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I have been wondering if math would be more enjoyable, if one was able to start a new field and come up with all the definitions, methods, etc. rather than starting where someone else ended. Consequently, I was wondering if any of you guys had in mind an unexplored, physically motivated and seemingly simple question that could possibly become a rich mathematical theory when studied (for example percolation theory and knot theory)? If not, do you know any really new mathematical fields (with again, simple real world motivations) that are coming into development?

Thanks,

Scott

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closed as not a real question by Pete L. Clark, Grigory M, Asaf Karagila, Qiaochu Yuan Aug 18 '11 at 15:56

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This is a bit too soft... and at this late an age, the likelihood of finding something "unexplored" looks rather small to me. The well-established portions of mathematics have quite a number of unsolved problems as it is, in any event... –  J. M. Aug 18 '11 at 9:14
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@J.M "and at this late an age, the likelihood of finding something "unexplored" looks rather small to me" -- Really? We've been discovering new mathematics for most of the last century (chaotic dynamics, percolation theory, knot theory, noncommutative geometry, information theory, quantum computing, ...) even if some mathematicans don't yet recognise them as mathematics. I don't see why this wouldn't continue. –  Chris Taylor Aug 18 '11 at 9:37
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I would imagine most things with ‘simple real world motivations’ are already well-developed. Sometimes so much so that they aren't even counted as mathematics any more, like computer science. Also, consider reading this paper of Gowers: The two cultures of mathematics. –  Zhen Lin Aug 18 '11 at 9:44
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@Chris: I said the likelihood is "small", not zero. :) –  J. M. Aug 18 '11 at 9:51
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@J.M., Small like $1 - \varepsilon\,$? ;-) –  cardinal Aug 18 '11 at 13:13