I've done mathematical research in the past and I actually think a lot of the practical methodology I've learned from software development could be incredibly useful to mathematicians. I'd love to work full-time on a selection of related research problems with a group of coworkers following a sort of "agile" process with quick morning standups, a centralized repository of works and proofs in progress, "proof reviews", Trello boards, and so on.

Would it actually work? I honestly don't know, but I'd seriously love to try it.