The mathematician is renowned for his work in game theory, winning the Nobel Prize for Economics in 1994.
His breakthroughs in maths – and his struggles with schizophrenia – were the focus of the 2001 film.
Russell Crowe, who played him, tweeted: “Stunned… My heart goes out to John & Alicia & family. An amazing partnership. Beautiful minds, beautiful hearts.”
The film’s director, Ron Howard, also tweeted his tribute to the “brilliant” John Nash and his “remarkable” wife.
Alicia Nash helped care for her husband, and the two later became prominent mental health advocates.
The two were thrown from their vehicle, police said. Media reports said the couple may not have been wearing seatbelts when they crashed.
Their taxi driver, and a passenger in another car, were also injured.
‘Genius’
Born in Bluefield, West Virginia, Nash first studied in Pittsburgh before moving to Princeton.
His recommendation letter contained just one line: “This man is a genius.”
Nash married Alicia Larde in 1957, after publishing some of his breakthrough works in game theory, which is the mathematical study of decision-making.
But he developed severe schizophrenia soon after, and Alicia had him committed for psychiatric care several times. The couple divorced in 1962.
“I was disturbed in this way for a very long period of time, like 25 years,” Nash said in an interview on the Nobel website.
The two stayed close, and his condition had begun to improve by the 1980s. They remarried in 2001.
The President of Princeton, Christopher Eisgruber, said he was “stunned and saddened” to hear of their deaths.
“John’s remarkable achievements inspired generations of mathematicians, economists and scientists who were influenced by his brilliant, groundbreaking work in game theory,” he said.
Even this week, Nash received the Abel Prize, another top honour in the field of mathematics.
Nash Equilibrium:
Great new mathematical ideas have a balance to strike – they must be precise enough to allow detailed conclusions to be drawn, and yet sufficiently loose that they can be useful in a wide range of problems.
The Nash Equilibrium, for which he won a Nobel Prize, is just such an idea. It offered something truly new – the ability to analyse situations of conflict and co-operation and produce predictions about how people will behave.
Nash’s famous equilibrium has grown to be perhaps the most important idea in economic analysis and has found application in fields as diverse as computing, evolutionary biology and artificial intelligence.
More recently it has been used in studies of corruption and also name-checked amidst the Greek financial crisis.
