Mathematician John Nash, a Nobel Prize winner whose longtime struggle with mental illness inspired the movie "A Beautiful Mind", was killed in a car crash along with his wife in New Jersey, state police said on Sunday.

The couple were in a taxi when the driver lost control, crashed into a guard rail and hit another car on Saturday afternoon on the New Jersey Turnpike, said police.

Nash, 86, and his wife, Alicia, 82, were thrown from the taxi and pronounced dead at the scene, New Jersey State Police spokesman Sgt. Gregory Williams added, declining to comment on media reports that they were not wearing seat belts.

Russell Crowe, who portrayed Nash in the Oscar-winning movie, said on Twitter that he was stunned by the deaths. "An amazing partnership. Beautiful minds, beautiful hearts," the Hollywood star wrote.

The taxi driver was taken to hospital with non-life threatening injuries and the driver of the other vehicle was also treated in hospital, police said. No charges had been filed, Williams added.

Nash was awarded the Nobel Prize for economics in 1994 for his work on game theory and the mathematics of decision-making.

The film "A Beautiful Mind" was loosely based on his battle with schizophrenia.