By the
Numbers
The Man Who Loved Only Numbers
By Paul Hoffman
Hyperion; 306 pp. $22.95
My Brain is Open
By Bruce Schechter
Simon & Schuster; 226 pp. $25.00
A Beautiful Mind
By Sylvia Nasar
Simon & Schuster; 466 pp. $25.00
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 Erdös, 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, Erdös 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-- though 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, Erdös 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 Erdös.
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. |