All (unless I've missed one?) the math breakthroughs are also coming from the relatively small number of mathematicians working at these companies, as opposed to the many orders of magnitude more mathematicians using LLMs for mathematics outside of the companies. I assume the missing link everywhere is being able to casually burn a few rainforests worth of tokens in pursuit of something publishable.

Depends on exactly where you draw the line at "breakthrough", but there's been at least a few novel and interesting results coming from outside mathematicians. Recently for example there were https://old.reddit.com/r/math/comments/1uxj3cy/after_openais... from Phillip Kerger at Berkeley, and https://www.erdosproblems.com/forum/thread/119/proof-claims from Samuel Korsky at Two Sigma (the latter of which was more of a collaboration between the human and machine, not a one-shot like several of the other results we've discussed).

No. Most of the results are from 3rd parties using publicly available models. The most impressive results have come from direct announcements, but most in total have not. Open AI have only announced 2 results and the total is up to a dozen or so now.