Srinivasa Ramanujan was an Indian mathematician who worked on number theory, infinite series and analysis. He said that he would have dreams of drops of blood (a symbol of his village deity, the goddess Namagiri Thayar), followed by complex mathematical equations. Even with the help of his formally-trained friend GH Hardy, he was only able to prove a small fraction of his insights.

Gregori Perelman is a Russian mathematician best known for solving the Poincare conjecture. He posted his results on arXiv in 2002-03, but never published them in a journal and never accepted any prize or money. He has expressed dismay over the lack of ethics in research.

Anon is a /sci/ user who in 2011 proved the current lower bound of a superpermutation for any size greater than 2 (the Haruhi Problem). Their proof has been archived for posterity, but we don’t know anything more about them.

There’s also Cleo from Math StackExchange. They’d drop answers to complex problems in a couple of hours with no work shown. It took another mathematician days and several pages of work to prove out one of Cleo’s answers.

Shinichi Mochizuki (the abc conjecture guy): elaborates further. You understand less.