Since I have been a lurker here for some time, and this is only my first question, I want to begin with: Hello everyone! Now, on to the question.

Mathematics has many different branches (or areas). But while some of them can be traced all the way back to Antiquity (geometry, number theory), some other have roots in Baroque (analysis), and still other have emerged only recently (complexity theory, category theory). The above classification is of course by no means complete, but maybe you can already see where am I heading:

Is something happening right now at the frontiers of mathematics that suggests that a new area will emerge in the nearest future? If yes, what is this branch (going to be) about? If no, are there any chances, do you think, that such a new area will appear sooner or later? Do you have any "wild guesses" what it could be about? Or maybe do you believe that mathematics per today is more or less complete?

Of course, in more broad terms I am interested where the modern mathematics is heading to, but I think the latter question would be too general. I hope the above formulation is more concrete, and, well, certainly it is a research-level question in some sense...


closed as not constructive by Dan Petersen, Bruce Westbury, Andy Putman, Dmitri Pavlov, Gerald Edgar May 27 '11 at 13:58

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    $\begingroup$ This question has nine upvotes and one vote to close as of now. If it is to remain open, I think it should at least be community wiki, as it does not have a single right answer, but is likely to generate a whole list of answers. $\endgroup$ – Harald Hanche-Olsen May 27 '11 at 11:41
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    $\begingroup$ Ten upvotes and no answer!? Isn't anyone's guess going to be just as good as mine? $\endgroup$ – Johan Wästlund May 27 '11 at 12:06
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    $\begingroup$ @Charles Matthews I am a newbie, so I guess I shouldn't be arguing, but I really don't understand reasons for putting the question down so quickly. I agree that "no major new areas is quite compatible with grossly incomplete", but then I used the phrasing "more or less complete" in the sense of "no new areas on the horizon", as should be clear from the context of my question. It seems also too mee that there are a lot of "subjective and argumentative" questions around that remain opened... $\endgroup$ – Borys Jagielski May 27 '11 at 14:27
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    $\begingroup$ it seems areas get closed before they can emerge ;-) $\endgroup$ – Suvrit May 27 '11 at 14:47
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    $\begingroup$ @Todd Thank you for answering, but I am not interested in arguing my points. I was just hoping to get an answer to the above question. Tough luck. :) $\endgroup$ – Borys Jagielski May 28 '11 at 13:01

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