How is the corresponding author on a (math) paper typically chosen?
My experience as a pure mathematician in the US is that there are essentially no benefits to being the corresponding author. When I was a postdoc and in grad school I was often the corresponding author, but I get the feeling it was mostly because I was often the most junior of the authors and the others didn't want to waste time navigating editorial websites, receiving emails from the journal, mailing people tex files, etc. I would say that if someone is a pure mathematician in the US, the number of times they've been a corresponding author for a paper will have absolutely no impact on their career.

(I should add that I believe that in other countries the situation may be markedly different.)