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RESEARCH PRODUCT

Coxeter on People and Polytopes

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H. S. M. Coxeter, known to his friends as Donald, was not only a remarkable mathematician. He also enriched our historical understanding of how classical geometry helped inspire what has sometimes been called the nineteenth-century’s non-Euclidean revolution (Fig. 35.1). Coxeter was no revolutionary, and the non-Euclidean revolution was already part of history by the time he arrived on the scene. What he did experience was the dramatic aftershock in physics. Countless popular and semi-popular books were written during the early 1920s expounding the new theory of space and time propounded in Einstein’s general theory of relativity. General relativity and subsequent efforts to unite gravitation with electromagnetism in a global field theory gave research in differential geometry a tremendous new impetus. Geometry became entwined with physics as never before, and higher-dimensional geometric spaces soon abounded as mathematicians grew accustomed not just to four-dimensional space-times but to the mysteries of Hilbert space and its infinite-dimensional progeny.