Paul Halmos: In His Own Words

Abstract

Paul Halmos died on October 2, 2006, at the age of 90. After his death, many people wrote about his career and praised both his mathematical and his expository skills. Paul would have complained about that: He often said he could smell great mathematicians, and he himself was not one of them.

But he was wrong. He was a master of mathematics in multiple ways, and he influenced mathematicians and mathematical culture throughout his career. Unlike most other master mathematicians, Paul’s legacy was not merely mathematics but rather advice and opinion about mathematical life—writing, publishing, speaking, research, or even thinking about mathematics. Paul wrote about each of these topics with an extraordinary mixture of conviction and humility. Mathematicians paid attention to what he wrote, and they often quoted it (and still do—“every talk ought to have one proof” ). They disagreed and frequently wrote rebuttals. They passed along his wisdom to their students, who passed it along to theirs. Paul Halmos’s writing affected the professional lives of nearly every mathematician in the latter half of the twentieth century, and it will continue to influence the profession for years to come.

How does one write about great writing? Explanations of great exposition always fall flat, like analyses of great poems or elucidations of famous paintings. Art is best exhibited, not explained.

And so here is a collection of excerpts from the writing of Paul Halmos, giving advice, offering opinions, or merely contemplating life as a mathematician—all in his own words.

This article first appeared in Notices of the AMS, 54 (2007), 1136–1144. Reprinted with permission.