I think there is an important complex relating to research mathematics you could call autodidacticism-contrarianism (A-C), but it is not so clear quite where the dividing line between the two parts lies.
We know (roughly speaking) that some major advances come when a big and rather public research programme reaches maturity and there is a payoff. Others, though, come from largely independent thought developed to some extent in isolation. It is "contrarian", usually, to think that some hard problem can be solved with existing tools when the general view is that it can't. It would be "autodidactic" to base such a view on knowledge of some more obscure parts of the literature. In either case there is an obstinacy that defies conventional expectation.
That said, my own experience and what I know of that of others would suggest a mixture of these independent-minded elements with what you could call the mainstream and socially-supported elements is what is most effective.
