In 1904 the French mathematician Henri Poincaré made a conjecture about three-­dimensional space that may help to explain the shape of the universe. Although it was crucial to the growth of the field of topology, Poincaré’s conjecture resisted proof for a century. When a Boston philanthropist announced a million-dollar prize for its solution in 2000 it was unclear whether he would ever have to pay.

Then, in 2002, a Russian mathematician named Grigori Perelman posted a terse paper to an online archive. In the course of tackling a broader problem, Perelman seemed to have miraculously swept away the remaining obstacles to proving the Poincaré conjecture. Soon the mathematical rumor mill was buzzing. The proof seemed genuine, but word was that Perelman had no plans to publish it.

This was only the beginning of the weirdness. After a brief trip to the United States with his mother in tow, Perelman retreated to St. Petersburg and ceased communication with all but a few colleagues vetting his work. He declined the Fields Medal, a gesture equivalent to snubbing the Nobel committee. He then resigned from the Steklov Institute in 2005 with a letter that read, “I have been disappointed in mathematics and I want to try something else.”

Image Credit... Illustration by Hugo Guinness

Why did Perelman turn his back on the world? This question haunts Masha Gessen’s “Perfect Rigor,” a dogged portrait of an elusive man. Gessen, a Russian-born journalist who has written books on the post-Soviet intelligentsia and on the pitfalls of genetic testing, is no stranger to the burdens of uncommon knowledge. Without a shred of help from Perelman himself, she charts the mathematician’s rise from quiet super-student to prickly genius, suggesting that the very perfectionism that fueled his work may have been the cause of his alienation.