At 21, he writes an idea so short it fits on barely one printed page. It will reshape economics. Then, at 30, his own mind turns against him, and for the next 35 years almost nobody thinks they will hear from him again.

**February 11, 1948. Pittsburgh.** A professor at Carnegie Tech sits down to recommend a 19-year-old student from Bluefield, West Virginia, to Princeton. The letter is only a few lines long. Its final sentence is the one people still quote: “He is a mathematical genius.”

Princeton takes John Forbes Nash Jr. that autumn. He arrives tall, restless and openly bored by lectures, preferring to pace the corridors of Fine Hall and work through problems entirely inside his own head.

**November 16, 1949.** Nash is 21. A paper of his is sent to the Proceedings of the National Academy of Sciences, and it runs to barely a page. In it, he describes a point in any game where no player can do better by changing their strategy alone, as long as everyone else keeps theirs.

That idea becomes the Nash equilibrium. Economists, military planners, business strategists and even biologists will lean on it for the rest of the century. His full doctoral thesis, finished in 1950, is 26-page thesis long.

That is not a typo. Twenty-six pages.

**1951.** He joins MIT as a young mathematics instructor, and students nickname him the Kid Professor. He chases problems older mathematicians have quietly given up on. In 1957 he marries Alicia Lardé, a physics student from El Salvador who first met him as her teacher.

**1959.** Alicia is pregnant with their son. Nash is 30 and one of the brightest young mathematicians in America, but his thinking is slipping away from him. Soon he becomes convinced the New York Times is carrying hidden messages meant only for him.

He is hospitalised, diagnosed with paranoid schizophrenia, and resigns from MIT.

**January 1961.** His wife, his mother and his sister make an agonising choice and commit him to Trenton State Hospital in New Jersey. He spends months there, receiving an aggressive treatment five days a week. When he comes out, the young man who once dazzled MIT has no post, few prospects and a marriage under unbearable strain.

In 1963, after years of turmoil, Alicia divorces him. She is raising their little boy largely on her own.

Through the rest of the 1960s he is admitted to hospitals again and again, often against his will. Economists are building whole careers on his idea, while the man himself has almost nothing: no job, no marriage and no clear road back.

**1970.** Nash has nowhere stable to go. Alicia, divorced from him for 7 years, makes a decision almost nobody would have blamed her for refusing. She takes him back into her home in Princeton. Not as her husband. As what she calls her “boarder.”

For years after that, students see a thin, silent man in purple sneakers drifting through the mathematics building. Before morning classes, he fills the blackboards with strange messages and number puzzles. They call him the Phantom of Fine Hall, and most have no idea his idea from 1949 is being taught in lecture halls around the world.

Princeton never sends him away. Colleagues tolerate his wandering, let him sit for hours in the library and, later, let him learn to use the computers. One mathematician who studied there remembered that Nash “rarely said anything and just wandered benignly through Fine Hall.”

Slowly, through the 1980s, something shifts. Nash later wrote that he gradually began to reject, one by one, the delusional lines of thinking that had ruled him, and no single day marks the change.

**October 1994. Stockholm.** The Nobel committee has a problem. One senior member fears Nash will embarrass the prize, and the argument spills onto the floor of the full academy. The award survives by only a handful of votes, the closest such vote the academy had ever seen.

Nash is 66 when he shares the Nobel Memorial Prize in Economic Sciences with John Harsanyi and Reinhard Selten, for work he did as a 21-year-old graduate student 45 years earlier.

Days later, Princeton’s mathematics department holds a reception in his honour. The room is only half full, and Nash heads to the refreshment table and mentions, to his astonished guests, that the cookies are better than usual today.

**2001.** Thirty-eight years after their divorce, John and Alicia marry again. That same year, a film about his life, A Beautiful Mind, reaches cinemas and goes on to win 4 Academy Awards. The couple also become quiet advocates for mental health, partly for their son, who lives with schizophrenia too.

**May 19, 2015. Oslo.** Norway’s King Harald V hands Nash, now 86, the Abel Prize, shared with Louis Nirenberg, for work far away from game theory. He becomes the only person ever to receive both the Abel Prize and the Nobel in economics.

Four days later, John and Alicia fly home to Newark and chat with Nirenberg at the airport for an hour before climbing into a taxi. About 12 miles from their front door, it crashes on the New Jersey Turnpike. They die together, he at 86 and she at 82.

His story is often told as genius defeating illness. The truth is slower and more human. In his own Nobel essay, Nash admitted that thinking rationally again was “not entirely a matter of joy.”

What carried him was not willpower alone. It was a wife who opened her door when she had every reason to keep it shut, and a university that let a silent man keep walking its halls until he found his way back.

Who in your life kept a door open for you when it would have been easier to close it?