Popular Science Review - Everything and More

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Review - Everything and More: a compact history of ∞ - David Foster Wallace

This is probably the strangest popular science book ever. Written by a novelist who is more used to obscuring the facts than presenting them, it's a roller-coaster experience of frustration and occasional enlightenment. Unfortunately, as with the roller-coaster ride, the experience is not everyone's idea of fun.

Although it's over 300 pages long Foster Wallace insists on referring to it as a booklet (I'd hate to see his idea of a long book). It's supposedly aimed at the non-technical reader, but unfortunately it doesn't make much sense without the parts that are really only comprehensible to a graduate student.

It's not a timeline oriented book, which is fine, linking instead by concept. Perhaps the strongest aspects are the often overlooked aspects of the way that calculus was taken from being the fudge that Newton and Leibniz created (that so upset philosopher and bishop George Berkeley) to rigorous work, thanks to the contribution of Dedekind and Weierstrass.

Foster Wallace comes down heavily on poor Aristotle, who deserves better than the slating he gets as 'the villain of our whole Story', and is also unfairly dismissive of Non Standard Analysis, the mathematics of the vanishingly small devised by Abraham Robinson in the 1960s.

Perhaps most irritating is the way the author peppers the text with so many unnecessary abbreviations that it seems more like a set of undergraduate lecture notes than a readable book. There are indubitably some good parts to this book, but the reader requires plenty of patience to work through the affectations of the style.

Also in paperback (June 2005):

Reviewed by Brian Clegg

Reader's comment (Melissa, Australia):

I couldn't agree with you more about the lack of readability of this book but what really annoyed me was the mathematical mistakes made by the author. It would be impossible for anyone to understand his description of limit concepts because he is quite frequently plain wrong. As a mathematician myself it frustrates me to see my subject presented in such a sloppy way, it is obvious he made no effort to check his proofs as any mathematics major would be able to correct him.

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