Mathematicians: An Outer View of the Inner World

Mathematicians, An Outer View of the Inner World, is an irresistible book. It consists of ninety-two positively stunning portraits by Mariana Cook (evidently the last pupil (or protégé) of Ansel Adams) accompanied by brief introspective essays by her subjects on the facing pages. The ninety-two subjects span the entire spectrum of the art, to use a loaded phrase, from theoretical computer science to harmonic analysis, from differential geometry to algebraic number theory.

The choice of subjects is outstanding: almost every one in the mathematical world has met or corresponded with at least some of these representative scholars, and many among the latter are household words. So it is that the personal reflections accompanying the marvelous photographic portraits more often than not come across as chats with friends or acquaintances, modulo the fact that there is certainly a general awareness that the invisible interlocutor is not a fellow mathematician. Still, it’s all “Mathematician Speak,” and all of us will feel entirely at home in the conversation.

This is much more than a coffee-table book: it’s the sort of thing that will gulp up oceans of time once the book is cracked by anyone in the field: turn the page and find another one whom you’ve heard of, or even know, and whose comments are a source of tantalizing interest, then do it again, and again… When the book arrived I intended to spend just a minute or two browsing through it: off by an order of magnitude.

So Mathematicians, An Outer View of the Inner World is bound to be a favorite in mathematical circles, and, in view of the objective fascination provided by the introspective prose of the players, also among those who interact with us mathematicians, from the members of our families to visitors from the real world resting a while in our living rooms. Put the book on your coffee table and watch what happens.

Here is a quiz:

1. Whose mother said: “If he hadn’t looked so bright, I might have been worried. He was really quite slow. He didn’t say his first sentence until he was twenty-four months old…”?
2. Who said: “I usually evade the question [of what kind of mathematician I am] by saying that I am a geometer in the broad sense, secure in the comfort that ‘God is a geometer’…”?
3. Who said: “In a sense mathematics is like the classical Chinese language --- very polished and very elegant…”?
4. Who said: “…any really good work in mathematics always has in it beauty, simplicity, exactness, and crazy ideas…”?
5. And who said this? “[T]he decisive ingredient [in my being admitted to Princeton for graduate school] turned out to be my mother’s insistence on including a large photo of her son taken as I teetered on the tip of the granite spire on North Palisade. Many years later I learned from Ed Nelson… that he was in the office with Fox when my late-arriving application was brought in. According to Ed, when Ralph tore open the envelope, the picture fluttered to the floor. Ralph picked it up and said, ‘Let’s admit this one.’ I had told my mother that it was completely inappropriate to include a picture and that they would make their decision on scholarly factors. She had been an actress and told me, ‘Everything is show business.’ On this occasion she was right.”

Answers can be found on pp. 172, 30, 38, 132, 72, respectively.

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.