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Can you name a mathematical theorem that is simple to state and relatively simple to prove, was essential to your research or to a work you found interesting and significant, has the potential to be applied in a wide variety of fields, and is not part of the curriculum of what "every mathematician should know"?

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4 
 Why are people voting to close? This seems like a perfectly reasonable question... – Igor Rivin Apr 27 2011 at 15:04
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 I voted to close because I dislike the kind of soft question where the OP expects everyone else to put more effort in answering the question than it was spent in asking it. – José Figueroa-O'Farrill Apr 27 2011 at 15:10
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 Answers will be a lot more useful if they come together with explanations for why the theorem satisfies (at least some of) the criteria in the question. – Dan Ramras Apr 27 2011 at 15:11
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 I would vote to close (if I could) as this is way too broad (as well as subjctive and argumentative); every mildly specialized technical result that is easy to state and not too complicated to prove seems to qualify as an answer. – quid Apr 27 2011 at 15:21
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 You might try looking at the Math Tricki: tricki.org – Ben Linowitz Apr 27 2011 at 15:42

closed as subjective and argumentative by José Figueroa-O'Farrill, Daniel Moskovich, Charles Siegel, Zev Chonoles, Bruce Westbury Apr 27 2011 at 15:27

1 Answer

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The nine lemma.

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