Mathematics is an ancient discipline, and it persists, and will continue to persist, in a changing world. But as a discipline it is also facing many challenges. At one time, mathematics was a natural choice of university and college study for many serious students. Now there is a vast range of studies and disciplines whose more immediate relationship to society, and the perceived rewards that accompany that immediacy, make mathematics a less natural choice. At the same time, mathematical techniques are permeating more and more disciplines and becoming more essential to those disciplines. This often occurs at the expense of a deeper understanding of mathematics, and at the expense of the precision, clarity of thought, and recognition of complexity that mathematics provides.

I had the pleasure of reading an early draft of this fine book. It reflects the author's desire to make mathematics accessible to a wide audience, without sacrificing the beauty and precision that characterizes the field—an excellent addition to the Carus Monograph Series. At its most exciting, mathematics reveals an order, and surprising connections and relationships, often where one may be least expecting them. And yet, it expresses that order, and the unexpected connections, in a very precise and unambiguous way, supported by arguments that carry conviction and are, with effort, universally recognizable. That is possibly what Max Dehn meant when he said that mathematics was the only subject that could be presented in an entirely undogmatic way.