Some good quotes:


"Not everything that counts can be counted; and not everything that can be counted counts." - Albert Einstein

"The real danger is not that computers will begin to think like men, but that men will begin to think like computers." - Sydney Harris
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

"A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction." - [Count] Lev Nikolgevich Tolstoy
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1989.

On Mathematics and Science:

Referee's report: "This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true." - Anonymous
In H.Eves Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988.

"An expert is a man who has made all the mistakes, which can be made, in a very narrow field." - Niels Bohr

"A Mathematician is a machine for turning coffee into theorems." - Paul Erdos

[upon losing the use of his right eye]
"Now I will have less distraction."- Leonard Euler
In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.

"Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore." - Albert Einstein
In A. Sommerfelt "To Albert Einstein's Seventieth Birthday" in Paul A. Schilpp (ed.) Albert Einstein, Philosopher-Scientist, Evanston, 1949.

"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Reader's Digest. Oct. 1977.

"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."- G.H. Hardy
A Mathematician's Apology, London, Cambridge University Press, 1941.

"One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it."- David Hilbert
In H. Eves Mathematical Circles Revisited, Boston: Prindle, Weber and Schmidt, 1971

"Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up."- Leopold Kronecker
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

[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."- E. Landau
J.E. Littlewood, A Mathematician's Miscellany, Methuen and Co ltd., 1953.

"In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished."- Gottfried Whilhem Leibniz
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.

"No human investigation can be called real science if it cannot be demonstrated mathematically." - Leonardo Da Vinci

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..."- J.E. Littlewood
A Mathematician's Miscellany, Methuen Co. Ltd, 1953.

"The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another." - Gösta Mittag-Leffler
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

"Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does." - , L. J. Mordell
In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.

"...from the same principles, I now demonstrate the frame of the System of the World."- Isaac Newton
Principia Mathematica.

[On the attention he received after finding the flaw in Intel's Pentium chip in 1994]
"Usually mathematicians have to shoot somebody to get this much publicity." - Thomas R. Nicely
Cincinnati Enquirer, December 18, 1994, Section A, page 19.

"We arrive at truth, not by reason only, but also by the heart." - Blaise Pascal
Pensees. 1670.

"Chance favors only the prepared mind." - Louis Pasteur
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988

"Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house." - Jules Henri Poincaré
La Science et l'hypothèse.

"Mathematical discoveries, small or great are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious."- Jules Henri Poincaré

"A good notation has a subtlety and suggestiveness which at times make it almost seem like a live teacher." - Bertrand Russell
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956

"This paper gives wrong solutions to trivial problems. The basic error, however, is not new." - Clifford Truesdell
Mathematical Reviews 12, p561.

"Every mathematician worthy of the name has experienced ... the state of lucid exaltation in which one thought succeeds another as if miraculously... this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work..." - Andre Weil
The Apprenticeship of a Mathematician.

"My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful." - Hermann Weyl
In an obituary by Freeman J. Dyson in Nature, March 10, 1956.

On Teaching:

"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Reader's Digest. Oct. 1977.

"When introduced at the wrong time or place, good logic may be the worst enemy of good teaching." - George Polyá
The American Mathematical Monthly, v. 100, no. 3.

"We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context." - Hermann Weyl
Unterrichtsblätter für Mathematik und Naturwissenschaften, 38, 177-188 (1932). Translation by Abe Shenitzer appeared in The American Mathematical Monthly, v. 102, no. 7 (August-September 1995), p. 646.

On Ability and Creativity:

"Natural abilities are like natural plants that need pruning by study." - Francis Bacon

"The creative person is both more primitive and more cultivated, more destructive and more constructive, a lot madder and a lot saner, than the average person." - Frank Barron

"There is no one definitive creative path. There are many ways to be creative – not only intuitive ways but organized, logical ways, too." - Theresa Bayer

"The essential ingredient for creativity is wasting time." - Anonymous

"The infinitely competent can be uncreative." - J. E. Littlewood
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

Chase and Max Quotes:

"Rewind. Rewind." - Chase Holdener, Age 1
After learning that his favorite parts of movies could be seen again by rewinding the video, Chase began requesting that we "rewind" real life so that he could experience happy moments again and again.

"If I drop a ball, is it falling or is it felling?" - Chase Holdener, Age 2

"But I have things that I have to do." - Chase Holdener, Age 2
Chase's response to Mom's statement that he needed to go to bed earlier.

"Mommy, I love you infinity, but I love myself infinity infinities." - Chase Holdener, Age 3

"Mathematics is for girls. Mommy studies mathematics. I'm going to be a rockamatician like Daddy." - Chase Holdener, Age 3

"I don't want to be the same thing as a moose!" - Chase Holdener, Age 3
Chase was clearly upset (we're talking real tears!) to learn that he was a mammal just like a moose.

"Is George Bush real?" - Chase Holdener, Age 3
This question came shortly after Chase went to his first baseball game (Colorado Rockies vs. Kansas City Royals in Denver). At the game he kept saying "these baseball players are real." It wasn't until the next day that I realized he had made the connection that some things on TV are real and others aren't. While watching Bush give a speech the following evening, Chase asked this question. Then he assured me that Clifford the big red dog is not real.

"Someday everybody here will be dead, and all of the buildings will be dust." - Chase Holdener, Age 3
Chase's exclamation to his preschool teacher after his visit to Elizabethtown, a ghost town in New Mexico.

"Zombies are dead people who come back to life. Pause. Jesus came back to life, so Jesus is a zombie." - Chase Holdener, Age 4

"Mommy, I'm frustrated. How do I know if I am real?" - Chase Holdener, Age 4

"They might as well charge $20" - Chase Holdener, Age 5
Chase's observation after seeing that a product was priced at $19.99.

"Five hundred and ninety five dollars is *a lot* for a dinner." - Chase Holdener, Age 5
Chase's statement after noticing the one missing decimal point among a list of $5.95 meals advertised on a restaurant's white board.

"Ah-goo" - Max Holdener, Age 3 months.

"Emma says that a googolplex is the biggest number. I told her that a googolplex plus one is bigger." - Chase Holdener, Age 6

Back to the Kenyon Homepage Back to the Math Homepage Back to JAH's Homepage