I have just read your most recent opinion and I am also studying Ehrhart polynomials. A beautiful example of a mathematician who did remarkable work late in his life was Eugene Ehrhart. Ehrhart was a school teacher. So in some ways he can be considered a mathematical amateur. (I think late in his life he was awarded a doctorate for his mathematical work.) I believe his brilliant work on what is now called Ehrhart polynomials was done when he was in his 60's.
I am sympathetic to Hardy's lament "Mathematics is a young man's game." When he wrote it he was deeply depressed and it was probably a personal lamentation of his own declining powers! Who really knows. What is truly sad is that so much of the mathematical world uncritically accepted this bogosity, just because Hardy said it! So much for the myth that mathematicians are such logical and rational thinkers!