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...