Coming of Age at Princeton with the Gods of Symmetry

“Symmetry, as wide or as narrow as you define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.”
—Hermann Weyl, Symmetry

KNOWN AS THE “PAPA DADDY” of Princeton mathematics professors, Solomon Lefschetz visited Cambridge in 1931, in search of suitable candidates for the illustrious Rockefeller research fellowships. He met Coxeter and invited him to apply. As a Rockefeller Fellow, Coxeter stood to benefit from a one-year research professorship at Princeton with a handsome monthly salary of $150,  a princely sum during the Great Depression, when the average American family income fell to $1,300 annually and unemployment was at 25 percent. The prospect no doubt pleased Coxeter immensely, and not for financial or self-gratifying reasons. Rather, it surely appealed to his humanism. Established in 1913 by John D. Rockefeller, and funded by the Rockefeller Foundation, the fellowships embodied a grand philanthropic enterprise to promote “the well-being of mankind throughout the world.”

Coxeter had a productive year at Princeton, his polytopes research proliferating to such an extent that Professor Lefschetz nicknamed him Mr. Polytope—“because I had long been specially interested in the figures which [Lefschetz] insisted were simply ‘polyhedra’ in space of any number of dimensions.” Coxeter understandably found this remark a tad dismissive, though Lefschetz’s was a perfectly proper definition of polytopes. On the whole, Coxeter said in a letter to his father polytopes are an “anathema” in America…