A Geometer ’ s View of Space - Time

Mathematicians have always struggled with the difficulty of describing to nonmathematicians what they do. This difficulty is said to account for all sorts of ills, such as meager federal funding for mathematics research, low student interest in mathematics, and lack of appreciation for mathematics as a force in human culture. The easiest way to deal with the difficulty is to describe applications of mathematics. The hardest way is to address mathematics head-on, in all its abstractions. In his book Poetry of the Universe: A Mathematical Exploration of the Cosmos, Robert Os-serman deftly combines these two approaches in a serious yet lively work. Most people have wondered from time to time about what the universe is like outside of what we can observe from Earth, though fewer have wondered why eu-clidean space is flat and a sphere is curved. Os-serman exploits readers' natural curiosity about the universe to take them on a remarkable journey through mathematical lands unfamiliar to most. Along the way, Osserman weaves together diverse strands of cultural, scientific, and mathematical developments , each of which makes an important contribution to the exposition. The danger in this tightly organized approach is that the reader is expected to remember too many different things in order to understand the overall picture. By some sleight of hand of which the reader remains unaware, Osserman devotes to each strand just the right emphasis and just the right amount of revisiting so that the strands illuminate the story that emerges, rather than obscuring it. A number of times, when reading about a particular topic in the book, I felt as if I were following a path through a densely packed forest that, while interesting, was unrelated to the main thrust of the book. It was delightful to emerge from the path to an open vista and see that the topic had strong and important connections to ones discussed earlier. The writing style is concise and elegant, un-adorned with flashy tricks that a writer less sensitive to the beauty of the subject might be