When We Cease to Understand the World

Chapter 3 opens with the story of Japanese mathematician Shinichi Mochizuki. On his blog in 2012, he claims to have found a solution to the mathematical problem a + b = c. His colleagues attempt to verify his findings, but they find it hopelessly complex. In order to find his solution, he has created a whole new branch of mathematics that “consists of a series of underlying relationships between numbers that are invisible at first sight” (62).

The narrative then goes back in time to Mochizuki’s early life. He is a painfully shy childhood prodigy. At 16 he goes to Princeton and at 23 he earns a doctorate. Then he returns to Japan to work as a research professor at the Research Institute for Mathematical Sciences at the University of Kyoto. Over the years, he becomes increasingly agoraphobic. He calls the new branch of mathematics he develops Inter-Universal Teichmüller Theory. To develop his solution to the problem a + b = c, he uses this Inter-Universal theory, which “required mathematicians to conceive of numbers in a radically different way” (64). However, Mochizuki refuses to give interviews or defend his work, which makes many people skeptical about his findings. In 2014, he agrees to present his work at a conference at the University of Montpellier, but he never appears, because he was ejected from the campus the day before. Then he takes down his blog and threatens to sue anyone who publishes his proofs. His colleagues feel he is suffering “Grothendieck’s curse.”

The rest of the chapter covers the story of eccentric French mathematician Alexander Grothendieck. Mochizuki is fascinated by Grothendieck’s theories and proved one of his conjectures in 1996. Mochizuki’s roommate at Princeton described finding Mochizuki one evening delirious and ranting about Grothendieck’s theory of the “heart of the heart” (66), of which Mochizuki later claimed to have no memory.

Grothendieck is active between 1958 and 1973 and proves some of the most difficult problems in mathematics. He wants to “achieve an absolute understanding of the foundations of mathematics” and so develops many different concepts (66). He works with single-minded focus for many years.

Labatut describes Grothendieck’s early life. His father is a revolutionary anarchist who is later killed by the Nazis in the gas chamber at Auschwitz. His mother is a writer and revolutionary who fights against the fascists in Franco’s Spain. His mother is sent to the Rieucros internment camp in France with other revolutionaries after the Spanish Civil War and Grothendieck lives there with her until he is 17. After the war, they live as grape pickers outside Montpellier, where he studies. His mother dies of tuberculosis in 1957.

Grothendieck is a gifted undergraduate student at the University of Montpellier, but as a stateless person, it is hard for him to get a job. As a student, he shows a propensity for graphomania, or obsessive writing. At 30, he conducts research at the Institute of Advanced Studies outside Paris. There, he embarks on a project to “re-establish the foundations of geometry and unify all the branches of mathematics” (70). He has a particular talent for using metaphorical language to describe his new concepts and in deploying extreme abstraction. In 1966, he wins the Fields Medal for his work. His ultimate goal is to discover what he called the motive or the “heart of the heart” that could describe every mathematical object (74).

In the 1960s, Grothendieck becomes involved in the revolutionary social movements in France of the day. In 1970, he resigns from the Institute of Advanced Studies after it accepts contracts from the French Ministry of Defense. Later that year, he renounces bourgeois life, becomes an ascetic, and founds a commune in his home focused on “his ideas on self-sufficiency and care for the environment” (77). In 1973, the police charge Grothendieck for harboring two Japanese monks who overstayed their visa, and a member of the commune attempts suicide. Grothendieck disbands the commune and lives in isolation in the village of Villecun for five years. Later, he teaches occasional courses at the University of Montpellier. From 1983 and 1986, he writes an idiosyncratic text outlining his views entitled Reaping and Sowing: Reflections and Testimonies from a Mathematician’s Past, which goes unpublished. In 1988, he nearly dies of starvation while trying to emulate the French mystic Marthe Robin, who was said to survive only on communion wafers for many years. One of his beliefs is that dreams come from an entity beyond humanity, Le Rêveur, or the Dreamer, and so he keeps a log of his dreams for years.

In 1991, Grothendieck cuts himself off from society entirely and donates his papers to the University of Montpellier. His whereabouts are unknown for nearly a decade until he resurfaces in the village of Lasserre near the Pyrenees. He believes that every night he is visited by a two-faced woman with whom he plays piano. In 2001, his house catches fire, and he begs the firemen to let it burn down. In 2010, he writes a letter to his friend Luc Illusie prohibiting any dissemination of his work. An American mathematician, Leila Schneps, discovers where he is living toward the end of his life. The two spent an afternoon in conversation where Grothendieck explains that he became a recluse to protect humanity from his work. They have some correspondence, but Grothendieck refuses to answer her questions about his findings. In 2014, he dies in a hospital of unknown causes.

A nurse reports that Grothendieck, shortly before his death, had a single visitor who spent five days taking notes. Two days later, the visitor is apprehended at the University of Montpellier archives attempting to set Grothendieck’s papers on fire. While the guards escort him off the campus, the visitor shyly explains that they should let him go because he has to present a lecture in the Department of Mathematics. (The visitor is Mochizuki.)