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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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closed as not constructive by José Figueroa-O'Farrill, Daniel Moskovich, Charles Siegel, Zev Chonoles, Bruce Westbury Apr 27 '11 at 15:27

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

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Why are people voting to close? This seems like a perfectly reasonable question... –  Igor Rivin Apr 27 '11 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 '11 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 '11 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 '11 at 15:21
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You might try looking at the Math Tricki: tricki.org –  Ben Linowitz Apr 27 '11 at 15:42
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