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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 Nov 30 '09 at 5:29
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    $\begingroup$ Why did a question with so much positive feedback get closed? $\endgroup$ – Romeo Nov 28 '10 at 23:21
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    $\begingroup$ Diminishing marginal utility. $\endgroup$ – Qiaochu Yuan Jan 31 '11 at 2:46
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    $\begingroup$ Closing this solved what problem? $\endgroup$ – Matt Brin Jan 18 '12 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 Nov 12 '13 at 3:03

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"'Imaginary' universes are so much more beautiful than this stupidly constructed 'real' one; and most of the finest products of an applied mathematician's fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts." - G.H. Hardy

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Mathematicians are born, not made. -- Henri Poincare

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    $\begingroup$ I disagree, Henri. Most strongly. $\endgroup$ – The Mathemagician Apr 28 '10 at 0:34
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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 Jan 15 '10 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 Feb 6 '10 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 Mar 21 '10 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 Mar 21 '10 at 23:54
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