Question

From A Mathematician’s Apology, G. H. Hardy, 1940: "I had better say something here about this question of age, since it is particularly important for mathematicians. No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. ... I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself."

Have matters improved for the elderly mathematician? Please answer with major discoveries made by mathematicians past 50.

Answer 1

The story with one's age is very simple : different persons can age very differently. If one takes care not to age in the wrong way for a given intellectual venture, then quite likely, one can pursue it for many decades ... And of course, mathematics is an intellectual venture ... A good example of how little physical condition is needed for pursuing an intellectual venture is given by the well known physicist Stephen Hawking ...

Answer 2

Uncle Petros proved Goldbach's conjecture just minutes before his death, when he was more than sixty.

Answer 3

Burnside proved the $p^aq^b$ theorem at age 53.

Answer 4

Fourier (1768 - 1830) presented his work Théorie analytique de la chaleur in 1822 at age 54.