Back in the 1950s it seemed that geometry as a discipline would soon be all but extinct. School teachers had to teach it to their pupils, of course, but as far as researchers were concerned, this particular branch of mathematics could barely offer them anything of even the slightest interest. All old hat, many mathematicians thought to themselves. Only one among them begged to differ. His name was Harold Scott MacDonald Coxeter.

Coxeter was born in London, England, on February 9, 1907. Already as a young schoolboy in one of London’s grammar schools, his astonishing mathematical talent attracted attention. When Coxeter Sr. introduced his son to Bertrand Russell, the philosopher advised that the young boy be tutored privately until old enough to study at Cambridge. Even at Cambridge, one of England’s foremost academic centers, it did not take long for Coxeter to gain the reputation of an extremely gifted mathematician. Cambridge’s most eminent philosopher, Ludwig Wittgenstein, chose him as one of only five students whom he admitted to his coveted lectures on the philosophy of mathematics.

Coxeter completed his doctoral studies at Cambridge and was then invited to Princeton University as a visiting scholar. Shortly before the outbreak of World War II he accepted a position at the University of Toronto. It was there in this rather remote city, far away from the rest of the world’s renowned mathematical centers, that Coxeter worked for over 60 years. Today H. S. M. Coxeter is considered one of the 20th century’s most eminent proponents of classic and modern geometry.

In 1938, with Europe and America facing political turmoil, Coxeter was quietly tucked away in his Toronto office, the walls of which were lined with mathematical models. His discoveries and theories went well beyond

mathematics, having significant impact on other areas, such as architecture and art. It was Coxeter’s work on polyhedra, such as dice and pyramids, and their higher-dimensional counterparts, called polytopes, that paved the way to the discovery of the C₆₀ molecule, whose shape resembles that of a soccer ball.¹

The famous geodesic dome, designed by the American architect Buckminster Fuller and built to mark Expo 67, the World's Fair in Montreal, is one of many constructs that made use of Coxeter’s discoveries.² One only has to look at how the thousands of triangles that make up this dome are joined together to understand that its actual construction is firmly based on Coxeter’s preparatory research.

Coxeter, endowed also with artistic gifts, particularly in music, was fascinated by the sheer beauty of mathematics throughout his life. His collaboration with the Dutch graphic artist M. C. Escher turned into one of the most interesting and fruitful partnerships in history between science and art. By the time he met Coxeter, Escher had become thoroughly bored with routinely placing fish after fish next to bird after bird on a blank canvas. His wanted to do something different. He hoped, in fact, to do nothing less than depict infinity. In 1954 the International Congress of Mathematicians took place in Amsterdam, and it was there that Coxeter and Escher were introduced to one another. The two men formed a friendship that would last a lifetime. Not long after this meeting, Coxeter sent one of his papers on geometry to his new friend so that he could read and perhaps comment on it. Despite his complete lack of mathematical knowledge, Escher was so impressed by the drawings with which Coxeter had illustrated the mathematics that he immediately began to create a set of graphics entitled “Circle Limit I–IV.”

By allowing shapes to be framed by circles and squares and then gradually decreasing their size as they approach the frames, Escher had achieved his goal: He had depicted infinity.

Coxeter was well aware that he was blessed. He ascribed his long life to his love for mathematics, his vegetarian diet, his daily exercise regime of 50 push-ups in one go, and his great devotion to mathematics. As he told one of his colleagues, he was never bored and got “paid to do what he loved to do.”

Coxeter was scheduled to give the plenary address to the Festival of Symmetry that was to be held in August 2003 in Budapest, Hungary. In February the 96-year-old Coxeter, still eager to play his part, wrote to the organizers that he very much would like to attend if indeed he would still be alive at that time. “Deo volente.” He would give a lecture on “absolute regularity,” he wrote. God wished for things to be different. Only a few weeks after having written the letter, on March 31, 2003, Coxeter passed away quietly at his home in Toronto.