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The King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry by Siobhan Roberts, Walker & Co, 2006

This biography of one of the greatest geometers of the twentieth century was a mixed bag for me. Donald Coxeter was a fascinating and brilliant man, and a list of his correspondents and admirers is a veritable who's who of twentieth century mathematicians, artists, and scientists. Donald was long-lived, even for a mathematician. He lived from 1907 – 2003, and was mathematically creative until nearly the end. A man of this rich creativity presents a formidable challenge to a biographer; how to sketch the trajectory of his life while neither getting bogged down in details on the one hand, or being superficial on the other.
A search on Amazon reveals that this book is the first published by Ms. Roberts, and the book definitely has some rough edges. I feel she needed more editorial guidance than she received. Ms. Roberts, who is not a mathematician, has apparently interviewed a number of Coxeter's colleagues at great length, and she has let them do the talking. As a result, I feel the absence of a strong author's voice, and a resulting fragmented picture of Coxeter. I found the book hard to plow through in places, which really surprised me given the strong interest that I have in Coxeter's work.
The flip side of this is that it is wonderful to read accounts from such luminaries as John Conway, Walter Whitely, Freeman Dyson, M. C. Escher (through his son, George), Buckminster Fuller and Douglas Hofstadter (who wrote the forward).
I found the glimpses of Coxeter's life outside of mathematics to be quite fascinating. He was a pacifist and a vegetarian, and seems to have been highly regarded as a person by most who knew him. His early life included problems with a withdrawn mother and an overbearing father, and a brief psychoanalysis by Freud's student, Stekel. I would have liked to have been told more about Coxeter the man.
Perhaps the best compliment I can pay the book is that I came away from it wishing that I had known Coxeter, and determined to read more of his work.

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