[tpudlik]

Very few self-taught people contributed to research in the 20th century. I can't speak with authority about mathematics, but in my own field (physics) the only self-taught researchers I can think of were people trained in allied fields (math, chemistry) who ran into physics problems in the course of work in their own discipline.

The root cause, I suppose, is that it takes much less time and effort to just get a PhD than to make an original research contribution, so most people get credentialed along the way. Academic programs also immerse you in current research work, making it possible to figure out where you could make contributions in the first place.