Thursday, May 14, 2009

"Zeeman, E Christopher (1925 - )
Technical skill is mastery of complexity while creativity is mastery of simplicity.
Catastrophe Theory, 1977."

Tuesday, May 12, 2009

"Whitehead, Alfred North (1861 - 1947)
Fundamental progress has to do with the reinterpretation of basic ideas.
W.H. Auden and L. Kronenberger The Viking Book of Aphorisms, New York: Viking Press, 1966."

Monday, May 11, 2009

"Whitehead, Alfred North (1861 - 1947)
It is a profoundly erroneous truism, repeated by all copy books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.
An Introduction to Mathematics."
"Whitehead, Alfred North (1861 - 1947)
No Roman ever died in contemplation over a geometrical diagram.
[A reference to the death of Archimedes.]
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972."
"Whitehead, Alfred North (1861 - 1947)
So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century.
The Aims of Education."
"Whitehead, Alfred North (1861 - 1947)
The science of pure mathematics ... may claim to be the most original creation of the human spirit.
Science and the Modern World."

Friday, May 8, 2009

"Warner, Sylvia Townsend
For twenty pages perhaps, he read slowly, carefully, dutifully, with pauses for self-examination and working out examples. Then, just as it was working up and the pauses should have been more scrupulous than ever, a kind of swoon and ecstasy would fall on him, and he read ravening on, sitting up till dawn to finish the book, as though it were a novel. After that his passion was stayed; the book went back to the Library and he was done with mathematics till the next bout. Not much remained with him after these orgies, but something remained: a sensation in the mind, a worshiping acknowledgment of something isolated and unassailable, or a remembered mental joy at the rightness of thoughts coming together to a conclusion, accurate thoughts, thoughts in just intonation, coming together like unaccompanied voices coming to a close.
Mr. Fortune's Maggot."
"Turgenev, Ivan Sergeievich (1818 - 1883)
Whatever a man prays for, he prays for a miracle. Every prayer reduces itself to this: `Great God, grant that twice two be not four'."
"Tietze
The story was told that the young Dirichlet had as a constant companion all his travels, like a devout man with his prayer book, an old, worn copy of the Disquisitiones Arithmeticae of Gauss.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."

Thursday, May 7, 2009

"Thomson, [Lord Kelvin] William (1824-1907)
Fourier is a mathematical poem."
"Sun Tze (5th - 6th century)
The control of large numbers is possible, and like unto that of small numbers, if we subdivide them.
Sun Tze Ping Fa."
"Smith, Henry John Stephen (1826 - 1883)
[His toast:]
Pure mathematics, may it never be of any use to anyone.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972."
"Shakespeare, William (1564 - 1616)
I cannot do it without comp[u]ters.
The Winter's Tale."
"Russell, Bertrand (1872-1970)
[Upon hearing via Littlewood an exposition on the theory of relativity:]
To think I have spent my life on absolute muck.
J.E. Littlewood, A Mathematician's Miscellany, Methuen and Co. ltd., 1953."
"Russell, Bertrand (1872-1970)
Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.
The Impact of Science on Society, 1952"
"Russell, Bertrand (1872-1970)
At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.
The Autobiography of Bertrand Russell ."
"Hugo Rossi

In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.
Mathematics Is an Edifice, Not a Toolbox, Notices of the AMS, v. 43, no. 10, October 1996."
"R. Rivest, A. Shamir, and L. Adleman
The magic words are squeamish ossifrage
[This sentence is the result when a coded message in Martin Gardner's column about factoring the famous number RSA-129 is decoded. See the article whose title is the above sentence by Barry Cipra, SIAM News July 1994, 1, 12-13.]"
"Renan, Ernest
The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life.
Souvenirs d'enfance et de jeunesse."
"Recorde, Robert (1557)
To avoide the tediouse repetition of these woordes: is equalle to: I will settle as I doe often in woorke use, a paire of paralleles, or gemowe [twin] lines of one lengthe: =, bicause noe .2. thynges, can be moare equalle.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."
"Pordage, Matthew
One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988."
"Poincar� Jules Henri (1854-1912)
Mathematical discoveries, small or greatare never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious."
"Poincar� Jules Henri (1854-1912)
The mind uses its faculty for creativity only when experience forces it to do so."
"Poincar� Jules Henri (1854-1912)
Thought is only a flash between two long nights, but this flash is everything.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956."
"Plutarch (ca 46-127)
[about Archimedes:]
... being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."
"Passano, L.M.
This trend [emphasizing applied mathematics over pure mathematics] will make the queen of the sciences into the quean of the sciences.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972."
"Pascal, Blaise (1623-1662)
Look somewhere else for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.
[Written to Fermat]
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."
"Pascal, Blaise (1623-1662)
Through space the universe grasps me and swallows me up like a speck; through thought I grasp it.
Pensees. 1670."
"Pascal, Blaise (1623-1662)
We are usually convinced more easily by reasons we have found ourselves than by those which have occurred to others.
Pensees. 1670."
"Thomas R. Nicely
Usually mathematicians have to shoot somebody to get this much publicity.
[On the attention he received after finding the flaw in Intel's Pentium chip in 1994]
Cincinnati Enquirer, December 18, 1994, Section A, page 19."
"Newton, Isaac (1642-1727)
[His epitaph:]
Who, by vigor of mind almost divine, the motions and figures of the planets, the paths of comets, and the tides of the seas first demonstrated."
"Newman, James, R.
The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956."
"Mathesis, Adrian
All great theorems were discovered after midnight.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988."
"Mann, Thomas (1875-1955)
A great truth is a truth whose opposite is also a great truth.
Essay on Freud. 1937."
"Mach, Ernst (1838-1916)
The mathematician who pursues his studies without clear views of this matter, must often have the uncomfortable feeling that his paper and pencil surpass him in intelligence.
'The Economy of Science' in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956."
"Luther, Martin (1483-1546)
Medicine makes people ill, mathematics make them sad and theology makes them sinful."
"Lobatchevsky, Nikolai
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988."
"Littlewood, J. E. (1885 -1977)
I read in the proof sheets of Hardy on Ramanujan: 'As someone said, each of the positive integers was one of his personal friends.' My reaction was, 'I wonder who said that; I wish I had.' In the next proof-sheets I read (what now stands), 'It was Littlewood who said...'
A Mathematician's Miscellany, Methuen Co. Ltd, 1953."

Wednesday, May 6, 2009

"Leibniz, Gottfried Whilhem (1646-1716)
Music is the pleasure the human soul experiences from counting without being aware that it is counting.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988."
"Leibniz, Gottfried Whilhem (1646-1716)
Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.
J. Koenderink, Solid Shape, Cambridge Mass.: MIT Press, 1990."
"de Laplace, Pierre-Simon (1749 - 1827)
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988."
"de Laplace, Pierre-Simon (1749 - 1827)
[said about Napier's logarithms:]
...by shortening the labors doubled the life of the astronomer.
In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969."
"de Laplace, Pierre-Simon (1749 - 1827)
Napoleon: You have written this huge book on the system of the world without once mentioning the author of the universe.
Laplace: Sire, I had no need of that hypothesis.
Later when told by Napoleon about the incident, Lagrange commented: Ah, but that is a fine hypothesis. It explains so many things.
DeMorgan's Budget of Paradoxes."
"de Laplace, Pierre-Simon (1749 - 1827)
Read Euler: he is our master in everything.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."
"Langer, Rudoph E.
[about Fourier] It was, no doubt, partially because of his very disregard for rigor that he was able to take conceptual steps which were inherently impossible to men of more critical genius.
In P. Davis and R. Hersh The Mathematical Experience, Boston: Birkh�ser, 1981."
"Lang, Andrew (1844-1912)
He uses statistics as a drunken man uses lamp posts -- for support rather than illumination.
Treasury of Humorous Quotations."
"Landau, E.
[Asked for a testimony to the effect that Emmy Noether was a great woman mathematician, he said:]
I can testify that she is a great mathematician, but that she is a woman, I cannot swear.
J.E. Littlewood, A Mathematician's Miscellany, Methuen and Co ltd., 1953."
"LaGrange, Joseph-Louis
[said about the chemist Lavoisier:]
It took the mob only a moment to remove his head; a century will not suffice to reproduce it.
H. Eves An Introduction to the History of Mathematics, 5th Ed., Saunders."
"Kline, Morris
Logic is the art of going wrong with confidence.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988."
"Kline, Morris
A proof tells us where to concentrate our doubts.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988."
"Kleinhenz, Robert J.
When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain's sheer face, encountering obstacles at every turn, often retracing one's steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countrysideand then noting the automobile road up the other side!"
"Kepler, Johannes (1571-1630)
Nature uses as little as possible of anything."
"Karlin, Samuel (1923 - )
The purpose of models is not to fit the data but to sharpen the questions.
11th R A Fisher Memorial Lecture, Royal Society 20, April 1983"
"Johnson, Samuel (1709-1784)
Sir, I have found you an argument. I am not obliged to find you an understanding.
J. Boswell The Life of Samuel Johnson, 1784."
"Jacobi, Carl
It is often more convenient to possess the ashes of great men than to possess the men themselves during their lifetime.
[Commenting on the return of Descartes' remains to France]
In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977."
"Ibn Khaldun (1332-1406)
Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.
The Muqaddimah. An Introduction to History."
"Holmes, Oliver Wendell
Descartes commanded the future from his study more than Napoleon from the throne.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."
"Hilbert, David (1862-1943)
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.
Report on Number Theory, 1897."

Tuesday, May 5, 2009

"Hilbert, David (1862-1943)
Wir mussen wissen.
Wir werden wissen.
[Engraved on his tombstone in Gttingen.]"

(We must know. We will know.)
"Hermite, Charles (1822-1901)
Abel has left mathematicians enough to keep them busy for 500 years.
In G. F. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992."

Monday, May 4, 2009

"Hardy, Godfrey H. (1877 - 1947)
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
A Mathematician's Apology, London, Cambridge University Press, 1941."
"Hardy, Godfrey H. (1877 - 1947)
Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
A Mathematician's Apology, London, Cambridge University Press, 1941."
"Halmos, Paul R.
Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
I Want to be a Mathematician, Washington: MAA Spectrum, 1985."
"Halmos, Paul R.
... the student skit at Christmas contained a plaintive line: 'Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams.'
I Want to be a Mathematician, Washington: MAA Spectrum, 1985."
"Hadamard, Jacques
The shortest path between two truths in the real domain passes through the complex domain.
Quoted in The Mathematical Intelligencer, v. 13, no. 1, Winter 1991."
"Graham, Ronald
It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, `Yes, it is true, but you won't be able to understand the proof.'
John Horgan. Scientific American 269:4 (October 1993) 92-103."
"Gordon, P
This is not mathematics, it is theology.
[On being exposed to Hilbert's work in invariant theory.]
Quoted in P. Davis and R. Hersh The Mathematical Experience, Boston: Birkh�ser, 1981."
"Goedel, Kurt
I don't believe in natural science.
[Said to physicist John Bahcall.]
Ed Regis, Who Got Einstein's Office? Addison Wesley, 1987."

Friday, May 1, 2009

"Gauss, Karl Friedrich (1777-1855)
You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.
In G. Simmons Calculus Gems, New York: McGraw Hill inc., 1992."
"Galton, [Sir] Francis (1822-1911)
Whenever you can, count.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956."