Friday, June 22, 2007

Best mathematics book review ever!

It's possible that I'm exaggerating a bit, but today I encountered the best mathematics book review ever!

I received my new issue of Bulletin of the American Mathematical Society today and I was glancing through the issue. I browsed through the article in question (a review of a two-volume treatise by Barry Simon about orthogonal polynomials on the unit circle), thinking that I was only going to leaf through the pages in about a minute, but then I noticed lots of historical facts, personal anecdotes, and jokes in both the main text in the footnotes. This review is written in a much more colloquial and light-hearted manner than one would expect from such an article.

The first paragraph sets the article's tone nicely:

NOTE. If the reader is interested in reading a comprehensive, magnificently written, and up-to-date history of orthogonal polynomials, I recommend turning to L. Golinskii and V. Totik [8] and Totik [30]. On the other hand, if the reader wants to see a fairly detailed but not overly technical review of Barry Simon’s book, then I suggest Simon’s article [24] despite the obvious conflict of interest. End of story, or at least it seems that way. However, my editor insisted that the story must go on, which explains why I agreed to write this review, which, when compared to [8], [30], and [24], is doomed to fail.

The first sentence of the next paragraph is even more spectacular: If you are still with me, then let’s get on with the definitions.

I didn't come close to reading the whole thing cover-to-cover because there was a lot of math in between the anecdotes. I'm sure I missed many amusing moments this way, but I stll got a lot out of my 10-15 minutes. (Besides, why would I want to let technical stuff get in the way of my enjoyment.)

In one notable sequence, the author of the review solicited comments from several experts in the field and included their views of the books being reviewed. Each one of them (with one exception, as I recall) was given a footnote to identify them. One very amusing thing was that the first of these guys, Harold Widom (as in Tracy-Widom distributions and the very academically talented Widom clan) was given a footnote whose text read, "Professor Widom needs no footnote." But that wasn't even the punchline... the punchline is that Harold's first name was misspelled in the article (at least at the location in which the footnote is used). Dude!

By the way, those of you like meta- should note that this blog entry is a review of a book review.

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