By the Numbers
The Man Who Loved Only Numbers
by Paul Hoffman
My Brain Is Open
by Bruce Schechter
A Beautiful Mind
by Sylvia Nasar
In an essay entitled The Maniac, G.K. Chesterton argued that madness is not so much a deficiency of reason as an excess of it. "Imagination does not breed insanity. Exactly what does breed insanity is reason. Poets do not go mad; but chess players do. Mathematicians go mad … but creative artists very seldom."
Like many of Chesterton's seductive propositions, this one is false. If you name a mad mathematician, I will counter you with a mad poet — a Cowper for a Cantor, a John Clare for an Alan Turing, a Poe (let's include borderline melancholics) for a Pascal. During one of his episodes of insanity, the mathematician John Forbes Nash, whose story is told in A Beautiful Mind, found himself sharing a locked facility with the poet Robert Lowell; a neat counterexample (as mathematicians say) to the Chesterton hypothesis.
Nash had made brilliant advances in the mathematical Theory of Games during the 1950s. Then in 1959, at the age of 30, he suddenly lapsed into paranoid schizophrenia. This disorder is known to have a strong genetic component (Nash's younger son is also a sufferer). Ms. Nasar does not make any argument — and I do not think there is any to be made — that Nash's line of work was a factor in his collapse. To the contrary, Nash himself attributed his marvelous recovery — he seems to have returned to normality gradually through the 1980s — not to any of the faddish "treatments" he endured, but to a determined effort to think rationally, aided by some light mathematical work. In 1995 he was awarded the Nobel prize for economics. (There is no prize for mathematics, but Nash's early work had proved valuable to theoretical economists.)
Paul Erdős, the subject of The Man Who Loved Only Numbers and My Brain is Open, was not mad, merely very eccentric. A mathematician who did important work on the prime numbers, Erdős was born in 1913 (a prime number, I cannot forbear noting, both forward and backward) and died a prime number of years later in 1996 (a prime backward and upside down — although not, alas, forward). All but the first two of those years were given up to mathematics — every day, every hour. He did nothing else; he wished to do nothing else. He had no possessions, no regular job, no home, no sex life, no interests outside math. All his friends were mathematicians. When they took him to movies or concerts, he fell asleep. He never watched TV or read fiction. His letters go like this: "Am in Sydney. Next week, Budapest. Let p be any odd prime …" He never spent a second trying to acquire any more money than his very frugal lifestyle required. When larger sums of money came to him, he gave them away as prizes for solving mathematical problems.
I must say that while it is fascinating to know that such a human being can exist, and live a life longer — and probably happier — than most, Erdős is a poor subject for biography. His life was his mathematics. Once you have described the math, there is very little else to say.
It would be a shame if anyone were to conclude from reading these books that you need to be a monomaniacal nerd to excel in math, and may go barmy. In fact, the majority of mathematicians are perfectly normal. John von Neumann, possibly the greatest mathematician of this century (in his spare time he invented the computer) was quite a boulevardier, fond of women, booze and fast cars. Descartes, who algebraized geometry, was a soldier and a courtier (he survived the first, but not the second). Karl Weierstrass, creator of the modern theory of functions, spent his four years at university drinking and fighting, and left without a degree.
The book of mathematicians, like the book of poets, includes all human types. There is no case to be made against math by exhibiting its weirder specimens, any more than there is a case to be made against football by citing O.J. Simpson. I fear that the case will be made none the less. In this sense these books are mildly subversive — ammunition for the armies of Unreason. "Let no-one ignorant of geometry enter," warned the inscription at the door of Plato's Academy. Math has never since enjoyed such prominent status in the curriculum of a liberal education, and nowadays must compete for students' attention with Jacques ("the tyranny of reason") Derrida and Michel ("reason is torture") Foucault. While mountebanks like that stalk the corridors of our universities, it does not help to portray math — the purest expression of human reason — as the domain of oddities like Nash and Erdős.
Nor does it help that all three of these books contain mathematical bloopers. Ms. Nasar comes off best here, but even she makes a pig's ear of explaining the fabulous Riemann hypothesis. Mr Hoffman, in a very embarrassing passage, makes it plain he does not understand the mathematical meaning of the word "transcendental." Bruce Schechter speaks of the "graceful catenaries" of the bridges over the Danube at Budapest. The cables of a suspension bridge form parabolas, not catenaries. I don't expect my dentist to know this stuff, but the authors of books about mathematicians really should.