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.
There's a lot of new and unexplored branches of math. I study finite subdivision rules, which were invented in the 80's and less than 50 papers discussing them explicitly. String theory in it's mathematical form is another.