Their infinite wisdom
Hotel guests come and go. But in the first decade of the 1900s, a pair of frequent Russian visitors to the Hotel Parisiana, near the Sorbonne on Paris’ Left Bank, stood out vividly. The children of the hotel’s proprietors, the Chamont family, remembered them into the 1970s as “hardworking” and “pious” men. The guests, Dimitri Egorov and Nikolai Luzin, were mathematicians, studying in Paris; they often prayed and went to church. The Russians were embarking on a grand project: exploring the unknown features of infinity, the notion that a quantity can always increase. Infinity’s riddles have fascinated intellectuals from Aristotle to Jorge Luis Borges to David Foster Wallace. In ancient Greece, Zeno’s Paradox stated that a runner who keeps moving halfway toward a finish line will never cross it (in effect, Zeno realized the denominator of a fraction can double infinitely, from 1/2 to 1/4 to 1/8, and so on). Galileo...