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I recently heard about a branch called tropical geometry developed by Professor Bergman. I was wondering if there´s a newest but yet unexplored math branch, and by newest I mean developed in the last 60 years, and by unexplored I understand a branch without a huge amount of written articles, books, given seminars or courses in the top universities. I am just asking for pure math branch, and not applied math or mathematical physics. Thanks.

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    I bet that there is about to be a huge boom in inter-universal Teichmuller theory.2012-10-15
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    Searching for "tropical" in the mathematics part of www.arxiv.org yielded 446 papers. The search "tropical" and "geometry" yielded 356 papers.2012-10-15
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    That´s a few quantity of articles, don´t you think so?2012-10-15
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    There's lots of new unexplored math. If you want to build a career, though, you can't just do "new and unexplored" math - you have to figure out what other mathematicians will find interesting. I gather that's much harder.2012-10-15
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    Wow, thats amazing, but i mean create in mathematics is not an easy labour you need to know a lot, for example, Riemann, Poincaré, Gothendieck, were full of knowledge, and they gift us new branches, i am looking for that branches that are now created2012-10-15
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    That's more papers than I have time to read in the near future.2012-10-15
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    Absolutely, but if you try to do the same with commutative algebra, look what you get2012-10-15
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    Blass-Gauss theory. I know it's the newest branch of mathematics because I just made it up. It has no papers, no theorems, and not even any definitions. All it has, so far, is a really good name.2013-08-13
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    I would say Hyperoperations! Definition of Hyperoperation is old but there aren't many papers on the topic, i mean papers with the world "hyperoperation". For example the extension of the hyperoperations to non-integer values. I may be wrong is obvious.2013-10-19
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    NF studies! Not new at all, but definitely under-researched (imo)! And after 70+ years it finally looks like there might actually be models of NF, so it's much less probable that it's a waste of time!2013-11-19
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    @AndreasBlass: I'm pretty sure a Blass-Gauss structure is a regular hypergraph whose elements are regular monoids. I just looked it up on theproofistrivial.com.2013-11-19
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    Apparently Shinichi Mochizuki has singlehandledly started a new branch of math in pursuit of the ABC theorem; he perhaps has a totally different approach to what numbers are. which is promising given the immense difficulties of number theory. It seems like it is going to take many mathematicians many years just to read what he has already done. Then maybe they'll give the field a name and people can work on it. Read about it here: http://projectwordsworth.com/the-paradox-of-the-proof/2013-12-22

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