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<title>Review: Fermat's Enigma by Simon Singh</title>
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<h1><cite>Fermat's Enigma</cite></h1>
<p class="author">by Simon Singh</p>
<div>
<div class="info"> <p class="cover"><img src="../covers/0-385-49362-2.jpg" alt="Cover image" /></p>
<table class="info">
<tr>
<td class="datahead">Publisher:</td>
<td class="data">Anchor</td>
</tr>
<tr>
<td class="datahead">Copyright:</td>
<td class="data">1997</td>
</tr>
<tr>
<td class="datahead">Printing:</td>
<td class="data">October 1998</td>
</tr>
<tr>
<td class="datahead">ISBN:</td>
<td class="data">0-385-49362-2</td>
</tr>
<tr>
<td class="datahead">Format:</td>
<td class="data">Mass market</td>
</tr>
<tr>
<td class="datahead">Pages:</td>
<td class="data">305</td>
</tr></table>
<p class="buy"><a href="http://www.powells.com/partner/28585/biblio/0-385-49362-2?p_isbn"><img src="../powells.png" alt="Buy at Powell's Books" /></a></p></div>
<div class="review"><p>
Fermat's Last Theorem is the infamous proposal that:
</p>
<blockquote><p>
<i>x<sup>n</sup> + y<sup>n</sup> = z<sup>n</sup></i>
</p></blockquote>
<p>
has no solutions for integer <i>x, y, z, n</i> and <i>n > 2</i>. It's
infamous for being very simple to state and understand, a variation on the
equation produced by the Pythagorean Theorem, but incredibly difficult to
prove. It's also infamous for Pierre de Fermat's maddening marginal note —
"I have discovered a truly marvelous demonstration of this proposition
which this margin is too narrow to contain." 350 years after Fermat wrote
this, the theorem was still unproven in the general case, although the
theorem for many specific values of <i>n</i> had since been proven.
</p>
<p>
<cite>Fermat's Enigma</cite> is a popular history of Fermat's Last Theorem and
the attempts to prove it, the partial successes and famous failures. It's
also the story of Andrew Wiles, a Princeton mathematics professor who
finally proved the theorem in a complex, brilliant proof that builds on
much of the power of modern mathematics and almost certainly did not
follow the same path that Fermat himself did. If, in fact, Fermat had
truly proven the theorem at all, something that we will probably never
know.
</p>
<p>
Singh comes to this subject with a serious structural problem: he's trying
to write a popular account that's accessible even to people who are hazy
on algebra and unfamiliar with basic proof technique, but he's trying to
tell the story of one of the most complex proofs in modern mathematics.
He tries to avoid the problem by talking about personalities instead of
mathematical details, mostly successfully. It helps that Fermat's Last
Theorem has been tackled by a collection of colorful geniuses, and even
the soft-spoken Wiles has a subtle dramatic charm. Still, he has to cover
enough of the mathematics for the reader to follow, and I found those
sections tedious and a little overdramatized. For example, I can see
using a domino analogy once to explain inductive proof, but Singh belabors
the analogy until it's painful and talks about infinite chains of infinite
dominos as if he doesn't understand that such setups are common in even
simple inductive proofs.
</p>
<p>
An excess of drama, cliche, and reptition are the largest problems with
this book. Explaining why Fermat's Last Theorem is so interesting
requires diving into areas of math that many readers have never paid
attention to, and I got the impression that Singh felt he had to create as
much drama as possible to keep people reading. Occasionally this works.
The circumstances around Wiles's proof are inherently dramatic, a great
conclusion to the story. But at times it feels forced, such as when Singh
goes on about the wonder of absolute mathematical proof and the supposedly
unique way that mathematicians are more rigorous than any other
profession. I enjoyed the bits of history and connection he uncovers and
explains despite his tone, rather than because of it. The book is based
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