The Saga of Mathematics: A Brief History

My first reason for picking The Saga of Mathematics off the shelf was that it looked "different". I personally have a soft spot for paperback books, since I believe that good mathematics should be concise, well organized, and affordable. Lewinter and Widulski's book satisfies all these attributes.

The book presents a brief history of mathematics and is directed at non-majors, or, as the authors put it, even "math-phobics". As such, it only covers a few topics, all of them in the mainstream of mathematical discovery, such as: ancient numeration systems, Pythagorean theorem, irrationality of the square root of 2, the Euclidean algorithm, the quadratic equation, the derivative, planetary motion, graphs and trees, non-euclidean geometries, binary arithmetic — just to name a few. The exposition is remarkably clear, and it contains an impressive number of proofs. What impressed me is that the proofs are all disguised as gentle explanations, and are very readable, even by people with no mathematical background, yet they are mathematically rigorous. In addition, the material is well researched, and every section of the book ends with a carefully chosen list of "suggested further readings". Numerous exercises at the end of each sections, and connections with music, science and general history make it suitable as a text for a liberal arts mathematics course.

The main competition for the Saga of Mathematics as a textbook are the new books directed at liberal arts majors which include modern topics, such as: consumer mathematics, voting and apportionment, fractals, etc. Lewinter and Widulski's book is unique in the category of "history of mathematics for liberal arts students", and comparing it to any of the books in the modern category would be like comparing apples and oranges. Although they are all directed towards the same audience, one teaches about the past, while the others are trying to show some of the future directions of mathematical research. It would be of great benefit for students to be engaged in a two-course sequence that would offer a sample of each.

How does the Saga compare to other brief history of mathematics books? Two recent such books were brought to my attention. The Story of Mathematics, by Richard Mankiewicz is a beautiful book, one that might be called a math "coffee table" book. It has beautiful color pictures, lots of historical quotes and reproductions, and it is printed on album quality glossy paper. This is a book for the lover of mathematics who wants to enjoy some of its history. It is very accessible, but it is not a textbook. In contrast, Math Through the Ages: A Gentle History for Teachers and Others, by William Berlinghoff and Fernando Gouvêa, is structured with math teachers in mind as its main audience. The book invites further exploration of the various chapters in mathematics through its structure: it starts with an overview of the history of mathematics, accomplished in roughly 60 pages, followed by 25 mathematical capsules. The capsules could be easily read independently, and placed in a timeline with the help of the overview. Unlike these books, the Saga of Mathematics is written for the "math hater", who will probably not read another book in the future, unless forced to do so. It has the least amount of information, and it looks more like a textbook, although a very short and unusually readable one.

Last, but not least, I have to say a few words about the presentation of the book. The Saga of Mathematics is written with humor, and illustrated with very good graphics, some of which are mathematical in nature, while others are just funny. As a reader, you will either love or hate the authors' sense of humor — it is certainly not middle-of-the-road, nor is it politically correct. Let me give a few quotes as samples:

• "The Babylonians used instead the sexagesimal system because they chose 60 as their base. While we are not sure why, we are fairly certain they did not have 60 fingers." — p.25

• "It was common belief that Christ would return to earth in the year 1000. As you probably are aware, he didn't." — p.109

• "In the 1100 in Paris, an innovative experiment was brewing¹." And then the footnote: "¹No, not beer — the monks preferred champagne." — p.125

This is an excellent book for the student with no mathematical background who wants to know the highlights of what mathematics was about in the last few thousand years and understand how it works.

Ioana Mihaila (imihaila@csupomona.edu) is Assistant Professor of Mathematics at Cal Poly Pomona. Her research area is analysis, and she is interested in mathematics competitions.