In his controversial book, "What is Mathematics, Really?" (Oxford University Press, 1997) Reuben Hersh argues that mathematics must be understood as a social phenomenon, as part of human culture. To this end, he proposes a philosophy of mathematics which he calls humanist, as opposed to the "mainstream" philosophies of Platonism, formalism, and intuitionism. The humanist philosophy is to be based on the actual practice of mathematicians. I will discuss Hersh's ideas (as well as those of some other writers, such as Paul Ernest, Penelope Maddy, and Saunders MacLane.) Among the topics considered are that of proof, intuition, the changing nature of mathematical concepts, and the question of whether mathematics is invented or discovered.

Joseph Auslander received his Ph.D. in Mathematics from the University of Pennsylvania in 1957, and has been at Maryland since 1962. His mathematical research is in the area of dynamical systems, in particular the abstract theory of topological dynamics. He is the author of the research monograph "Minimal flows and their extensions."

Professor Auslander is a member of the CHPS advisory board. His review of the above mentioned book of Reuben Hersh is to appear in the SIAM Review.

Fall 1999