The King of Infinite Space

I have been reading Siobhan Roberts’s splendid King of Infinite Space, a biography of the geometer Donald Coxeter. Here is a quotation by John Horton Conway from the front leaf of the book.

Many mathematicians the world-over were enchanted with the beauty and elegance of Donald Coxeter’s work. Although I never studied with Coxeter, in many ways I consider myself an honorary student of this great geometer. Why is it that Coxeter is affectionately remembered by so many mathematicians? Siobhan Roberts makes the answer quite clear in King of Infinite Space, an elegant biography of an elegant man.

Roberts also provides an interesting background to Twentieth Century mathematics. Coxeter kept alive the visual in mathematics as opposed to trends toward excessive formalism.

Coxeter wrote some of the best math textbooks of all time. I first ran into his Introduction to Geometry while browsing in a library in Iowa shortly after I left college. The book contains a bumper crop of ideas and results. I grew tired of checking out the book from libraries and bought a copy for myself. The book is one of the best purchases I ever made. The book starts with concepts from high school geometry and ends with differential geometry and four-dimensional space.

Roberts’s biography is first rate. You do not need to be a math whiz to appreciate the life and work of Donald Coxeter.