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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


Why are people voting to close? This seems like a perfectly reasonable question... –  Igor Rivin Apr 27 '11 at 15:04
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
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
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
You might try looking at the Math Tricki: tricki.org –  Ben Linowitz Apr 27 '11 at 15:42

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