on June 17, 2012
This Wealth of Numbers is a compilation of one hundred texts on mathematics for the general audience, à la Martin Gardner but starting in 1481! Very few well-known authors in this compilation, apart from Voltaire, Euler, Carroll, Pólya, van der Waerden, Shaw, Rademacher, Toeplitz. and Feynman... I must acknowledge I did not read each entry in detail over breakfast, either by laziness about the old English style or because the topic was not of direct interest to me. This leads me to wonder who would appreciate the book. The styles and contents are quite mixed, from puzzles to historical entries, to older and newer ways of introducing basic notions, to science-fiction (for the very last entry) [if not Anathem!]... A linear reader, going from page 1 to page 365, must thus be quite open-minded if this reader does not want to skip anything. The book can however be seen as a terrific source for short illustrations in talks and classes. (The only missing feature is that a critical assessment of the texts, so that readers could be warned about mistakes and misconceptions of the writers.)
A few gems I appreciated: the wrong resolution of a probability problem by (the highly obscure) L. Despiau in 1801 (page 19); from a contemporary of Bayes, Banson's 1760 way of extracting square roots (page 46); Wells' 1714 limpid introduction to trigonometry (page 94) that reminded me very much of the way my daughter was taught the same a few weeks ago; Ball's 1892 reproduction of Kempe's false proof of the four-colour theorem (page 118); a 1561 entry on maritime maps by Martin Cortés, son of the conquistador Hernán Cortés (pages 153-154); Patridge's 1648 description of Napier's "speaking rods" (also known as "Napier's bones", page 157) that reminded me of my slide rule in high school (that I learned to use the year before the pocket calculator was allowed at exams, just like the pinched cards I had to handle the year before terminals got accessible in my statistics graduate school!); Voltaire's amazing 1733 eulogy of Newton, against Leibniz and Bernoulli (page 178); Eicholz' and O'Daffer's 1964 explanation of set theory axioms within the "New Math" pedagogy, just a few years before I learned them in primary school (pages 278-281); LOGO programming on the Spectrum 48K (!) by Gascoigne in 1985 (pages 282-289), quite in tune with the LISP and ADA programing languages my wife was learning at the time, while I stuck to Pascal...; Playfair's 1798 chart of exchange balance between England and Ireland (page 306); Richard Feynman's very honest acknowledgement of the primacy of mathematics, even though he wished it could be different (pages 320-321). I am sure other readers would find at least as much entries, if not necessarily the same ones, to their taste.