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.''
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.''
``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.''
``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.''
``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.''
``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.
`` "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." ''
``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.''
``I imagine most of that stuff on the information highway is roadkill anyway.''
``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.''
``My dearest Miss Dorothea Sankey
``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.''
``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.
``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.''
`` '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.''
``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.' ''
``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.''
``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.''
``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. ''
``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.
``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.
``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).
``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.
["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.
Cecil Rhodes own sardonic paraphrase of the criteria for a Rhodes Scholarship:
``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.
``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?"
``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).
``Then, owls and bats,
From Robert Browning's (1841) Pippa Passes, which also contains "God's in his Heaven, all's right with the world."
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.
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.
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.
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.''
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
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.' ''
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.'"
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.''
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 David Berlinski's "A Tour of the Calculus" (Pantheon Books, 1995)
`` 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)''
A serious "best title" candidate...
``It's generally the way with progress that it looks much greater than it really is.''
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."
``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.''
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.''
``Mathematicians are like pilots who maneuver their great lumbering planes into the sky without ever asking how the damn things stay aloft.
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.''
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.''
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.''
``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.''
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,''
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.
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
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.''
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.''
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.''
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." ''
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." ''
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.''
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)
``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.''
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?''
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.''
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.''
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.
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.''
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.''
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.''
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?
Interview with Allyn Jackson from page 672 of The Notices of The AMS, June-July 1999
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." '
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.''
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.
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.''
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?''
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.''
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.)
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. ''
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.
From "Elbert F. Fox: An Early Pioneer", American Math Monthly 107 (2000) 105-128.
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!" "
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.
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.''
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.
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. ''
Quoted from the article "One Hundred Years of Quantum Physics" in Science August 11, pages 893-898.
``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.''
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.
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."
"Capitalism is the extraordinary belief that the nastiest of men, for the nastiest of reasons, will somehow work for the benefit of us all."
"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."
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."
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.' "
From Claude Shannon's (1916-2001) obituary.
"The price of metaphor is eternal vigilance"
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!"
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:
On page 5 of Where Mathematics Comes From, Basic Books, 2000.
"The early study of Euclid made me a hater of geometry."
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."
"All physicists and a good many quite respectable mathematicians are contemptuous about proof."
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,!"
"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."
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."
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."
Distinguishing effortless early learning of language and social customs from later labourious general purpose concept acquisition, Egan writes:
In Kieran Egan's, Getting it Wrong from the Beginning -- Major Mistakes in the Project to Educate Everybody (in press).
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."
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.'"
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.)
"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.
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'."
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..."
" `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
`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).'
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."
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. "
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.
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.
Martin Davis, Visiting Scholar UC Berkeley, Professor Emeritus, NYU. Following up on queries on the Historia Mathematica list, Jan 12, 2002.
"  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.  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.  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.  Inventions then cannot, in nature, be a subject of property. "
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."
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."
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."
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."
Samuel Taylor Coleridge then launches into an ode on mathematics, the first verses of which are as follows:
" On a given finite line
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."
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.
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.'"
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.
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.''
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).
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."
"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."
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."
On his Vancouver home page.
"The plural of 'anecdote' is not 'evidence'."
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."
"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."
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.
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."
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."
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:
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. ''
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."
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. "
From Making the Connection: Research and Practice in Undergraduate Mathematics, M. Carlson and C. Rasmussen (Eds), MAA Notes, in press.
Tucker: It is probably false.
Greenwood: ... my apologies to Professor Lefschetz, look for a proof and for
a counterexample at the same time.
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.
Tucker: It is probably false.
Greenwood: ... my apologies to Professor Lefschetz, look for a proof and for a counterexample at the same time.
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
-- 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
a billion dollars over the long term. Do not be surprised if we place
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
charge, doctors and washing machines.
-- Don't be evil. We believe strongly that in the long term, we will be
-- 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."
-- 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."
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."
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."
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."
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.
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."
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."
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."
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.
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.
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.
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."
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.
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.
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.
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?
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.]
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.
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.
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."
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."
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 (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 (1820 - 1884)
"Rigour is the affair of philosophy, not of mathematics."
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.
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!"
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'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)
"Logic is the hygiene the mathematician practices to keep his ideas healthy and strong."
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.
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, "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."
I'm not sure what it means, but I like it!
'Thirst for knowledge' may be opium craving
"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."
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."
Like so many Einstein quotes, this appears everywhere and seemingly without direct attribution.
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:
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.
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."
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."
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."
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"
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."
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."
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.
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."
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."
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."
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?"
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.’“
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."
"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."
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."."
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."
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]"
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.”
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.
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."
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.