## Joining the Delights of Reading and the Fascinations of Math

Fermat's Enigma

by Simon Singh

My Brain Is Open

by Bruce Schechter

The Man Who Loved Only Numbers

by Paul Hoffman

Men of Mathematics

by E.T. Bell

History of Pi

by Peter Beckmann

e: The Story of a Number

by Eli Maor

The Nothing That Is

by Robert Kaplan

An Imaginary Tale

by Paul Nahin

The Penguin Dictionary of Curious and Interesting Numbers

by David Wells

What Is Mathematics, Really?

by Reuben Hersh

The Night is Large

by Martin Gardner

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John Kenneth Galbraith remarks in one of his books that if you've ever worked on a farm nothing else ever seems
like work. Those of us who
have studied mathematics at university level can make a similar claim. If you've ever grappled with advanced math, the
study of other subjects
seems like a joke. How we used to scoff at friends pursuing subjects like English! "What, they're giving you a
degree just for *reading
novels*? Hooo-hooo!" And it was a stock comment among math students whose girlfriends were non-mathematicians
that when we went to their
rooms we browsed their books; but when they came to our rooms they *never* tried to browse our books. The study
of higher math makes you a
terrible intellectual snob.

My own math snobbery, though I shall not deny its existence, was softened and muted by the awareness that I am
no good as a mathematician. I
loved the subject, and still love it; but alas, it is an unrequited love. I hit the wall with a topic called Functional
Analysis, of which let it
be sufficient to say that if you feel fairly sure that three dimensions of space are quite enough for anyone to cope
with and four dimensions a
concept properly belonging to the realm of science fiction, try developing theorems in a space with an *infinite
number* of dimensions. Yet
still I cannot shake off the old affection. I love to browse my college textbooks and am a keen consumer of books about
math aimed at a general
readership, of which there is something of a flurry at the moment.

I think it started with Andrew Wiles's proof of Fermat's last theorem, which made newspaper headlines in 1993.
(It later turned out that the
proof was flawed; but Wiles fixed the flaw, and the theorem can now be taken as definitively proved, after 360 years of
concentrated effort by the
best minds on the planet. You think math is hard? You don't know the half of it.) Simon Singh wrote the whole business
up in *Fermat's
Enigma*, which attained the well-nigh oxymoronic status of a math bestseller two years ago. Singh's history was a
bit wobbly — he
had the Dark Ages ending in the seventeenth century — but his math was excellent and it was refreshing to
see my old flame on the
bestseller lists.

At about the same time the death of the number theoretician Paul Erdős occasioned no less than two
biographies: Bruce Schechter's *My
Brain Is Open* and Paul Hoffman's *The Man Who Loved Only Numbers*, both published last year. I thought at
the time that this was a bit
over the top for a man to whom pretty well nothing happened, who had no interests whatever outside math, who fell
asleep when not in the company of
mathematicians and whose most intimate letters went like this: "Am in Sydney. Next week Budapest. Let *p*
be any odd
prime …" Neither
of the authors was very sure-footed with math, either. Hoffman betrayed a gross misunderstanding of the concept
"transcendental number"
while Schechter thought the cables of a suspension bridge form catenaries. Really! Still, either book (I cannot see who
would need to read
*both*) is worthwhile as a portrait of the extremes of human oddity.

Anyone who executes the biography of a mathematician labors in the shadow of E.T. Bell's 1937 classic *Men of
Mathematics* . I have
mislaid two or three copies of this book on my travels but always ended up buying a new one. For any person who wishes
to have any acquaintance
whatsoever with the Queen of the Sciences, Bell is simply indispensable. He not only knew his math, he succeeded in
what I, having mixed a good
deal with mathematicians, would have thought an impossible task: he humanizes his subjects. There is, for example, the
heartbreaking story of
Évariste Galois. Challenged to a duel, Galois sat up through the night before the encounter:

All night … he had spent the fleeting hours feverishly dashing off his scientific last will and testament, writing against time to glean a few of the great things in his teeming mind before the death which he foresaw could overtake him. Time after time he broke off to scribble in the margin "I have not time; I have not time," and passed on to the next frantically scrawled outline. What he wrote in those desperate last hours before the dawn will keep generations of mathematicians busy for hundreds of years.

He was killed in the duel, of course, and — as Bell remarks, barely restraining his own feelings, "buried like a dog."

Still, as interesting as biographies of mere human beings can be, there is nothing to beat biographies of
*numbers*. I possess three
of these: Peter Beckmann's *History of Pi*, Eli Maor's *e: The Story of a Number*, and — in an
advance copy from the
publishers, who will have the book out this fall — Robert Kaplan's *The Nothing That Is*, subtitled
*A Natural History of
Zero*. The first of these is not as much fun to read as it should be; the second is very nearly a
textbook — masses of footnotes;
the third I can recommend on content, though not on style. Still making its leisurely way to my door from Amazon.com
(what exactly does
"usually ships in 24 hours" *mean*, Mr. Bezos?) is Paul Nahin's *An Imaginary Tale*, which
tells the story of
*i*, the mathematical symbol for the square root of minus one.

For a more, shall we say, *social* approach to the secret lives of numbers, a must-buy for anyone who
has, or wants to acquire, a
feeling for the little devils is David Wells's *The Penguin Dictionary of Curious and Interesting Numbers* . You
might not think there is
anything very curious or interesting about 371, or 5282, or 111,777; but Mr. Wells will set you straight. (371 equals
the sum of the cubes of its
digits; 5282 is the number of ways you can place 8 non-attacking rooks on a chessboard; 111,777 is "the least
integer not nameable in fewer
than nineteen syllables," a famous paradox — count the syllables in that description.)

Math is not all numbers, of course. Since the time of Pythagoras twenty-five hundred years ago, math has played
a part in deeper
speculations about meaning, natural laws, and the structure of "reality" (one of the few words, said Vladimir
Nabokov, that mean nothing
without quotes). The best recent venture into this territory has been Reuben Hersh's *What Is Mathematics,
Really?* Well, what is it? What,
exactly, is the status of mathematical truths? Do they exist out there somewhere, waiting for us to discover them by
painstaking inquiry, or
stumble upon by chance, or seize by a sudden flash of insight? Or are mathematical truths mere social entities, like
marriages, sonatas or
declarations of war, which would not exist if there were no human beings? Suppose there *were* no human beings:
would two plus two still be
equal to four? Hersh covers the whole territory very readably and offers a clear conclusion. I do not myself agree with
that conclusion; but Hersh
is one of those writers who forces you to take out your most fundamental assumptions and examine them carefully.

And then, of course, there is Martin Gardner. Having brought up the name I had better stop right here, or I
shall fill the *Globe*
with praises of this brilliant and prolific writer, who for many years kept *Scientific American* on my
subscription list (it has since
fallen off) with his "Mathematical Games" column. As well as having done more for mathematics than any human
being alive, Mr. Gardner is,
I can personally attest, an outstanding specimen of that near-extinct species, the American gentleman. Yes, yes, I
shall stop … just buy
Gardner's book of essays *The Night is Large* and encounter one of the most interesting minds of our age.