Infinite Ascent

July 11, 2005
No one knows for sure when mathematics went from being a functional system for keeping track of sheep to a philosophical system that transcended the objects it counted, but as well-known science writer Berlinski (Tour of the Calculus
) tells readers, around 500 B.C. Pythagoras elevated mathematics into a religion. It has kept its near-mystical status ever since. (Even students instructed in its arcane languages can only gape at how numbers dictated where missing elementary particles like positrons and quarks were to be found.). Readers may have heard of the short-lived Évariste Galois, killed in a duel over a woman, but here they will come to understand his importance to group theory, his thoughts scribbled down the night before his death. Non-Euclidean geometry led to Einstein's universe, and Berlinski introduces us to the German scientists who opened the door to multiverses: Gauss, Cantor and Riemann. Finally, we encounter Kurt Gödel, who threw the acolytes of mathematics into a panic with his incompleteness theorem. Readers will need to remember some of their high school math to benefit from Berlinski's discussions of calculus and complex numbers, but his engaging style should attract many readers, science buffs and generalists alike to this excellent entry in Modern Library's Chronicles series.