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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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closed as no longer relevant by Scott Morrison Apr 28 '10 at 17:51

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In order to motivate examples in the first class in congruence theory, my teacher remarked that the beginning chapters of the Holy Bible mathematically said entail the following: "Let the days of the week be congruent modulo seven." – Unknown Jun 12 '10 at 17:07
Why did a question with so much positive feedback get closed? – Romeo Nov 28 '10 at 23:21
Diminishing marginal utility. – Qiaochu Yuan Jan 31 '11 at 2:46
Closing this solved what problem? – Matt Brin Jan 18 '12 at 18:35
@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. – Qiaochu Yuan Nov 12 '13 at 3:03

94 Answers 94

Who can does; who cannot do, teaches; who cannot teach, teaches teachers.

Paul Erdos.

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Terrible. If you enjoy mathematics, why wouldn't you want to share that joy with others? If you are going to have children some day, why not make sure their teachers are going to be educated about what mathematics really is? – Steven Gubkin Jan 19 '10 at 18:45
I think the quote is about how things are, not how things are supposed to be. – darij grinberg Mar 21 '10 at 18:22
There is a variant of the quote: "Those who can't do teach, those who can't teach teach gym."-Red Dwarf – Sean Tilson Jan 31 '11 at 6:32

Mathematicians are born, not made. -- Henri Poincare

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I disagree, Henri. Most strongly. – The Mathemagician Apr 28 '10 at 0:34

"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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Boy, was he wrong or what? – Harry Gindi Jan 15 '10 at 22:46
The quote could benefit by being put into a better context. Here it is:… but Poincare was making a pretty important point that IMO you've missed. – Ryan Budney Feb 6 '10 at 5:50

"Mathematics consists of proving the most obvious thing in the least obvious way." - George Polya

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No. – darij grinberg Mar 21 '10 at 18:24
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”? – L Spice Mar 21 '10 at 23:54

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