On Not Reading Singh’s Fermat’s Enigma

Posted by jns on 8 May 2008

For a few days recently I was reading Simon Singh’s book, Fermat’s Enigma : The Quest to Solve the World’s Greatest Mathematical Problem (New York : Walker and Company, 1997, 315 pages). However, I stopped reading after about 80 pages.

The reason had nothing to do with the subject, which was interesting and developing reasonably well. Finding out more about Fermat, his work and his life and his time, and learning some about the man who has apparently proved Fermat’s notorious “last theorem” (Wikipedia on Fermat’s Last Theorem can fill you in on those details if you want) was all to my liking.

What was not to my liking was Singh’s writing. It was writing that was too loose, too flabby when dealing with subjects that I feel require more precision in their presentation. Writing a popular treatment about a mathematical or scientific subject is no time for technically sloppy or carelessly inaccurate prose. Writing for the scientifically or technically unsophisticated reader demands care. I’m sure you’re aware by now that this is an idée fixe for me, and for Ars Hermeneutica.

There were no major transgressions but a pile-up of minor infractions to the point that it was irritating. Let’s look at a few examples.

Mathematical theorems rely on this logical process [of proof] and once proven are true until the end of time. Mathematical proofs are absolute. To appreciate the value of such proofs they should be compared with their poor relation, the scientific proof. [p.21]

In one sense you could say that once proven mathematical theorems are true, in the sense that once proven they stayed proved. However, the sentence is sloppy and ambiguous as a result, suggesting that perhaps the theorem was not true before it was proven.

That is not the way mathematicians look at theorems and proofs, however. Theorems are seen more as emergent truths of a mathematical system, statements that have always existentially true but unknown to be true before they are discovered and their truth established by means of proof.

It’s akin to finding a rock and saying “I recognize this as a sedimentary rock, so it will henceforth be a sedimentary rock.” Most of us would look askance at such a statement with the obvious reaction: “Wasn’t it always a sedimentary rock, even before anyone saw it?”

Arguing in the author’s favor, I suspect that he didn’t mean his sentence this way; rather, he wanted to make the point that once the truth of a theorem is established by proof, that proof remains valid unless an error is discovered in the proof or some problem is discovered in the mathematical system in which the theorem and proof is embedded. However, that’s not what he wrote.

As for that bit about “their poor relation, the scientific proof”–it will take at least another entire essay for me to deal with the issues raised by that “poor relation” jibe (it doesn’t upset me that much) and the lack of understanding surrounding the reference to “scientific proof” (that does upset me quite a bit).

Together Fermat and Pascal would discover the first proofs and cast-iron certainties in probability theory, a subject that is inherently uncertain. [p. 40]

Yikes! According to the book-jacket, Mr. Singh has an advanced degree in particle physics. A great deal of experimental particle physics means looking at decay products of high-energy nuclear interactions, processes that are governed by probabilities. Exact probabilities in many cases. He should know better than to write that probability theory is “inherently uncertain.” Probability theory is a mathematical discipline with exact results, and those exact results describe processes that are inherently uncertain. To ascribe “inherent uncertainty” to a discipline whose subject is “inherent uncertainty” is naive and/or thoughtless, and does nothing here to keep the unsophisticated reader from getting confused.

Fermat’s panoply of theorems ranged from the fundamental to the simply amusing. Mathematicians rank the importance of theorems according to their impact on the rest of mathematics. [p. 66]

I simply found this statement bizarre, suggesting as it does that there are mathematicians someplace whose job it is to rank the importance of theorems to the world of mathematics. Do they have a list they check against? Where do they publish their list of theorems, ordered by importance?

Of course Mr. Singh is talking figuratively, looking for an “objective” way to describe the importance of Fermat’s theorem, but he does it again with sloppy writing that suggests something quite other than what he intended.

Instances like these kept cropping up and their irritation overwhelmed me by around page 80. I knew by then that I wouldn’t enjoy reading the book and it didn’t even seem worth the bother of finishing so that I could write a negative book note–I much prefer guiding potential readers towards good books rather than away from bad books.

Part of my professional mission, though, is to consider how we (the big “we” of those who write science for general consumption) communicate science, and how we can communicate it better. Sometimes that means looking at examples of miscommunication so that we can improve. Think of is as an engineering approach (as Henry Petroski does in his excellent books) in which failure has much to tell us about how to succeed.