Here is an unlikely candidate for real-life hero: a geometry professor. H. S. M. "Donald" Coxeter, a classical geometer interested in shapes, lines, vertices, polygons and the visualization of such geometric entities, saved the world from being overtaken by formalists who wanted to algebra-ize everything in geometry. Coxeter is not well known by most people; his geometry encompassed higher dimensions than most of us can think about. But he was truly a hero for the mathematicians who knew him and worked with him, and he did make differences in their discipline that have proved to have surprisingly widespread and even practical results. He has had the good fortune, four years after the end of his long life, to be the subject of a full and admiring biography _King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry_ (Walker) by Siobhan Roberts. Roberts is a journalist who interviewed Coxeter himself over a period of two years toward the end of his life, and has interviewed many leading mathematicians and scholars who were the best ones to explain the exalted status in which Coxeter is held. Roberts's book is not a geometry text; she give analogies about Coxeter's work and hints at its themes rather than going into any mathematical detail, so even if you are intimidated by mathematics, you can get an idea of Coxeter's thoughts and just why he was such a revolutionary. This makes not only for an interesting biography, but an agreeable tour of just how mathematics has gotten done in the past few decades.
Coxeter, born in London in 1907, was one of the mathematicians that broke the rule that doing math is a young man's game. He did make his first discoveries when he was thirteen, but was active until his death in 2003, still writing, proving, and presenting. He was a student at Cambridge, and in 1936 he immigrated to Toronto and took a teaching post at the university there, where he remained for the rest of his life. There are many descriptions of cranky mathematicians in these pages, but Coxeter was never like that. A fellow mathematician said, "He was almost courtly. He was very gentle, even when he managed to show you that you were thinking like an idiot." He had the archetypal lack of interest in any practical applications of his ideas, appalled that his lovely theories could be sullied by practical utility. He firmly believed in pictures, visualization, and intuition, putting himself successfully at odds with the formalists who had inspired the New Math that was taught in grade schools forty years ago. His insistence on visual appeal linked him to M. C. Escher who incorporated mathematical ideas into his art. Coxeter even wrote explications of certain Escher prints; that he did so gratified the artist, but privately the non-mathematician Escher said that the "hocus-pocus text is no use to me at all." Coxeter also had a close, not always collegial, relationship with Buckminster Fuller, whose geodesic domes he admired.
Coxeter's professional life was without reproach. His family life was much less than perfect. Part of the problem was that he had all the bumbling of an absent-minded professor, causing his wife Rien to screech names at him in her native Dutch. Coxeter conceded, "I was not able to love Rien as fully and completely as one should his wife," but when she developed Alzheimer's, he took uncharacteristically close care of her bathing, dressing, and feeding. Neither of their two children had interest in mathematics. His daughter "ran hot and cold on his status as a mathematical legend," but escorted the elderly Coxeter to his last conferences. She said, "Dad would hate to be equated with Elvis Presley, but Elvis gave people some moments of joy, happiness, inspiration. And if that's what Dad's work does for these people, that's wonderful. Personally, I get more from Elvis Presley." She isn't the only one, of course, but Roberts's delightful biography can't help but show even non-mathematicians just how important a figure Coxeter was. Do not fret that you don't understand all the math here. Coxeter once admitted that even in the geometry that he loved, "There are so many branches of the subject in which I am almost as ignorant as the proverbial man in the street."