🇺🇸John
Nash

In 1950, John Forbes Nash Jr. submitted a doctoral dissertation to Princeton University that was twenty-seven pages long. It contained one central idea. That idea — the Nash equilibrium — became the foundation of modern game theory and transformed economics, evolutionary biology, political science, and international relations. Nash was twenty-two years old. His dissertation supervisor wrote a letter of recommendation that consisted of a single sentence: "This man is a genius." Nash received the Nobel Memorial Prize in Economic Sciences forty-four years later, in 1994. In the intervening decades, he had suffered one of the most devastating episodes of mental illness in the history of science and recovered — slowly, quietly, without medication, on the campus of Princeton — in a way that no one had predicted and that he himself could not fully explain.

John Forbes Nash Jr. was born on June 13, 1928, in Bluefield, West Virginia, the son of an electrical engineer and a former schoolteacher. He was a difficult, solitary, and self-sufficient child who preferred books and solitary projects to other children, taught himself Latin and chemistry from library books, and showed an early and particular gift for finding original solutions to problems. At Carnegie Mellon University, he began as a chemical engineering student, switched to chemistry, and finally settled in mathematics — a subject where his talent was so obvious that a professor wrote him a letter of recommendation containing only five words: "He is a man of genius."

He arrived at Princeton in 1948 for his doctoral work. The mathematics department at Princeton in the late 1940s was arguably the greatest concentration of mathematical talent in the world, anchored by the Institute for Advanced Study and home to Albert Einstein, John von Neumann, and a graduate student body of exceptional quality. Nash was competitive, arrogant, and visibly unusual even in this company. He was also, by every account, brilliant in a way that was immediately apparent. He worked on problems across topology, algebraic geometry, and game theory, and it was in game theory — then a brand new field — that he produced his landmark result.

The Nash equilibrium is a concept in game theory — the mathematical study of strategic decision-making. In any situation where multiple players make decisions that affect each other (a negotiation, a market, an arms race, an election), a Nash equilibrium is a state in which no player can improve their outcome by unilaterally changing their strategy, given what everyone else is doing. It is, in other words, a condition of stable mutual best-response. John von Neumann had proved that equilibria existed in zero-sum games — games with a winner and a loser — but most real-world situations are non-zero-sum. Nash proved that equilibria exist in any finite, non-cooperative game. This generalization was the key move. It meant that game theory could be applied to almost every human interaction where strategy matters.

At thirty, Nash was at the height of his powers — a faculty member at MIT, recently married, working on what promised to be the greatest achievement of his career: a proof that would solve one of the most profound open problems in pure mathematics. Then, in early 1959, he began to change. He made strange announcements at a conference. He became paranoid, convinced that foreign governments were sending him messages through the New York Times. He resigned from MIT in March 1959, believing he was about to be named Emperor of Antarctica. He was hospitalized, diagnosed with paranoid schizophrenia, and began a thirty-year period of mental illness in which he was periodically institutionalized, wandered Princeton as a ghost-like figure known to students as "the Phantom," and produced no mathematics of note.

The recovery, when it came, was slow and entirely self-directed. By the late 1980s, Nash had begun to re-emerge. He was, in his own account, able to choose not to act on delusional thoughts — to observe them and set them aside rather than be controlled by them. He returned to mathematics. When the Nobel committee called in October 1994, he was living quietly in Princeton with his wife Alicia, to whom he had been reconnected after decades of separation. Sylvia Nasar's biography A Beautiful Mind (1998) and the subsequent film brought his story to a global audience. In 2015, he and his wife were killed in a taxi accident returning from the airport after he had collected the Abel Prize — mathematics' highest honor — in Oslo. He was eighty-six years old.