PROFESSOR STEWART’S INCREDIBLE NUMBERS

The erudite British math professor revels in the wonders of numbers.

Stewart (Emeritus, Mathematics/Univ. of Warwick; The Mathematics of Life, 2011, etc.) adopts the framework of the chapters as subjects to elucidate the charms of the digits one to 10, adding separate chapters for special numbers including zero, negative numbers, rationals and irrationals, pi, e, the imaginary number i (the square root of minus 1) and so on. For each, the author provides historical context—e.g., many 19th-century mathematicians found the notion of infinity abhorrent. Stewart’s approach works well early on, giving a nice sense of how math has evolved to ever larger number systems that have many applications beyond pure mathematics. However, Stewart tells about the remarkable findings of great mathematicians rather than showing how they were obtained. This is partly because the proofs involved are too complex or technical, requiring some knowledge of calculus or complex numbers. Yet even in simpler cases where Stewart shows steps in a proof, his explanations are terse and may assume too much on the part of readers. (On the other hand, he is expansive in giving the names and dates of those who carried out calculations of the square root of 2 or pi to a zillion places.) The degree of sophistication grows in the latter half of the text, as Stewart discourses on fractals, musical scales, packing problems, Rubik’s cubes, string theory and encryption, including an analysis of the celebrated German enigma code of World War II. The topics defy any logical sequence, so a discussion of wallpaper patterns can be followed by the famous birthday problem in which it turns out that the probability of two people in a group having the same birthday is greater than 50 percent in a group as small as 23 people.

Stewart receives an A for telling us how vast, wonderful and useful are all the members of the world of numbers but a lower grade for his explanation of the whys and wherefores.