The End of Error

Preface

“The purpose of mathematics is to eliminate thought.” —Philip G. Saffman (1931 – 2008)

The class laughed hard when Professor Saffman said this in a classroom lecture in 1978. The class, a third-year undergraduate course in applied math that was required for many majors at Caltech, had a well-earned reputation as being a difficult one. It certainly seemed to us at the time that mathematics was failing miserably at “eliminating thought.”

But Saffman’s observation was wise and profound.The elaborate abstract structures mathematicians build make it unnecessary to “think” about the problems they address. Once the math is done, problems can ...