If you are interested in the beauty of mathematics, you must go out and buy Robin Wilson's absolutely stunning book of mathematical stamps, a book which traces the history of mathematics through images on the postage of countries around the globe.

Why mathematics on stamps, you may wonder? After all, there are illustrations of mathematical ideas as well as portraits of mathematicians in other media. If we limit ourselves to just that mathematics which has been pictured on stamps, we cannot give a full or balanced history of mathematics. And the United States has very rarely portrayed a mathematician or a mathematical idea on its own postage stamps.

But what Robin Wilson shows us in this book is that many countries hold mathematicians in sufficiently high regard to display their images on stamps, whereupon they then appear on thousands of envelopes carrying mail from one person to another. It is then not just political figures whose names become household words. Anyone who receives or sends a letter may take some interest in learning about the accomplishments of a famous mathematician. Thus, the French learn something about Descartes, Pascal, Cauchy, and Galois; the Germans about Gauss, Leibniz, and Dedekind; the Irish about Hamilton; and the Norwegians about Abel. The Soviet Union celebrated such mathematicians as Sonya Kovalevskaya, Pafnuty Chebyshev, and Nikolai Lobachevsky, while the Belgians honored Adolphe Quetelet and Simon Stevin. Asian countries have also honored their great mathematicians: Ibn-al-Haitham appears on a Pakistani stamp; Omar Khayyam on one from Dubai; Jamshid al-Kashi on one from Iran; Zu Changzhi on a Chinese stamp; Seki Kowa on one from Japan; Ramanujan on an Indian stamp; and Mohammad ibn Musa al-Khwarizmi on a stamp from the Soviet Union (since he was probably born in the former Soviet Republic of Uzbekistan).

Naturally, many countries have also honored mathematicians from elsewhere, because their influence has been global. Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, and Isaac Newton, among others, appear on stamps of many countries. Wilson has shown but a small sample of these, including some which make some effort to represent the ideas of these great men.

Many countries in fact believe that mathematical ideas are worth presenting on stamps to teach their populations. For example, in 1971 Nicaragua issued a series of ten stamps depicting the "ten mathematical formulae that changed the face of the earth." Most of these formulas are, of course, physical formulas, such as Einstein's formula expressing the equivalence of mass and energy and Newton's law of gravitation. But these also include the Pythagorean theorem and the relationship of logarithms to exponentials. Several more sophisticated ideas have appeared explicitly on stamps, including the basic formulas for the quaternions on an Irish stamp, the factorization of an ideal as a product of prime ideals on a German stamp, and the statement of Fermat's Last Theorem on a Czech stamp.

The relationship of art and mathematics is well-recorded on stamps. Wilson includes many examples of Renaissance art illustrating the beginnings of perspective as well as examples of twentieth century art illustrating the new geometries of the nineteenth century. Similarly, we see stamps dealing with the history of computing, from one of the earliest mechanical calculating devices invented by William Shickard, through the analytical engine of Charles Babbage, the stored-program computer of John von Neumann, and the invention of the World Wide Web by Tim Berners-Lee in the 1990s.

In his book, Wilson takes a very broad view of mathematics. Thus he includes sections on such topics as Mathematical Recreations, Map-Making, Calendars, Halley's Comet, Mathematical Physics, and Metrication along with the more standard topics. In every section there is a brief survey of the topic, closely tied to the pictured stamps. These surveys can be read with pleasure by undergraduates as well as high school students with a reasonable background.

As the author notes, this book is not a "history of mathematics", although it is organized historically. It is not just a collection of beautiful images, because it does contain text explaining the stamps. And it is not a textbook, although it is a book one could easily share with students. It is just a fascinating book in which you can lose yourself for hours, one which may inspire you to go out and find new mathematical stamps (such as the recently issued French stamp honoring Fermat), and one which may convince you to write to the U.S. Stamp Advisory Board imploring them to consider putting mathematicians and mathematical ideas on U.S. stamps.

And although you may believe that it is only dead mathematicians who appear on stamps, the final stamp in this book pictures Robin Wilson himself.

Victor J. Katz (

[email protected]) has collected mathematical stamps for many years and used many of them to illustrate his textbook,

*A History of Mathematics: An Introduction* (2

^{nd} ed., Addison-Wesley, 1998). He has long been interested in the history of mathematics and its use in the classroom and has in recent years directed three NSF-funded projects dealing with these issues. In particular, the

*Historical Modules* project has developed self-contained modules showing teachers how to use the history of mathematics in teaching numerous topics in the secondary curriculum.