US mathematician John Nash, whose life story was turned into the Oscar-winning film A Beautiful Mind, has died in a car crash, local media has reported.

Nash, 86, and his wife Alicia were both killed when their taxi crashed in New Jersey, the reports said.

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 film.

Russell Crowe, who played him in the film, tweeted: "Stunned... My heart goes out to John & Alicia & family. An amazing partnership. Beautiful minds, beautiful hearts."

The reports said the couple may not have been wearing seatbelts when they crashed.

Earlier this week, Nash received the Abel Prize, another top honour in the field of mathematics.

John Nash, seen here receiving an honorary doctorate in 2011, was one of the developers of game theory. Photo : AFP