Editors' Note: This essay was reprinted in the Magazine from the Proceedings of the International Congress of Mathematicians (American Mathematical Society, 1987), the congress held in Berkeley, California, 1986.

An undergraduate in mathematics at the University of Chicago, Grabiner went on to take her PhD at Harvard in the history of mathematics. Her books, The Calculus as Algebra/J. L. Lagrange 1736–1813 (Garland, 1990) and The Origins of Cauchy's Rigorous Calculus (MIT, 1981), are among the growing number of pieces she has written on the development of analytic geometry and calculus, with journal articles on Descartes, Fermat, Lagrange, Maclaurin, Weierstrass, and Cauchy. For her paper delivered at the Berkeley Congress she was awarded the Carl B. Allendoerfer Award by the MAA in 1989. This she added to her two other Allendoerfer Awards (1984, 1996) and her two Lester R. Ford Awards (1984, 1998). She has been given more awards for expository writing by the MAA than any other author.

Grabiner is the Flora Sanborn Pitzer Professor of Mathematics at Pitzer College, one of the Claremont colleges in California.

Introduction

Since this paper was first given to educators, let me start with a classroom experience. It happened in a course in which my students had read some of Euclid's Elements of Geometry. A student, a social science major, said to me, “I never realized mathematics was like this. Why, it's like philosophy!” That is no accident, for philosophy is like mathematics.