Theorems Quotes

• If only I had the Theorems! Then I should find the proofs easily enough.

  Bernhard Riemann

  Easy, Enough, Mathematics

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• Any good theorem should have several proofs, the more the better.

  Michael Atiyah

  Should Have, Proof, Should

  "Interview with Michael Atiyah and Isadore Singer". Interview with Martin Raussen, Christian Skau, www.researchgate.net. February 2005.

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• Young men should prove theorems, old men should write books.

  G. H. Hardy

  Book, Writing, Math

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• We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"

  Gian-Carlo Rota

  Jobs, Writing, Math

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• If we knew what it was we were doing, it would not be called research, would it?

  Albert Einstein

  Love, Inspirational, Funny

  "Personal Quotes/ Biography". www.imdb.com.

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• A mathematician is a device for turning coffee into theorems.

  Paul Erdos

  Witty, Humorous, Coffee

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• A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.

  Stefan Banach

  Analogies, Proof, Theory

  "Banach Spaces and Their Applications in Analysis: Proceedings of the International Conference at Miami University, May 22-27, 2006, in Honor of Nigel Kalton's 60th Birthday" by Beata Randrianantoanina, Narcisse Randrianantoanina, Walter de Gruyter, (p. 5), 2007.

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• There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down.

  Paul Erdos

  Men, Three, Firsts

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• Economists often like startling theorems, results which seem to run counter to conventional wisdom.

  Joseph Stiglitz

  Running, Wisdom, Results

  Autobiographical Essay for the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, www.nobelprize.org. 2001.

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• God has the Big Book, the beautiful proofs of mathematical theorems are listed here.

  Paul Erdos

  Beautiful, Book, Math

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• Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

  Paul Halmos

  Math, Errors, Trial And Error

  "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

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• One geometry cannot be more true than another; it can only be more convenient.

  Henri Poincare

  Mathematics, Geometry, Convenient

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.85, Modern Library

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• The principle is so perfectly general that no particular application of it is possible.

  George Polya

  Knowledge, Math, Principles

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

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• Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century.

  Richard Askey

  Science, Germany, Analysis

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• Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

  Paul Halmos

  Math, Science, Errors

  "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

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• In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real."

  Chen-Ning Yang

  Beautiful, Real, Science

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• Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

  Imre Lakatos

  Numbers, Criticism, Doe

  Imre Lakatos (1976). “Proofs and Refutations: The Logic of Mathematical Discovery”, p.5, Cambridge University Press

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• Murphy's Law, that brash proletarian restatement of Godel's Theorem.

  Thomas Pynchon

  Law, Murphy, Brash

  "Gravity's Rainbow". Book by Thomas Pynchon, 1973.

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• My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.

  Bill Bryson

  Science, Work Out, Royal

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• There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

  George Polya

  Teaching, Writing, Science

  "How to Solve It" by George Polya, 2nd edition, (p. xv), 1957.

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• For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that by growing up with a few very powerful theorems one comes to appreciate how certain ideas can be used as tools to think with over a lifetime. One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea of all is the idea of powerful ideas.

  Seymour Papert

  Children, Growing Up, Powerful

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• We are on the verge: Today our program proved Fermat's next-to-last theorem.

  Alan Perlis

  Today, Lasts, Next

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• The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.

  Barry Mazur

  Long, Humanity, Lasts

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• ... fain would I turn back the clock and devote to French or some other language the hours I spent upon algebra, geometry, and trigonometry, of which not one principle remains with me. Stay! There is one theorem painfully drummed into my head which seems to have inhabited some corner of my brain since that early time: "The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides!" There it sticks, but what of it, ye gods, what of it?

  Jessie Belle Rittenhouse

  Squares, Two Sides, Brain

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• The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.

  Kurt Gödel

  Development, Well Known, Mathematics

  Kurt Gödel, S. Feferman (1986). “Kurt Gödel: Collected Works: Volume I: Publications 1929-1936”, p.145, Oxford University Press

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