In 2003, David Foster Wallace wrote an account of how mathematicians have dealt with aspects of infinity throughout history for W. W. Norton & Co.’s series “Great Discoveries”. At some point I got a copy as a present, and have now read it. In 300 pages – and I doubt it was supposed to run that long, as Wallace refers to the work repeatedly as a “booklet”, he traces the history of the problem of calculating infinite and infinitesimal quantities, or calculating with them – in short, how math has dealt with the enormously huge and the incredibly tiny – from the Greek philosopher-mathematicians to the 19th century German mathematician-philosophers, with a quick nod towards 20th century math which has (in Wallace’s account) mostly succeeded in demonstrating the 19th century solutions have their own problems and forced mathematicians to figure out how to deal with that.
Wallace’s style is engaging from one sentence to the next, but the overall structure of the book ends up a bit muddled, as he attempts to present at times incredibly complicated concepts in an understandable framework. For the most part – though as a mathematician (low-grade) I may not be the best person to judge – he succeeds, though I judge the “optional” technical explanations periodically inserted would have been better maintained as integral parts of the book. The final effect is much like the legendary Japanese garden technique where a great deal of care goes into presenting a final appearance of perfect naturalness: but this by its own rules prevents other qualities of line or symmetry.
Everything and More was a good reminder for me of the puzzles and paradoxes that attract me to some of the more theoretical parts of math, though I would hardly say I understand it all. At one point, Wallace describes Leibniz – he of the calculus – as a “lawyer/diplomat/courtier/philosopher for whom math was sort of an offshoot hobby”, footnoting this description, “Surely we all hate people like this,” but I suspect Wallace himself of similar gifts, given how easily he, acknowledged mainly as a writer, converses of complicated mathematical topics. It is also evident from Wallace’s fulsome praise for the man that he had at least one great teacher, a Dr. Goris.
If you have any interest in mathematics – especially its quirks and paradoxes – and are prepared for a reading experience complete with concept-induced headaches, I’d recommend this one.