What is mathematics and what should it be?

Abstract

In the classic “The Mathematical Experience,” Reuben Hersh and Philip Davis gave a fresh look at mathematics and mathematicians and showed us that notwithstanding Plato and Hilbert, mathematics is a human activity and culture and its pretensions to absolute truth are unfounded. Mathematics is what mathematicians do!. This leitmotif was further expanded in the wonderful “sequel” Descartes’ Dream: The World According to Mathematics, also with Davis, and the more philosophical “What Is Mathematics, Really?", written by Reuben all by himself. The fact that mathematics is what (human) mathematicians do is further expounded, beautifully, in Loving and Hating Mathematics, written in collaboration with Vera John-Steiner, that, inter alia, debunks G.H. Hardy’s stupid quip that “Mathematics is a young men’s game,” by describing many excellent women mathematicians and many excellent “old” mathematicians.