Greg EganGreg Egan. He's a very renowned science fiction writer who holds a bachelor degree in mathematics. He wrote, as a coauthor, 2 articles which were published in peer-reviewed journals, one of them is with John Baez. The first one was written when he was approximately 40 years old.
There's also more eccentric example of Andrew BealAndrew Beal, which is much more known in the world of poker. He made however one minor conjecture in number theoryminor conjecture in number theory for whose proof or disproof he offers $100,000.
And there's also a list on wikipedialist on wikipedia which might be worth going through.
Edit: (nov-2018) Some recent progress by G. Egan has been made with an anonymous 4chan-member, on a problem on permutations.