Sorry about that. I was on the "amateur" side, because he so clearly fits the definition in the technical sense: he was never paid to do math. However, I just asked Google Books for "fermat was a mathematician" and "fermat was an amateur mathematician"; both queries primarily showed RS math books, but the first gave 151 hits and the second 17. So unless someone can come up with a counterargument, I guess he should be called a mathematician tout simple, with clarification elsewhere that he earned his sous lawyering.