A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. ↗
I don't feel any different than I did when I was 40. But I realize mathematically, I'm equidistant between that and 80. I'll keep doing this for a while, but I'm not going to be one of these people who hang on just for the sake of being on the air. ↗
For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics? ↗