In his previous science book, "Archimedes to Hawking", Cliff Pickover explored the great laws of science and the lives of the physicists and chemists who discovered the laws. In the "Math Book", Pickover takes on the great moments or milestones of mathematics. While the great laws of physics were almost all named by the early twentieth century, scientific milestones continue to be established. Thus, the mathematical milestones of the "Math Book" are documented into the twenty-first century.
The publishers have provided Pickover with a challenging format. Each milestone is described on just one page, and each is accompanied by a full page image on the facing page. These limitations restrict the scope of the presentation for each subject. However, having as many as 250 milestones has allowed Pickover to expand some subject areas into more than one related milestone.
The images are absolutely beautiful. They include paintings, diagrams, photos, and computer-generated art. Among the best are a close-up photo of the game of Go, a map of the Internet as the illustration for the Konigsberg Bridges, the Gray Code using a diagram taken from a US patent, and the Archimedes Spiral as exemplified by a fiddlehead fern.
Many of the milestones cover esoteric theoretical areas of mathematical analysis. This was not my best subject in school. However, because of the latitude provided by having 250 topics to cover, Pickover is able to include more technology-related topics. He has authored many math books, for example, "Wonders of Numbers", "A Passion for Mathematics", "The Mobius Strip", and this year, an updated paperback edition of "The Loom of God." However, he is also a down-to-earth scientist. The topics in this book include such concrete subjects as the bed sheet folding problem, public key cryptography, Rubik's Cube, and my favorite, cicada-generated prime numbers. Not all milestones were charted by humans!
Is every possible milestone included? Even with 250 topics, and yes there are exactly 250, Pickover invites the submission of additional milestones. Before reading the book, I had some expectations of what topics should be covered in the milestones. Upon reading, I found that almost all of my ideas were included.
However, I do have a suggestion for an additional milestone, Legendre Polynomials. These polynomials, well-known to physicists, are used to express the form of atomic wave functions. Thus, they underlie the very fabric of matter. If you can include Bessel Functions, why not have Legendre Polynomials? There must be other milestones to suggest. Perhaps the "Math Book" can become an example of Hilbert's Grand Hotel. Even when the hotel is full, there is always room for another guest.