THE GRAPES OF MATH

Forget the bad pun of the title; this is a first-rate survey of the world of mathematics by a British practitioner of the art.

Yes, there is art in doing math, an aesthetic delight in the kind of creation that leads to an aha experience at what a proof reveals. Bellos (Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math, 2010, etc.) compares it to the punch line of a joke. He begins with chapters revealing how deep-seated are our feelings about numbers: why seven is special and one is the “yang” and masculine, while two is “yin” and feminine. He follows up with an amazing finding on the abundance of numbers beginning with one or two and the paucity of higher initial digits in any stories you read in the paper but also in populations, stock prices, etc.—a phenomenon known as Benford’s Law. The author then moves on to geometry, algebra, calculus, the laws of logic and the nature of proofs, always with an eye toward showing how an esoteric discovery so often has practical applications. The beautiful, longish S segment of a curve called the clothoid turns out to be the transition path used by trains and roads when moving from a straight to a circular path to avoid jolting passengers. Sometimes the going gets tough (e.g., fractals), and Bellos advises skipping to the beginning of the next chapter, where he always starts with elementary concepts. In this way, the author leads readers by the hand through such marvels as pi and the exponential constant e, noting how often mathematicians deplored new concepts like imaginary numbers, not to mention infinity. Indeed, part of the book’s charm lies in the sketches of notables—e.g., the modest genius of Leonhard Euler, the dysfunctional Bernoulli family and the bitter Leibniz-Newton feud over who invented calculus.

Great reading for the intellectually curious.