & Co., 1899). "How extremely stupid not to have thought of that!" (T.H. Huxley) Thomas Henry Huxley (1825--1895). Huxley, known as Darwin's Bulldog' for his tireless defense of Darwin, was initially unconvinced of evolution. Converted by the Origin of Species', he is recorded (much like Briggs) as saying "How extremely stupid not to have thought of that!" "All truths are easy to understand once they are discovered; the point is to discover them." (Galileo Galilei, 1564-1642) Galileo's view is apparently not a view shared by all. The following thoughts on quantum theory by various scientists come from the NYT of Dec 26, 2005. "On quantum theory, I use up more brain grease than on relativity." (Albert Einstein to Otto Stern in 1911) "Those are the crazy people who are not working on quantum theory." (Albert Einstein referring to the inmates of an insane asylum near his office in Prague, in 1911) "I could probably have arrived at something like this myself, but if all this is true then it means the end of physics." (Albert Einstein, referring to a 1913 breakthrough by Niels Bohr) "Anyone who is not shocked by quantum theory has not understood a single word." (Niels Bohr) "I don't like it, and I'm sorry I ever had anything to do with it." (Erwin Schrödinger about the probability interpretation of quantum mechanics) "What we observe is not nature itself, but nature exposed to our method of questioning." (Werner Heisenberg, 1963) "You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem." (Richard Feynman, 1982) "Logic is the hygiene the mathematician practices to keep his ideas healthy and strong." (Hermann Weyl, 1885 - 1955) Weyl brings us full circle back to rigour. Math Will Rock Your World. A generation ago, quants turned finance upside down. Now they're mapping out ad campaigns and building new businesses from mountains of personal data. "These slices of our lives now sit in databases, many of them in the public domain. From a business point of view, they're just begging to be analyzed. But even with the most powerful computers and abundant, cheap storage, companies can't sort out their swelling oceans of data, much less build businesses on them, without enlisting skilled mathematicians and computer scientists. The rise of mathematics is heating up the job market for luminary quants, especially at the Internet powerhouses where new math grads land with six-figure salaries and rich stock deals. Tom Leighton, an entrepreneur and applied math professor at Massachusetts Institute of Technology, says: "All of my students have standing offers at Yahoo! and Google." Top mathematicians are becoming a new global elite. It's a force of barely 5,000, by some guesstimates, but every bit as powerful as the armies of Harvard University MBAs who shook up corner suites a generation ago." Business Week Cover Story January 23, 2006. "The formulas move in advance of thought, while the intuition often lags behind; in the oft-quoted words of d'Alembert, "L'algebre est genereuse, elle donne souvent plus qu'on lui demande."" (Edward Kasner, 1905) Edward Kasner, "The Present Problems of Geometry," Bulletin of the American Mathematical Society, (1905) volume XI, p.285. "Science is a differential equation. Religion is a boundary condition." (Alan Turing, 1912 - 1954) I'm not sure what it means, but I like it! 'Thirst for knowledge' may be opium craving Neuroscientists have proposed a simple explanation for the pleasure of grasping a new concept: The brain is getting its fix. The "click" of comprehension triggers a biochemical cascade that rewards the brain with a shot of natural opium-like substances, said Irving Biederman of the University of Southern California. He presents his theory in an invited article in the latest issue of American Scientist. "While you're trying to understand a difficult theorem, it's not fun," said Biederman, professor of neuroscience in the USC College of Letters, Arts and Sciences. "But once you get it, you just feel fabulous." The brain's craving for a fix motivates humans to maximize the rate at which they absorb knowledge, he said. I think we're exquisitely tuned to this as if we're junkies, second by second." (Irving Biederman, 2006) "We [Kaplansky and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury." (Irving Kaplansky, 1917-2006) Quoted in Paul Halmos' Celebrating 50 Years of Mathematics. "The war became more and more bitter. The Dominican Father Caccini preached a sermon from the text, Ye men of Galilee, why stand ye gazing up into heaven?'' and this wretched pun upon the great astronomer's name ushered in sharper weapons; for, before Caccini ended, he insisted that geometry is of the devil,'' and that mathematicians should be banished as the authors of all heresies.'' The Church authorities gave Caccini promotion." From A History of the Warfare of Science with Theology in Christendom by Andrew Dickson White, Chapter 3, Section 3. An online copy is at: www.cscs.umich.edu/~crshalizi/White/. "Equations are more important to me, because politics is for the present, but an equation is something for eternity." (Albert Einstein) Like so many Einstein quotes, this appears everywhere and seemingly without direct attribution. • "Never Ascribe to malice that which is adequately explained by incompetence." (Napolean Bonaparte?) • "Misunderstandings and neglect occasion more mischief in the world than even malice and wickedness. At all events, the two latter are of less frequent occurrence." (Goethe in The Sorrows of Young Werther) • "You have attributed conditions to villainy that simply result from stupidity". (Robert Heinlein in the Logic of Empire (1941). He calls this the "devil theory" of sociology. • "Many journalists have fallen for the conspiracy theory of government. I do assure you that they would produce more accurate work if they adhered to the cock-up theory." (Bernard Ingam, 1932- who was Thatcher's press secretary.) This is now also called Hanlon's Razor (1980). I'm here to help. (With the Poincare conjecture. As for the family, you're on your own.) Poincare conjectured that three-dimensional shapes that share certain easy-to-check properties with spheres actually are spheres. What are these properties? My fellow geometer Christina Sormani describes the setup as follows: "The Poincare Conjecture says, Hey, you've got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball. [Grigory] Perelman and [Columbia University's Richard] Hamilton proved this fact by heating the blob up, making it sing, stretching it like hot mozzarella, and chopping it into a million pieces. In short, the alien ain't no bagel you can swing around with a string through his hole." (Jordan Ellenberg) In Who Cares About Poincare Million-dollar math problem solved. So what? from Slate Posted Friday, Aug. 18, 2006, at 11:59 AM ET Thank you for your reply. I certainly understand what it means to recall something and have the trail disappear! The reason I inquired, as in my Tobias conversations with George and his comments re how Tobias influenced him by "feeding" him thousands of geometry problems to solve (see More Mathematical People, Albers et al. (eds.) , Harcourt Brace Jovanovich, 1990), he never indicated that he (George) had any input to Tobias' work. In fact, it went the other way in one important instance. As you may not have encountered it, I cite the following. George wrote in his paper "Reminiscences about the origins of linear programming," 1, 2, Operations Research Letters, April 1982 (p. 47): ""The term Dual is not new. But surprisingly the term Primal, introduced around 1954, is. It came about this way. W. Orchard-Hays, who is responsible for the first commercial grade L.P. software, said to me at RAND one day around 1954: 'We need a word that stands for the original problem of which this is the dual.' I, in turn, asked my father, Tobias Dantzig, mathematician and author, well known for his books popularizing the history of mathematics. He knew his Greek and Latin. Whenever I tried to bring up the subject of linear programming, Toby (as he was affectionately known) became bored and yawned. But on this occasion he did give the matter some thought and several days later suggested Primal as the natural antonym since both primal and dual derive from the Latin. It was Toby's one and only contribution to linear programming: his sole contribution unless, of course, you want to count the training he gave me in classical mathematics or his part in my conception. " A lovely story. I heard George recount this a few times and, when he came to the "conception" part, he always had a twinkle in his eyes. (Saul Gass) In a September 2006 SIAM book review, I asserted George Dantzig assisted his father Tobias---for reasons I believed but cannot now reconstruct. I also called Lord Chesterfield, Chesterton (gulp!). "Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity." (Mary Somerville, 1780-1872) Quoted in Martha Somerville, Personal Recollections of Mary Somerville (Boston, 1874) Today's outcome may end the interest in future chess matches between human champions and computers, according to Monty Newborn, a professor of computer science at McGill University in Montreal. Professor Newborn, who helped organize the match between Mr. Kasparov and Deep Blue, said of future matches: "I don't know what one could get out of it at this point. The science is done." Mr. Newborn said that the development of chess computers had been useful. "If you look back 50 years, that was one thing we thought they couldn't do," he said. "It is one little step, that's all, in the most exciting problem of what can't computers do that we can do." Speculating about where research might go next, Mr. Newborn said, "If you are interested in programming computers so that they compete in games, the two interesting ones are poker and go. That is where the action is." (Dylan Loeb McClain) From a report of the defeat of world champion Vladimir Kramnik by Deep Fritz in Once Again, Machine Beats Human Champion at Chess NYT, December 5, 2006. "Je n'ai fait celle-ci plus longue que parceque je n'ai pas eu le loisir de la faire plus courte.(I have only made this letter rather long because I have not had time to make it shorter.)" (Blaise Pascal) From Pascal's Lettres provinciales, 16, Dec 14, 1656. [Cassell's Book of Quotations, London,1912. P.718.] Similar quotes are due to Goethe and perhaps to Augustine and Cicero. Of course, identifying with one's captors is nothing new. Perhaps the most famous example is the 1973 Norrmalmstorg bank robbery in Stockholm. During the five days they were held hostage, the bank employees came to sympathize with the robbers and defended them against the police. (Globe and Mail, January 2007) Describing the origin of the Stockholm Syndrome. Try looking up the Jerusalem Syndrome and recently named Paris Syndrome (2004). What other cities have such an honour? "Bulls don't run reviews. Bulls of 25 don't marry old women of 55 and expect to be invited to dinner. Bulls do not get you cited as co-respondent in Society divorce trials. Bulls don't borrow money. Bulls are edible after they have been killed." (Ernest Hemingway, 1925) From Napoleon's love letter found in laundry room (Toronto Star, June 4, 2007). "Another lot of interest is a letter written by Ernest Hemingway to the American poet and critic Ezra Pound in 1925, explaining why bulls are better than literary critics." Memorable Ends 1. Here lies Ezekial Aikle. Aged 102. The good die young. 2. Here lies an Atheist. All dressed up. And no place to go. 3. A tomb now suffices him for whom the world was not enough. (Alexander the Great) 4. The body of Benjamin Franklin, printer (like the cover of an old book, its contents worn out, and stript of its lettering and gilding) lies here, food for worms. Yet the work itself shall not be lost, for it will, as he believed appear once more. In a new and more beautiful edition, corrected and amended by its Author. (Benjamin Franklin) 5. She did it the hard way. (Bette Davis) 6. The best is yet to come. (Frank Sinatra) 7. That's all folks! (Mel Blanc - voice of Bugs Bunny) 8. I told you I was ill. (Spike Milligan) 9. Ope'd my eyes. Took a peep. Didn't like it. Went back to sleep. 10. Called back. (Emily Dickinson) (Various) Posted by Joanna Sugdden, July 24th London Times. Franklin's epitaph has been banned in Texas school texts (it is clearly anti-Christian). And Bloomberg can also flash a hard-edged candor. At the breakfast with business leaders, he scoffed at a question about whether the schools' emphasis on math and reading testing was taking away from the "richness" of education in subjects such as art and music. "Well, I don't know about the 'richness of education,' " he said, his voice thick with sarcasm. "In my other life, I own a business, and I can tell you, being able to do 2-plus-2 is a lot more important than a lot of other things." ... Giuliani seized on it to bolster his campaign's theme, saying, "Today's arrests remind us that we are at war." Bloomberg offered a noticeably milder response: "You can't sit there and worry about everything. You have a much greater danger of being hit by lightning than being struck by a terrorist. Get a life." (Michael Bloomberg) "This computer, although assigned to me, was being used on board the International Space Station. I was informed that it was tossed overboard to be burned up in the atmosphere when it failed." (Anonymous) Science, August 3, 2007, p. 579: "A NASA employee's explanation for the loss of a laptop, recorded in a recent report by the U.S. Government Accountability Office documenting equipment losses of more than$94 million over the past 10 years by the agency."

"Rick Wilson, a Republican consultant based in Florida who has worked for Rudolph W. Giuliani, the former New York mayor, and Katherine Harris, the former Florida congresswoman, among others, said that most states have their own expressions for the circumstances under which open secrets stay secret. In Florida, he said, it's the 'Three County Rule': no girlfriends within three counties of your home district. In New York, it's the 'Bear Mountain Compact': nobody talks about what politicians do with their free time once they've crossed the Bear Mountain Bridge en route to Albany from points south."
(Abby Goodnough)

From Oh, everyone knows that (except you) in the NYT of Sept 2, 2007.

Easy as 1, 2, 3 -- Except for The Maybes. Why No One Can Count On Those Delegates

"The lesson is not to trust the numbers too much. If math were a guy, math would be a pompous guy, the sort who's absolutely always sure about everything and never apologizes when he's wrong. And the fact is, math isn't actually ever wrong, not technically. Math is a perfectly logical and intelligent guy. He just sometimes makes the wrong assumptions. "

(Libby Copeland)

From Washington Post Friday, April 25, 2008.

" the problem of course presents itself already when you are a student and I was thinking about the problem on and off, but the situation was more interesting than that. The great authority in those days was Zygmund and he was completely convinced that what one should produce was not a proof but a counter-example. When I was a young student in the United States, I met Zygmund and I had an idea how to produce some very complicated functions for a counter-example and Zygmund encouraged me very much to do so. I was thinking about it for about 15 years on and off, on how to make these counter-examples work and the interesting thing that happened was that I realised why there should be a counter-example and how you should produce it. I thought I really understood what was the background and then to my amazement I could prove that this "correct" counter-example couldn't exist and I suddenly realised that what you should try to do was the opposite, you should try to prove what was not fashionable, namely to prove convergence. The most important aspect in solving a mathematical problem is the conviction of what is the true result. Then it took 2 or 3 years using the techniques that had been developed during the past 20 years or so. .. "
(Lennart Carleson, 1966)

From 1966 IMU address on his positive solution of Luzin's 1913 conjecture that the Fourier series of every square integrable function converges a.e. to the function.

"In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. "You mean an actual number?" Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, "All right, take 57."

But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. "He doesn't think concretely." Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. "He really never worked on examples," Mumford observed. "I only understand things through examples and then gradually make them more abstract. I don't think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It's just very strange. That's the way his mind worked.""

(Allyn Jackson, 2004)

From a two-part biography in the Notices of the AMS.

"The letter was written in German in 1954 to philosopher Eric Gutkind. It is to be auctioned in London, England, on Thursday by Bloomsbury Auctions, and is expected to fetch between $12,000 and$16,000 US. Einstein writes "the word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honourable but still primitive legends which are nevertheless pretty childish.""

From a letter by Einstein auctioned in May 2008 as described on CBC.

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others."

(Carl Friedrich Gauss, 1777-1855)

From an 1808 letter to his friend Farkas Bolyai (the father of Janos Bolyai).

"The difficulty lies, not in the new ideas, but in escaping the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds"

(John Maynard Keynes, 1883-1946)

Quoted in K E Drexler, Engines of Creation: The Coming Era of Nanotechnology, New York, 1987.

"He is like the fox, who effaces his tracks in the sand with his tail."

(Niels Abel, 1802-1829)

Regarding Gauss' mathematical writing style quoted in G. F. Simmons, Calculus Gems New York: Mcgraw Hill, 1992, p. 177.

"We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work."

(Richard Feynman, 1918-1988)

In his 1966 Nobel acceptance lecture.

"Gauss could be a stern, demanding individual, and it is reported that this resulted in friction with two of his sons that caused them to leave Germany and come to the United States; they settled in the midwest and have descendants throughout the plains states. I was living in Greeley, Colorado, when I read this in 1972; looking in the phone book, I found a listing for a Charlotte Gauss living two blocks from my apartment! After considerable internal debate, I called her and found that she was indeed related to Gauss.

My wife, Paulette, and I visited several times with Charlotte and her sister Helen; they were bright, alert, and charming young women, ages 93 and 94, respectively. Their father, Gauss' grandson, had been a Methodist missionary to the region, and he had felt it unseemly to take pride in his famous ancestor (maybe there were some remnants of his father's feelings on leaving Germany); they were nevertheless happy to talk Gauss and their family. They showed us a baby spoon which their father had made out of a gold medal awarded to Gauss, some family papers, and a short biography of Gauss written by an aunt. I vividly remember Helen describing the reaction of one of her math teachers when he discovered he had a real, live, Gauss in his class."

(Jim Kuzmanovichi)

Quoted from http://www.wfu.edu/~kuz/Stamps/Gauss/Gauss.html.

"Forget the 'precautionary principle.' The amount of risk to which the public should be exposed is greater than zero."

(Michael Krauss)

Quoted from "Too cautious" in the Financial Post, June 20, 2008.

"Knowing things is very 20th century. You just need to be able to find things."

(Danny Hillis)

On how Google has changed the way we think as quoted in Achenblog, July 1 2008.

"McCain would also be wise to study the etymology of his "maverick" image. The term entered the political lexicon because of one Samuel Augustus Maverick, a land owner, legislator, and former mayor of San Antonio who was the grandfather of Maury Maverick, the famous New Dealer who described democracy as "liberty plus groceries." Samuel Maverick stubbornly refused to brand his calves and let them roam wherever they wanted. Other ranchers who encountered these free-spirited yearlings referred to them as "mavericks." Journalists later employed the term to describe politicians who bucked the party line and struck an independent course."

(John Podesta and John Halpin)

From 'The Maverick' gets the branding iron in the Politico July 17, 2008.

"Of course I believe in luck. How otherwise to explain the success of those you dislike?"

(Jean Cocteau)

From Making His Own Luck. Eugene Robinson writing about Obama, July 17, 2008.

His ambition to write may have prompted an exchange with T. S. Eliot, then in his late 50s, on the day they met in 1946, when Mr. Giroux, “just past 30,” as he recalled the moment in “The Oxford Book of Literary Anecdotes,” was an editor at Harcourt, Brace. “His most memorable remark of the day,” Mr. Giroux said, “occurred when I asked him if he agreed with the definition that most editors are failed writers, and he replied, ‘Perhaps, but so are most writers.’“

(T. S. Elliot)

From Robert Giroux, Publisher, Dies at 94 . New York Times, Sept 5, 2008.

" For those who had realized big losses or gains, the mania redistributed wealth. The largest honest fortune was made by Thomas Guy, a stationer turned philanthropist, w ho owned £54,000 of South Sea stock in April 1720 and sold it over the following six weeks for £234,000. Sir Isaac Newton, scientist, master of the mint, and a certifiably rational man, fared less well. He sold his £7,000 of stock in April for a profit of 100 percent. But something induced him to reenter the market at the top, and he lost £20,000. "I can calculate the motions of the heavenly bodies," he said, "but not the madness of people."

(Isaac Newton)

Quoted by Christopher Reed in "The Damn'd South Sea”, Harvard Magazine, May-June 1999. See Newton on Cosmology.

"When asked about the interruptions to her career caused by three marriages and three divorces, she shrugs. "You can like 'em," she jokes about men, "but it doesn't mean you have to sample every single one."

...
“Toward the end of the writing process, Proulx will often work 16 hours a day. "I love shaping things, pruning out the unnecessary, shaping unshapely sentences. After things are published I never read them again. I never, ever read reviews." (In the case of "Fine Just the Way It Is," that's just as well, since the reviews have been mixed.)."

(Annie Proulx)

Quoted by Susan Renolds in "Annie Proulx no longer at home on the range", LA Times, October 18, 2008.

"Genetics by second nature Growing up in Arlington, Virginia, Buckler had unlimited access to a personal computer, on which he designed his own games. To him, genetics is basically life's equivalent of computer programming. "There are not many rules: You get to recombine and to mutate, but you can make incredibly complex things." Buckler laughs, giving his boyish smile: "And it's more rewarding to do genetics than programming."."

(Edward Buckler)

Quoted by Elizabeth Pennisi in "EDWARD BUCKLER PROFILE: Romping Through Maize Diversity”, Science, 3 October 2008, pp. 40 – 41.

"Every once in while during a crisis or history-altering event, you run across a quote or an observation that sort of summarizes events on the ground, in a nutshell. Former U.S. Federal Reserve Chairman Paul Volcker articulated one such observation during a recent chat he had with PBS' Charlie Rose. "It seems to me what our nation needs is more civil engineers and electrical engineers and fewer financial engineers," Volker said."

(Joseph Lazaro)

Posted Oct 24th 2008 3:56pm at www.bloggingstocks.com.

EDITOR’S ENDNOTES "Jeffrey Lagarias (University of Michigan), Colin Mallows (Avaya Labs), and Allan Wilks (AT&T Labs–Research) submitted the following correction to their article "Beyond the Descartes Circle Theorem," which appeared in the April, 2002 issue: We have an historical and a mathematical correction. First, it has been brought to our attention that Frederick Soddy, who won a Nobel Prize in Chemistry (1921) for the discovery of isotopes, did not receive a knighthood (in the English honours list). Davies [loc. cit.] quotes a letter from his nephew, Dr. Kenneth Soddy: "He suffered a good deal of what might be termed persecution during the first World War . . . It was the recollection of these troubles that made him decline Honours later on." Besides his scientific work, Soddy loved mathematics and worked on it as a hobby. He also wrote several books setting forth unpopular economic views. Our awarding him a spurious knighthood is an example of the "Matthew effect" the phenomenon by which famous people become more famous, and less famous people become less famous. Unfortunately this error has propagated to Mumford et al. [Indra's Pearls]"

(Dan Velleman)

American Mathematical Monthly, Oct 2008, page 769. See also Robert K. Merton, “The Matthew effect in science,” Science 159 (1968) 56–63.

“Considering that past, perhaps the most incisive comment on Mr. Obama’s election actually came long ago. The Rev. Dr. Martin Luther King Jr. addressed the Hawaii Legislature in 1959, two years before Mr. Obama was born in Honolulu, and declared that the civil rights movement aimed not just to free blacks but “to free the soul of America.”

Mr. King ended his Hawaii speech by quoting a prayer from a preacher who had once been a slave, and it’s an apt description of the idea of America today: “Lord, we ain’t what we want to be; we ain’t what we ought to be; we ain’t what we gonna be, but, thank God, we ain’t what we was.”

(Nicholas Kristof)

From "The Obama Dividend," NYT, November 5, 2008.

""The collapse of communism pushed China to the center and [America] to the extreme,” said Ben Simpfendorfer, chief China economist at Royal Bank of Scotland.

The Madoff affair is the cherry on top of a national breakdown in financial propriety, regulations and common sense. Which is why we don’t just need a financial bailout; we need an ethical bailout. We need to re-establish the core balance between our markets, ethics and regulations. I don’t want to kill the animal spirits that necessarily drive capitalism — but I don’t want to be eaten by them either."

(Thomas Friedman)

From "The Great Unravelling," NYT, December 16, 2008.

"The orbit of any one planet depends on the combined motions of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect."

(Isaac Newton, 1687)

Both Cosmology and Commerce are complicated. See G. Lake, T. Quinn and D. C. Richardson, "From Sir Isaac to the Sloan Survey: Calculating the Structure and Chaos Due to Gravity in the Universe,"Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1997, pg. 1-10.

"John Tierney always wanted to be a scientist but went into journalism because its peer-review process was a great deal easier to sneak through. Now a columnist for the Science Times section, Tierney previously wrote columns for the Op-Ed page, the Metro section and the Times Magazine. Before that he covered science for magazines like Discover, Hippocrates and Science 86.

With your help, he's using TierneyLab to check out new research and rethink conventional wisdom about science and society. The Lab's work is guided by two founding principles:

1. Just because an idea appeals to a lot of people doesn't mean it's wrong.
2. But that's a good working theory.
From http://tierneylab.blogs.nytimes.com.

"I don’t think of myself as having gone squishy. I think of myself as having grown sober. And my conservative critics? On them, I think the most apt verdict was delivered by Niccolo Macchiavelli, 500 years ago: “This is the tragedy of man. Circumstances change, and he does not.”

(David Frum)

From "Lies about me, and the lying liars who tell them," National Post, March 28, 2009. Compare various of quotes above by Keynes and those of some of the many bankers and economists who are now suffering buyer's remorse.

"The late Huw Wheldon of the BBC once described to me a series, made in the early days of radio, about celebrated exiles who had lived in London. At one stage, this had involved tracking down an ancient retiree who had toiled in the British Museums reading room during the Victorian epoch. Asked if he could remember a certain Karl Marx, the wheezing old pensioner at first came up empty. But when primed with different prompts about the once-diligent attendee (monopolizing the same seat number, always there between opening and closing time, heavily bearded, suffering from carbuncles, tending to lunch in the Museum Tavern, very much interested in works on political economy), he let the fount of memory be unsealed.Oh Mr. Marx, yes, to be sure. Gave us a lot of work e did, with all is calls for books and papers. His interviewers craned forward eagerly, to hear the man say: And then one day e just stopped coming. And you know whats a funny fing, sir? A pregnant pause. Nobodys ever eard of im since! This, clearly, was one of those stubborn proletarians for the alleviation of whose false consciousness Marx had labored in vain.

(Christopher Hitchens)

In the The Revenge of Karl Marx in The Atlantic, April 2009.

Here endeth the Seder.

This year our ceremony still contains some time for reflection, and some ability to remain on the same topic for more than a minute or two. But next year, may our ceremony be faster, divided into bite-sized chunks, and with each utterance no more than 140 characters. And so we say together,

(Carl Elkin, 2009)

"If you're worried that lions are eating too many zebras, you don't say to the lions, 'You're eating too many zebras.' You have to build a fence around the lions. They're not going to build it."

(Judge Richard A. Posner)

"One of the most prominent proponents of free-market capitalism is having second thoughts" in Huffington Post, April 20, 2009. A week earlier he wrote in "Shorting Reason" (The New Republic of April 15):

"They want a pedigree, or a sacred text, to lend authority to their thesis, and they want to champion the liberal Keynes over the conservative Friedman.

Hence their appropriation of the term "animal spirits" from a famous passage in The General Theory "Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits--of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.... Thus if the animal spirits are dimmed and the spontaneous optimism fades, enterprise will fade and die.... It is our innate urge to activity which makes the wheels go round, our rational selves choosing between the alternatives as best we are able, calculating where we can, but often falling back for our motive on whim or sentiment or chance."

"John Maynard Keynes wrote that ideas, “both when they are right and when they are wrong, are more powerful than is commonly understood. Indeed the world is ruled by little else.” This idea popularized by Professor Singer — that we have ethical obligations that transcend our species — is one whose time appears to have come."

(Nicholas Kristof)

in Humanity Even for Nonhumans (for better or worse) in NYT, April 8 2009.

"Maddox was always a believer in the possibilities of science, reluctant to accept that it could cause problems as well as solve them. When a wave of environmental pessimism swept over the Western world in the early 1970s he was one of the few to resist. He published a book, The Doomsday Syndrome (1972), denouncing the gloom as overdone.
...
after retiring as Nature Editor he wrote a scientific tour d’horizon,
What Remains to be Discovered, asserting that far from approaching the end of its glorious run, science was only just beginning to tackle a multitude of new problems. The future offered an infinity of possibilities, most of them attractive."

From the London Times obituary of John Maddox (1925-2009).

""6. We have a patriotic duty to stand up against Washington taxes!" Just the opposite. We have a patriotic duty to pay taxes. As multi-billionaire Warren Buffett put it, "If you stick me down in the middle of Bangladesh or Peru or someplace, you'll find out how much this talent is going to product in the wrong kind of soil. I will be struggling thirty years later. President Teddy Roosevelt made the case in 1906 when he argued in favor of continuing the inheritance tax. "The man of great wealth owes a particular obligation to the state because he derives special advantages from the mere existence of government."

(Robert Reich)

From "A Short Citizen's Guide to Kooks, Demagogues, and Right-Wingers," in the Huffington Post April 15 (Tax Day).

"The most complete unfolding of his later sense of things can probably be found in a quite astonishing book-length interview published by the magazine Research as the self-standing Research No 8/9 (1984) but he remained unfailingly eloquent until the end of his life, as the interviews assembled in Conversations (2005) attest. "At times", he said in 2004, "I look around the executive housing estates of the Thames Valley and feel that [a vicious and genuinely mindless neo-fascism] is already here, quietly waiting its day, and largely unknown to itself ... What is so disturbing about the 9/11 hijackers is that they had not spent the previous years squatting in the dust on some Afghan hillside ... These were highly educated engineers and architects who had spent years sitting around in shopping malls in Hamburg and London, drinking coffee and listening to the muzak."

(The Independent)

April 21 Obituary of JG Ballard.

"A heavy warning used to be given [by lecturers] that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety. Some pictures, of course, are not rigorous, but I should say most are (and I use them whenever possible myself)."

(J. E. Littlewood, 1885-1977)

From Littlewood's Miscellany (p 35 in 1953 edition). Said long before the current graphic, visualization and geometric tools were available.

Assorted Americans on Paris (collected in 2003)
"France has neither winter nor summer nor morals. Apart from these drawbacks it is a fine country. France has usually been governed by prostitutes." --Mark Twain.

"I would rather have a German division in front of me than a French one behind me."---General George S. Patton.
"Going to war without France is like going deer hunting without your accordion."---Secretary of Defense Donald Rumsfeld.

"We can stand here like the French, or we can do something about it."---Marge Simpson.

"As far as I'm concerned, war always means failure."---Jacques Chirac, President of France.

"As far as France is concerned, you're right."---Rush Limbaugh.

"The only time France wants us to go to war is when the German Army is sitting in Paris sipping coffee."---Regis Philbin.

"The French are a smallish, monkey-looking bunch and not dressed any better, on average, than the citizens of Baltimore.

True, you can sit outside in Paris and drink little cups of coffee, but why this is more stylish than sitting inside and drinking large glasses of whisky I don't know."---P.J O'Rourke (1989).

"You know, the French remind me a little bit of an aging actress of the 1940s who was still trying to dine out on her looks but doesn't have the face for it."---John McCain, U.S. Senator from Arizona.

"You know why the French don't want to bomb Saddam Hussein? Because he hates America, he loves mistresses, and wears a beret. He is French, people."--- Conan O'Brien.

"I don't know why people are surprised that France won't help us get Saddam out of Iraq. After all, France wouldn't help us get Hitler out of France either."---Jay Leno.

"The last time the French asked for 'more proof' it came marching into Paris under a German flag." ---David Letterman

"Only thing worse than a Frenchman is a Frenchman who lives in Canada."---Ted Nugent.

"The favorite bumper sticker in Washington D.C. right now is one that says, 'First Iraq, then France.'"---Tom Brokaw.

"What do you expect from a culture and a nation that exerted more of its national will fighting against Disney World and Big Macs than the Nazis?"---Dennis Miller.
"It is important to remember that the French have always been there when they needed us."---Alan Kent.

"They've taken their own precautions against al-Qa'ida. To prepare for an attack, each Frenchman is urged to keep duct tape, a white flag, and a three-day supply of mistresses in the house."---Argus Hamilton.

"Somebody was telling me about the French Army rifle that was being advertised on eBay the other day--the description was, 'Never shot. Dropped once.'"---Rep. Roy Blunt (MO) ).

"The French will only agree to go to war when we've proven we've found truffles in Iraq."---Dennis Miller.

<"Question: What did the mayor of Paris say to the German army as they entered the city in WWII?

Answer: Table for cent milles m'sieur?"

"Do you know how many Frenchmen it takes to defend Paris? It's not known, it's never been tried."---Rep. R. Blount (MO).

"Do you know it only took Germany three days to conquer France in WWII? And that's because it was raining."--John Xereas, Manager, DC Improv.
"The AP and UPI reported that the French Government announced after the London bombings that it has raised its terror alert level from Run to Hide. The only two higher levels in France are Surrender and Collaborate."

" The rise in the alert level was precipitated by a recent fire which destroyed France's white flag factory, effectively disabling their military."

"French Ban Fireworks at Euro Disney (AP), Paris, March 5, 2003, The French government announced today that it is imposing a ban on the use of fireworks at Euro Disney. The decision comes the day after a nightly fireworks display at the park, located just 30 miles outside of Paris, caused the soldiers at a nearby French army garrison to surrender to a group of Czech tourists."

"Roberts’s opinion drew an incredulous dissent from Stevens, who said that the Chief Justice’s words reminded him of “Anatole France’s observation” that the “majestic equality” of the law forbade “rich and poor alike to sleep under bridges, to beg in the streets, and to steal their bread.”"

(Jeffrey Toobin)

Anotole France's famous observation in an incisive if depressing analysis of the Chief Justice: No More Mr. Nice Guy in the New Yorker.

"During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned, as completely as at Edinburgh and at school. I attempted mathematics, and even went during the summer of 1828 with a private tutor (a very dull man) to Barmouth, but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra.This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense. "

(Charles Darwin)

From the Autobiography of Charles Darwin.

"He made little in public of his famous grandfather, Sigmund, who in 1938 followed other members of his family in migrating to Britain beginning in 1933, the year Hitler came to power — “refugees from the Nazis before the habit caught on,” as Sir Clement, a secular Jew like many in his family, said many years later. He said he remembered his grandfather, who died in London in 1939, mostly as a faltering old man with oral cancer. “He was not, to me, famous,” he said, but rather “a good grandfather in that he didn’t forget my birthdays.”

"[He] had a testy relationship with his older brother Lucian, the artist, now 86, who is regarded by many critics as one of the greatest Realists of the past century. Late in life Sir Clement told The Observer newspaper he had no interest in reconciling with his brother. “I’m not great at forgiving,” he said.“If I decide I don’t like someone, that’s it.

(John F. Burns)

In "Clement Freud, Wit, Politician and Grandson of Famous Psychoanalyst, Dies at 84", NYT, April 16, 2009.

Three "laws" of prediction
• "When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
• "The only way of discovering the limits of the possible is to venture a little way past them into the impossible.
• "Any sufficiently advanced technology is indistinguishable from magic."

(Arthur C. Clarke)

From Wikpedia

"The first of the three laws, previously termed Clarke's Law, was proposed by Arthur C. Clarke in the essay "Hazards of Prophecy: The Failure of Imagination", in Profiles of the Future (1962). The second law is offered as a simple observation in the same essay; its status as Clarke's Second Law was conferred on it by others. In a 1973 revision of his compendium of essays, Profiles of the Future, Clarke acknowledged the Second Law and proposed the Third in order to round out the number, adding "As three laws were good enough for Newton, I have modestly decided to stop there." Of the three, the Third Law is the best known and most widely cited. [It was used by JPL reporting on gravitational boosting]"

"It was because Hopkins’s superiors in England had so little use for him…that they encouraged him to take a position as Professor of Greek and Examiner in Classics at the Royal University of Ireland, in Dublin. This prestigious-sounding post actually involved teaching elementary Latin and grading a truly staggering number of tests: six examinations times seven hundred and fifty students, according to Hopkins, for a total of forty-five hundred papers every year.

"Such was the life of Gerard Manley Hopkins, who fortuntely was able to write a little poetry amidst all that grading. His lament about this predicament has its own poetic quality:

"From the college, he issues a series of increasingly desperate cries for help. “The melancholy I have all my life been subject to has become in late years not indeed more intense in its fits but rather more distributed, constant, and crippling."

Review of of “Gerard Manley Hopkins” by Paul Mariani in the New Yorker May 11, 2009.

"Such reversals have led the veteran Silicon Valley technology forecaster Paul Saffo to proclaim: “never mistake a clear view for a short distance.”"

(John Markoff)

A look at Strong AI being back in style in The Coming Superbrain NYT, May 23, 2009.

"These aspects of exploratory experimentation and wide instrumentation originate from the philosophy of (natural) science and have not been much developed in the context of experimental mathematics. However, I claim that e.g. the importance of wide instrumentation for an exploratory approach to experiments that includes concept formation also pertain to mathematics."

(Hendrik Sorenson)

From his 2008 preprint "How Experimental is Experimental Mathematics?" discussing Franklin's argument that Steinle's notion of exploratory experimentation" facilitated by widening technology" (as in pharmacology, astrophysics, medicine, and biotechnology) is leading to a reassessment of what legitimates experiment; in that even a local model" is not now prerequisite.

Relatedly, as Dave Bailey and I wrote recently

In a provocative 2008 article entitled "The End of Theory:" The Data Deluge Makes the Scientific Method Obsolete" Chris Anderson, the Editor-in-Chief of Wired, heralds a new mode of scientific inquiry where exploding repositories of data, analyzed using advanced mathematical and statistical techniques in the same manner as Google has analyzed the Internet, are sufficient to render the traditional scientific method (hypothesize, model, test) obsolete:
"The new availability of huge amounts of data, along with the statistical tools to crunch these numbers, offers a whole new way of understanding the world. Correlation supersedes causation, and science can advance even without coherent models, unified theories, or really any mechanistic explanation at all. There's no reason to cling to our old ways. It's time to ask: What can science learn from Google?''

Kevin Kelly, in a response to Anderson's article, makes a more modest statement:

"My guess is that this emerging method will be one additional tool in the evolution of the scientific method. It will not replace any current methods (sorry, no end of science!) but will complement established theory-driven science. ... The model may be beyond the perception and understanding of the creators of the system, and since it works it is not worth trying to uncover it. But it may still be there. It just operates at a level we don't have access to.''
And it may not be there in some circumstances; both in mathematics and in what we properly call reality.

"The empirical spirit on which the Western democratic societies were founded is currently under attack, and not just by such traditional adversaries as religious fundamentalists and devotees of the occult. Serious scholars claim that there is no such thing as progress and assert that science is but a collection of opinions, as socially conditioned as the weathervane world of Paris couture. "

(Timothy Ferris)

From The Whole Shebang: A State of the Universe(s) Report, Simon and Shuster, 1998, pg. 1.

"My larger target is those contemporaries who—in repeated acts of wish-fulfillment—have appropriated conclusions from the philosophy of science and put them to work in aid of a variety of social cum political causes for which those conclusions are ill adapted. Feminists, religious apologists (including "creation scientists"), counterculturalists, neo-conservatives, and a host of other curious fellow-travelers have claimed to find crucial grist for their mills in, for instance, the avowed incommensurability and underdetermination of scientific theories. The displacement of the idea that facts and evidence matter by the idea that everything boils down to subjective interests and perspectives is—second only to American political campaigns—the most prominent and pernicious manifestation of anti-intellectualism in our time."

(Larry Laudan)

From Science and Relativism, University of Chicago Press, 1990, pg. x.

"So to summarise, according to the citation count, in order of descent, the authors are listening to themselves, dead philosophers, other specialists in semiotic work in mathematics education research, other mathematics education research researchers and then just occasionally to social scientists but almost never to other education researchers, including mathematics teacher education researchers, school teachers and teacher educators. The engagement with Peirce is being understood primarily through personal engagements with the original material rather than as a result of working through the filters of history, including those evidenced within mathematics education research reports in the immediate area. The reports, and the hierarchy of power relations implicit in them, marginalise links to education, policy implementation or the broader social sciences."

(Tony Brown)

From "Signifying "students", "teachers" and "mathematics": a reading of a special issue Published online: 28 May 2008, Springer Science + Business Media B.V. 2008.

Enter Don Tapscott, who is looking at the challenges the digital revolution poses to the fundamental aspects of the University.

"Universities are finally losing their monopoly on higher learning", he writes. "There is fundamental challenge to the foundational modus operandi of the University — the model of pedagogy. Specifically, there is a widening gap between the model of learning offered by many big universities and the natural way that young people who have grown up digital best learn."

The old-style lecture, with the professor standing at the podium in front of a large group of students, is still a fixture of university life on many campuses. It's a model that is teacher-focused, one-way, one-size-fits-all and the student is isolated in the learning process. Yet the students, who have grown up in an interactive digital world, learn differently. Schooled on Google and Wikipedia, they want to inquire, not rely on the professor for a detailed roadmap. They want an animated conversation, not a lecture. They want an interactive education, not a broadcast one that might have been perfectly fine for the Industrial Age, or even for boomers. These students are making new demands of universities, and if the universities try to ignore them, they will do so at their peril.

Contrary to Nicholas Carr's proposition that Google is making us stupid, Tapscott counters with the following:

My research suggests these critics are wrong. Growing up digital has changed the way their minds work in a manner that will help them handle the challenges of the digital age. They're used to multi-tasking, and have learned to handle the information overload. They expect a two-way conversation. What's more, growing up digital has encouraged this generation to be active and demanding enquirers. Rather than waiting for a trusted professor to tell them what's going on, they find out on their own on everything from Google to Wikipedia."

(Don Tapscott)

The Edge describing his article The impending demise of the university.

Britain pays its penny to poke a stick at Susan Boyle
In one of the few commentaries written by a man, Thomas Sutcliffe at The Independent draws uncomfortable parallels with the treatment of the insane in the 18th century.

“You could pay a penny to visit Bedlam (or Bethlehem mental hospital) and chortle at the deranged. You were even allowed to poke them with a stick if they failed to caper or roar in a satisfactory way

and can ease our disquiet about the ethics of such a spectacle by reassuring ourselves that none of these people are under restraint. They choose to take part and, in so choosing, sign up to the loss of dignity that often comes with participation … The novelty with Susan Boyle was that she sang well enough to get through to the final, elevating her from temporary comic relief into a real person whose health and well-being might arouse our protective sympathy. I doubt very much that she is the first participant to have been left in a state of anxiety by the stress and exposure of such programs, though she is probably the first person whose reaction has had any kind of widespread media coverage.”

(Araminta Wordsworth)

From a Financial Post compendium on June 2, 2009.

Borwein's Five Laws of Travel
1. 1. Distance Independence. "It is an easy 15 minute walk" covers anything from 500 to 5000 metres.
2. 2. Time Invariance. You will learn all the relevant details of how to negotiate your host city and the like adequately, exactly twenty-four hours before your departure. This is independent of the length of your stay.
3. 3. Universal Expressions. Beware of such expressions as they have no fixed meaning. They include: "Free Internet," "Easy Access to Beach" and "Full Continental Breakfast."
4. 4. Travel Agents. Never travel with a travel agent who has never travelled. They will rarely make reasonable bookings and will often make infeasible ones.
5. 5a. First Law of Directions. Never rely on oral directions given in a foreign language. All consonants sound the same after one or two city blocks while left and right are nearly always wrong and wronger.
6. 5b. Second law of Directions. All directions written or oral given by a host will be missing on salient detail that is so obvious to any local as to be unrememberable. This applies to geography, computer access and much else.

(Jonathan Borwein)

Based on decades of personal experience.

"And yet since truth will sooner come out of error than from confusion."

(Francis Bacon, 1561-1626)

From The New Organon (1620) in The Works of Francis Bacon, James Spedding, Robert Ellis and Douglas Heath (eds.) (1887-1901), Vol. 4, p. 149.

"In closing, I offer two examples from economics of what I hope to have said. Marx said that quantitative differences become qualitative ones, but a dialogue in Paris in the 1920's sums it up even more clearly:
FITZGERALD: The rich are different from us.
HEMINGWAY: Yes, they have more money."

(Phillip Anderson)

in "More Is Different," Science, New Series, Vol. 177, No. 4047. (Aug. 4, 1972), pp. 393-396.

• Try the following large collections of Mathematical Quotes from: Platonic Realms and from Furman

We start at the end where the most recent quotes lie.

• Revised 01/06/2009 by Jonathan Borwein.