Alistair Macintosh Wilson, a teacher and freelance writer, was formerly an international weight lifter and NASA astrophysicist. In the preface to his book, he explains that as a child, he desired to learn mathematics "as a story", but was unable to locate any books which presented the subject in that way. THE INFINITE in the finite is his attempt to satisfy his boyhood desire, and in the opinion of this reviewer, succeeds in the endeavor.
Interweaving history with legend, Wilson introduces the reader to a wealth of mathematical concepts. Combining mathematical terminology with the vernacular, formal development with informal explanation, he is able to acquaint the general reader with increasingly more sophisticated ideas, such as closure, duality, and so on. He focuses on the "why" of mathematics, whether addressing mathematics itself or the success of mathematical processes. For example, why did the Babylonians choose base sixty rather than the more natural two or ten? Chang Tsang's method certainly seems to work, but why does it work?
Throughout the book, Wilson doesn't miss the opportunity to ask "what if": Will the Euler number for a polyhedron remain the same if the polyhedron has a hole in it? He explores multiple methods for accomplishing a task, such as the construction of a right triangle, or for attempting to solve a problem. For example, he traces the "Cattle problem" of Archimedes to its ultimate solution by the Ujjaini mathematician Bhaskaracharya (AD 1114-1185), and then to the rediscovery of the solution by Lagrange in 1768. In doing so Wilson gives the reader an understanding of how different cultures contributed to the growth of mathematics. Indeed, he masterfully demonstrates how mathematics arises from problems, slowly opening the doors to the solutions of these problems by traversing history. For example, he engages the reader in attempts to solve the aha problems of the Egyptians, Babylonians, Chinese and Greeks, and then demonstrates how these problems led to the birth of algebra.
THE INFINITE in the finite introduces us to the mathematical contributions of many cultures, including the Babylonian, Greek, Egyptian, African, Indian, Chinese, and Islamic, and discusses their shared problems and methods and their innovations. The book is rich historical context for these contributions and elaborating ancients myths connected to them. Yet, it also gives modern interpretations of classical concepts, such the illustration of the golden mean in the Boeing 747 jumbo jet.
In reading this "story" of mathematics, I learned quite a bit of history, marvelled in the ancient legends, and enjoyed the comfortable environment that Wilson creates for his reader. This book is an excellent choice for a mathematics club, and for those who are interested in understanding how mathematics has developed and been applied to the problems of specific eras.
Elena Anne Marchisotto (firstname.lastname@example.org) is professor of mathematics at California State University, Northridge, and is co-author (with Philip Davis and Reuben Hersh) of The Mathematical Experience, Study Edition.