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.

November 15, 2005
A mathematician, lecturer, and essayist (A Tour of the Calculus), Berlinski offers an imaginative and readable romp through the history of mathematics. To help lay readers understand abstract mathematical ideas, he embeds discussions of these major conceptsNumber, Proof, Groups, Sets, etc.into ten engaging and highly approachable chapters. Within each chapter, the author follows the concept through time, weaving into the narrative lively anecdotes or observations about the primary characters involved. Thus, we learn that Euclid moves directly into his argument without preliminaries and that Galois lost his life at the age of 20 in a duel over a ladys honor. Berlinski renders the history of mathematics a great human story that has shaped our world. His brief, accessible account is appropriate for academic and large public libraries. (Index not seen.)Barbarly Korper McConnell, California State Univ. Lib., Fullerton

Copyright 2005 Library Journal, LLC Used with permission.

September 15, 2005
Mathematicians are people, too, and come in all types: mystics such as Pythagoras, misanthropes like Newton. Along with Euclid, Descartes, Leibniz, Euler, Gauss, Galois, Riemann, Cantor, and Godel, they animate Berlinski's lively history of the least popular school subject. Yet even solid-C survivors of geometry can recall math's rhapsodic allure in a problem solved or a window opened on some cosmic truth, such as Euclid's axiom that through a point off a line, there passes only one line parallel to the other line. Alas, as Berlinski archly elaborates, this self-evident idea bugged centuries of mathematicians doubtful about its validity, as have many things in math ever since Pythagoras freaked out about irrational numbers. Berlinski has a light but incisive style by which he conveys the inner turmoil and triumph, or tragedy in the case of 20-year-old Evariste Galois, who invented group theory the night before he was killed in an 1832 duel, an invention marking the greatest discoveries in mathematical history. Subtly instilling the interconnectedness of the specific concepts, Berlinski releases math from its textbook script and restores its majestic drama.(Reprinted with permission of Booklist, copyright 2005, American Library Association.)