1089 and All That - A Journey into Mathematics

Rating:
Summary: Short is beautiful
Review: This is a delightful short book, not just about mathematics, but actually doing it. Each of the 16 chapters touches on a well-chosen piece of important mathematics. The coverage is broad (in math terms: number theory, algebra, geometry, combinatorics, proof, topology, calculus, differential equations, chaos and catastrophy, and applications as well). The many (black and white) illustrations (including cartoons) make for fast reading, and before you know it, you have finished another chapter. There are numerous connections between chapters.

The book has no preface or introduction; you just jump in. (The library copy that I borrowed had lost its dust jacket, and I looked in vain for an explanation of the "purpose" of the book. Why did the author write it? But once I started reading, that question quickly turned out to be irrelevant.) The single page of references for further reading is well chosen. The index spans almost four pages. The typography and layout are beyond reproach. The writing style is concise, informative, precise, inviting, and certainly not dry (reflective and historic tidbits are interspersed).

Some minor comments. (1) The (algebraic) explanation of the 1089 number trick does not mention the role of the requirement (which is mentioned) that the first and last digit of the starting number need to differ 2 or more. (2) The reader needs the ability to deal with formulae involving variables, including raising to a power, and ellipses (... to denote infinite series). I don't think this is a limitation for the seriously interested reader. (3) The book is somewhat biased towards "continuous" mathematics, rather than "discrete" mathematics. This is easily explained by the author's background, and again I didn't find it a limitation. My background is more in "discrete" than "continuous" math. I did learn a few new things from the book, such as Malfatti's circles-in-triangle problem, Kakeya's unsolvable needle-turning problem, and the upside-down pendulum theorem. (These may seem strange to you to include in a short math book, but they serve their purpose well.)

In such a short book it is very difficult to please everyone. The author has done a wonderful job. Everyone should know at least this much (about) mathematics.