‘Beautiful Mind’ mathematician John Nash killed

Nash won the Nobel prize for economics in 1994, but most people know Nash from the Oscar-winning 2001 movie that depicted his mathematical genius and his schizophrenic delusions.

Russell Crowe, the actor who played Nash, tweeted: “Stunned…my heart goes out to John & Alicia & family. An amazing partnership. Beautiful minds, beautiful hearts.”

Ron Howard, the movie’s director, called John Nash “brilliant” and his wife “remarkable” in a tweeted tribute. “It was an honor telling part of their story,” he said.

Born in West Virginia, his recommendation letter to Princeton contained just one line: “This man is a genius.”

Nash wrote a 28-page thesis as a Princeton University graduate student that detailed what would eventually become known as the “Nash equilibrium,” a solution for a non-cooperative game involving two or more players. Game theorists and economists use the theorem to predict the best outcome for several players acting simultaneously where there is no benefit for players to change strategy, because of the actions of the other players in the game.

But for almost 25 years, Nash’s life was rocked by paranoid delusions and hallucinations. His wife, Alicia, had John committed for psychiatric care numerous times. She also helped care for him herself.

The couple’s love story is central to “A Beautiful Mind.” Alicia and John were divorced in 1962, but they stayed close as he began to improve in the 1980s. They remarried in 2001.

After John recovered, his “Nash equilibrium” had influenced everything that is affected by competition: foreign affairs, politics, biology and economics.

“John’s remarkable achievements inspired generations of mathematicians, economists and scientists who were influenced by his brilliant, groundbreaking work in game theory,” said Christopher Eisgruber, the president of Princeton, in a statement.