Question

Quantitatively speaking, which subject area in mathematics is currently the most research active?

Answer 1

i think it depends on how narrow or broad you define “subject area”. The broader the subject, the more research falls under it. So probably something like “algebra” would have a lot of research falling under it, vs. specifically something like “finite group theory” which is a sub field of algebra (correct me if im wrong)

Answer 2

Even if the subjects are well-defined, deciding by publication count is not a good idea. Should a 200-300 hundred pages paper on Memoirs of AMS represent the same “activeness” as a 10 pages paper on PAMS? And should 10 major breakthroughs on Annals represents the same “activeness” as 10 papers on, for example Journal of Algebra?

By the way it’s funny to see from the link how toxic MO used to be (actually still is). I’m surprised that quid was not with his bunch of question qualification police.

Answer 3

100% PDE. if by the number of papers.

The least should be algebra

Answer 4

Machine learning, by far

Answer 5

Algebraic Geometry is my answer.

As for how I'd measure it, ideally I'd look at what course has been the most frequently added as new to graduate level courses in research universities. Those topics may not be pumping out papers right this moment, but I think it would be the most accurate way to see which direction research is heading. It's also why I'd answer algebraic geometry, it's caught on like wildfire in the last few years and I've seen a few new courses on it at various universities in my area.

Answer 6

I don't think this is a question with a meaningful answer.

Answer 7

machine learning :-)

Edit: make the already obvious ironic smiley more obvious