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Figured out

We don’t understand the math, but can we get the mathematicians?

By Mark Feeney
August 23, 2009

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“Figure,” as a noun, has multiple meanings. It can be a number: “I’ll write up those figures for you.” A person: “an eminent figure in the field.” A shape: “the figure of a triangle.” Those meanings intersect in Mariana Cook’s new book, “Mathematicians: An Outer View of the Inner World.” It consists of 92 black-and-white portraits of just what its title says: figures who, at the highest level of their profession, work with figures.

The idea of a collection of portraits of mathematicians seems on the face of it as irrational as the square root of two. Intellectually opaque, the practice of higher mathematics is visually null. It can be understood, at least by a few people, but that doesn’t mean it can be seen. Mathematics is like theology or poetry that way. Mathematics is a kind of poetry, actually. But poets have a long history of being photogenic. Mathematicians most emphatically do not. There has yet to be a mathematician maudit, or a Byronic mathematician (other, that is, than Byron’s daughter, Ada).

Yet there are ways in which the idea of mathematician portraits makes sense. Celebrity in this culture has long been its own justification, and some of Cook’s sitters wouldn’t look amiss as boldface names: John Nash of “A Beautiful Mind” fame; Sir Roger Penrose, the cosmologist; Benoit Mandelbrot, the father of fractal geometry (who, in fact, has a memoir coming out in October).

Nor does an argument have to be made for the intrinsic intellectual fascination of mathematics. It’s a fascination that transcends understanding - or even renders it irrelevant. If anything, mathematics’s being so esoteric to so many people can work to enhance its allure. “Conformal dynamics”? “Galois cohomology”? “Unipotent flows on quotients of Lie groups”? There’s verbal magic in such abstruseness (see, mathematics really is a kind of poetry). Precisely because we can’t glimpse the world mathematicians see, the prospect of glimpsing the faces of those who can becomes all the more intriguing.

John Horton Conway of Princeton has the shaggy, Bagginsy look of an anorak-wearing hobbit. With his moony face and high forehead, Andrei Okounkov, also of Princeton, seems so preposterously young (even though he’s 40) and very Russian. You don’t have to know that Michèle Vergne is director of research at the Centre National de la Recherche Scientifique to assume she’s French. Such cool appraising eyes, such unemphatic unflappability: Her membership in the sorority of Marguerite Duras and Simone de Beauvoir and Marguerite Yourcenar is as plain as the nose on Nicolas Sarkozy’s face.

Cook’s work extends photography’s tradition of vocational portraits. What may well be the single greatest discrete project in the history of the medium, August Sander’s “People of the 20th Century,” consists in large part of individuals presented as professional archetypes. “Irving Penn: Small Trades,” with more than 250 photographs by Penn of tradespeople, opens next month at the Getty Museum. There are numerous lesser examples: serial portraits of lifeguards, supermodels, firefighters, cowboys, soldiers, athletes, tenant farmers, and so on.

It’s pretty obvious with each of those occupations how a photographer might go about presenting them visually: tools, uniforms, workplaces, even physical types. Walker Evans’s photographs in “Let Us Now Praise Famous Men” don’t have captions. They don’t need captions. Everything about his pictures of the Gudger, Ricketts, and Woods families locates them in a socioeconomic context. Yet conveying the professional identity of a mathematician, someone whose work is so utterly interior and veiled, doesn’t faze Cook.

Sets of numerals and symbols on a board - equations, in other words - that’s about it for mathematics made visible. Cook manages the considerable feat of limiting the number of blackboards and whiteboards to four. “What’s the ontology of mathematical things?” asks Conway. (Each portrait has an accompanying autobiographical text.) “In what sense do they exist? There’s no doubt that they do exist, but you can’t poke and prod them except by thinking about them.” You can’t photograph them, either.

So what about the ontology of mathematical thinkers? Although Cook’s 92 sitters can’t necessarily be taken as a representative sample, they’re as extensive a survey as there’s likely to be. And looking at them we see a profession that largely defeats stereotyping.

Four sitters wear sweater vests, and two wear socks with sandals. But two others wear leather jackets - and one (French, bien sur) sports a pair of quite nifty socks. There’s only one pipe smoker, one bow-tie wearer, and one turtleneck wearer. Canceling out the latter, perhaps, is the turtle that can be seen crawling across a table in the portrait of Kenneth Ribet of the University of California at Berkeley.

Twenty-two of the mathematicians have beards, and two have mustaches. There are more women than you’d likely think, though: a dozen. Two of them are daughters of mathematicians with their own portrait in the book. Further evidence for a predisposition to mathematics is the presence of two sets of brothers: the Feffermans (of Princeton and the University of Chicago), and the Browders (of Princeton, Rutgers, and Brown). Their father was Earl Browder, the onetime head of the American Communist Party. Where’s Joe McCarthy when you need him: Are you now or were you ever a mathematician?

Expectations keep getting defeated. Dennis Parnell Sullivan of the City University of New York and Stony Brook University looks like Rupert Murdoch. Nicholas Michael Katz of Princeton looks like William Faulkner. Richard Ewen Borcherds of Cal-Berkeley looks like Red Sox third baseman Mike Lowell. There’s even a viscount, Pierre Deligne, of the Institute for Advanced Study, but you’d never know it to look at him.

Then again, what exactly do viscounts look like? Do they differ much in appearance from counts, for example? It’s all rather perplexing, this business of trying to infer activity from appearance. Maybe the biggest difference between mathematics and photography is just this: So much of the intellectual appeal of the former lies in its being one of the very few aspects of life in which no value derives from distinguishing appearance from reality. The two are effectively the same. That’s definitely not true of photography. Conversely, this may be the one way in which looking at photographs of mathematicians resembles doing mathematics. “I think,” Okounkov says, “mathematics requires imagination more than any other ingredient.”

Mark Feeney writes about photography for the Globe and can be reached at mfeeney@globe.com.