Donald Coxeter (1907-2003) was a world-class mathematician, described by many as “the greatest geometer of the twentieth century”. This book chronicles his life and his work in a highly interesting and appealing fashion. The first two thirds of the book chronicles Coxeter’s life, from his early childhood interests to his studies and work at Cambridge, then to Princeton, and finally to Toronto. Roberts weaves a rich narrative of Coxeter’s life and his contributions to mathematics, peppering it with mathematical and historical tidbits, and also revealing the quirks and idiosyncrasies that humanize a talented and creative man. It is interesting to read anecdotes about the notable mathematicians and others with whom Coxeter worked or knew: Albert Einstein, Buckminster Fuller, G. H. Hardy, M. C. Escher, Benoit Mandelbrot, Paul Erdös, and Douglas Hofstadter, among others. The author gives an overview of twentieth century geometry, including a chapter on the Bourbaki, and she notes the difficulties Coxeter encountered being a classical geometer at this time. In fact, she credits him as almost single-handedly saving the tradition of classical geometry. The second part of the book discusses the applications of Coxeter’s mathematics, as well as works influenced by it: geodesic domes, modems, computer science, protein folding, zeolites, the structure of carbon 60 (C60), Escher’s “Circle Limits” and other works of art, to name a few. Future possible applications are discussed in the latter chapters. The mathematics itself is not too difficult for a reader with a secondary mathematics background and for those interested, seven appendices and extensive endnotes give more details. This is not a short book, but it is very intriguing, informative and enjoyable to read.

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