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Some famous quotes often give interesting insights into the vision of mathematics that certain mathematicians have. Which ones are you particularly fond of?

Standard community wiki rules apply: one quote per post.

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    $\begingroup$ There are 10 kinds of people in the world, those that understand binary and the other 9. $\endgroup$
    – Jonathan Kariv
    Commented Nov 30, 2009 at 5:29
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    $\begingroup$ Why did a question with so much positive feedback get closed? $\endgroup$
    – Romeo
    Commented Nov 28, 2010 at 23:21
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    $\begingroup$ Diminishing marginal utility. $\endgroup$
    – Qiaochu Yuan
    Commented Jan 31, 2011 at 2:46
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    $\begingroup$ Closing this solved what problem? $\endgroup$
    – Matt Brin
    Commented Jan 18, 2012 at 18:35
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    $\begingroup$ @Matt: standards for what kind of questions people want on MO have changed over time, and keeping this question opens gives a false impression to new users of what kind of questions we want on MO. It's less confusing to close it. This happens on other SE sites as well; many of the most popular questions on StackOverflow, for example, are also closed. There's also the more practical issue that if it's open people keep adding answers and, again, the marginal utility of each additional answer is decreasing. $\endgroup$
    – Qiaochu Yuan
    Commented Nov 12, 2013 at 3:03

94 Answers 94

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Mathematicians are born, not made. -- Henri Poincare

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    $\begingroup$ I disagree, Henri. Most strongly. $\endgroup$
    – The Mathemagician
    Commented Apr 28, 2010 at 0:34
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6a cc d æ 13e ff 7i 3l 9n 4o 4q rr 4s 9t 12vx

Explanation given by Newton to Leibniz in response to the latter's request for details about Newton's newly developed method of fluxions and fluents, in the form of an anagram for «Data æquatione quotcunque fluentes quantitates involvente fluxiones invenire, et vice versa».

Who's not shared the feeling that Leibniz must have felt at getting this response when reading obscure explanations in the literature? :P

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    $\begingroup$ Ah! I've always assumed the anagram was something more clever, and have wondered what that sentence can possibly anagram to! So he just gives a list of letter counts... that's so cheap! $\endgroup$
    – Willie Wong
    Commented Mar 21, 2010 at 19:47
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"There are, therefore, no longer some problems solved and others unsolved, there are only problems more or less solved, according as this is accomplished by a series of more or less rapid convergence or regulated by a more or less harmonious law. Nevertheless an imperfect solution may happen to lead us towards a better one."

Henri Poincare

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    $\begingroup$ Boy, was he wrong or what? $\endgroup$
    – Harry Gindi
    Commented Jan 15, 2010 at 22:46
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    $\begingroup$ The quote could benefit by being put into a better context. Here it is: books.google.ca/… but Poincare was making a pretty important point that IMO you've missed. $\endgroup$
    – Ryan Budney
    Commented Feb 6, 2010 at 5:50
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"Mathematics consists of proving the most obvious thing in the least obvious way." - George Polya

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    $\begingroup$ No. $\endgroup$
    – darij grinberg
    Commented Mar 21, 2010 at 18:24
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    $\begingroup$ Darij, this is a sentiment with which one can agree or disagree (I agree about the content of many undergraduate mathematics courses, but disagree about much mathematics beyond that), but surely it's courteous to offer a bit more than “No”? $\endgroup$
    – LSpice
    Commented Mar 21, 2010 at 23:54
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