Greg Egan is a professional science fiction writer who moonlights as a mathematician. He has done some good work in pure math, e.g.: https://en.wikipedia.org/

Greg Egan is a professional science fiction writer who moonlights as a mathematician. He has done some good work in pure math, e.g.: https://en.wikipedia.org/wiki/Egan_conjecture https://en.wikipedia.org/wiki/Egan_conjecture There are others like him. If you're sufficiently smart/motivated and have a day job that's conducive to side-project intellectual effort, sure it's possible for an amateur to make contributions.