Inspired by the comparison of programming languages by [GitHub](https://github.com/) and [Stack Overflow](https://stackoverflow.com/) activity (e.g. [this one for 2015](http://redmonk.com/sogrady/2015/01/14/language-rankings-1-15/)) I decided to look at the popularity of mathematical disciplines by using data from both [arXiv](http://arxiv.org/) and [MathOverflow](https://mathoverflow.net/) (see also my motivation for [getting a dump of arXiv metadata](https://academia.stackexchange.com/questions/38969/getting-a-dump-of-arxiv-metadata)). Here it is:


[![arXiv vs MathOverflow - popularity of disciplines][1]][1]


  [1]: https://i.sstatic.net/p5UQI.png

It's based on all data until January 2015. For MO there is little dependence of popularity of topics over time; for arXiv there is some, but it does not change the plot in any drastic way (due to arXiv growth the lifetime average is close the the average from the last 5 years).

There is some (positive) correlation between the number of questions here and the number of preprints on arXiv, per discipline. Of course, there are many factors that come into play:

* the number of people interested in a given field,
* coverage of people (not all mathematicians are here, not all - are posting to arXiv), 
* difficulty to ask a question,
* difficulty to write a paper,
* etc.

I am not a (real) mathematician, and not even a frequent MO user; so I may be missing some explanations, which are obvious for everyone in a given field. 

Do you know plausible explanations why certain fields lie above, or below, the regression line?

(I have some guesses, but don't want to mix this answer with a very partial response.)