From the Editors

Reuben Hersh is probably the best-known proponent of social constructivism as a philosophy of mathematics, which was implicit in his two books with Philip Davis and made explicit in his own What is Mathematics, Really? His viewpoint results in his reading widely, not only philosophers of mathematics, but also sociologists, anthropologists, linguists, and others who have something to say about how mathematics develops. He tends to expand the topics generally considered part of the philosophy of mathematics. In this chapter, he explores several topics from a social constructivist viewpoint: why the existence and nature of mathematical objects are important, why it is important to study mathematical practice from a scientific perspective, and the apparent timelessness of mathematical results.

Reuben Hersh is an Emeritus Professor of Mathematics and Statistics at the University of New Mexico (www.math.unm.edu/~rhersh/). His mathematical work has been primarily in partial differential equations and random evolutions. In addition to his research work, he has written a number of expository articles, including “Non-Cantorian set theory” (with Paul J. Cohen), Scientific American (1967), “Nonstandard analysis” (with M. Davis), Scientific American (1972), “How to classify differential polynomials,” American Mathematical Monthly (1973), and “Hilbert's tenth problem” (with M. Davis), Scientific American (1973) (which won the Chauvenet prize). His two books with Philip Davis, The Mathematical Experience (1980) and Descartes' Dream (1986), explore certain questions in the philosophy of mathematics, and the role of mathematics in society.