Books: None of it quite adds up

A Beautiful Mind

by Sylvia Nasar Faber pounds 17.99

Some time during the last 12 months, algebra became cooler than alcopops. Good Will Hunting made quadratic equations sexy, and Simon Singh's Fermat's Last Theorem ensured that no dinner party was complete without a name-check for the Taniyama-Shimura conjecture. Sylvia Nasar's - a biography of the Nobel prize-winning mathematician John Nash - rides this Zeitgeisty tide.

Nash was born in Bluefield, West Virginia in 1928. A brilliant but unspeakably arrogant young man, he had reinvented game theory by the age of 21, and was subsequently recruited by RAND, the US government's top-secret Cold War think-tank. But by his thirties, he had been diagnosed as schizophrenic, and his delusions rapidly overwhelmed his life. Abandoning legitimate research, he became absorbed in numerological calculations, chalking up his conclusions about "Krypto-Zionist conspiracies" on the blackboards of Princeton. "Mao Tse-tung's Bar Mitzvah was 13 years, 13 months and 13 days after Brezhnev's circumcision," he once announced.

He spent the next three decades decoding messages from aliens, which he believed were communicating with him via the pages of The New York Times. By 1995, he was all but forgotten by the academic establishment - though his early ideas continued to exert a powerful influence upon the work of economists and mathematicians. Then two remarkable events occurred - he was awarded a Nobel prize, and his schizophrenia went into remission. Today, he is back at work, lecturing on the international circuit and pursuing his research. He spends his spare time playing chess and watching repeats of Doctor Who.

Nasar's book offers a calculatingly attractive mixture of madness, genius and maths-for-bluffers. It gives the lay person a summary of some important theories, and so helps assuage that anxiety of ignorance on which books like Fermat's Last Theorem have depended for their success. But it also satisfies the gut suspicion that anyone who can understand partial differential relations must pay the price with some crippling emotional or social dysfunction. And dysfunctional is too tired a word to characterise the savage eccentricities in Nash's personality. Before his years of madness, Nash was so strange that even other mathematicians considered him odd. More than odd, in fact. Unremittingly obnoxious would be nearer the mark.

Nasar's attitude to this obnoxiousness is one of the central difficulties of her book. As she accumulates carefully footnoted anecdotes of his cruelty, selfishness and bombast, its title seems less and less efficacious. She details trivial matters like Nash's attempts to creep up on pigeons and kick them, and serious ones such as his efforts to evade responsibility for his first child and its mother.

Even in the chapter dealing with his life today, there seems to be plenty of boorishness left in his character. Nasar's sympathy for Nash is attractive and infectious, but it also encourages an equivocation that mars some of her insights into the relationship between his life and work.

For instance, she is wary of drawing conclusions about one of Nash's strongest character traits, his predilection for nasty pranks. An academic colleague, Martin Shubik, recalls that "Nash's idea of a joke was to unscrew the electric light bulb in the bathroom. There was a glass shade under the bulb, which he filled with water. Did he intend to electrocute me? I'm not sure that he didn't intend to." Perhaps he did. As a boy, Nash had tried to persuade his sister to sit in a rocking chair to which he had attached live electric wires.

Nasar insists on the separateness of Nash's life and work, offering the brilliance of the latter as compensation for the shabbiness of the former. However, her own evidence indicates that his contributions to game theory and his practical joking share a common theme: how do you get one over on the other guy? This one-upmanship seems to have extended to all areas of his life. Nash's first girlfriend complains about how he always wanted "something for nothing". And he clearly took delight in humiliating his students. "His ideas about the classroom had more to do with playing mind games than pedagogy," writes Nasar. But she doesn't want to pollute the purity of Nash's mathematical achievements by suggesting that they were an abstraction of his bullying. Or at least she doesn't want to be seen to be making the connection.

Perhaps for similar reasons, she employs a similar subtlety when dealing with her subject's sexuality and politics. She draws no conclusions about his participation in Cold War strategy - despite the disturbing fact that his contributions to game theory were formulated in the context of outwitting the Russians in a putative nuclear war. She is equally unjudgemental when describing how Nash would use mathematical arguments to justify his perversely right-wing opinions. (He once told a class of undergraduates that American citizens' voting rights should be made proportional to their income.) We are also told he believed that miscegenation would result in the "deterioration of the racial line". So did he have some more sinister eugenic opinions that Nasar does not want to divulge?

She is even more equivocal about his sexuality: she relates how he formed a series of "emotional attachments" to other male graduate students. Lloyd Shapley, a fellow mathematician with whom Nash was once intimate (and with whom he spent many evenings playing a logic game called "Fuck your Buddy") now denies that they were ever close friends.

Nasar details Nash's sexual relationships with women (the book is dedicated to his wife, Alicia Larde Nash), but she also devotes much attention to his dismissal from RAND, which followed his arrest on indecent-exposure charges in a gay cottage on Muscle Beach.

The word "bisexual" is conspicuous by its absence from her book. Is she vague out of consideration for Nash and his family? Impossible to say. But there are certainly absences and elisions in this biography, and a strong sense that Nasar has omitted several terms from the equation of Nash's life. Those with an algebraic turn of mind may, however, be able to calculate the missing values.