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.

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