US mathematician John Nash, who inspired the film A Beautiful Mind, has been killed along with his wife in a car crash in New Jersey.

The Nobel-prize winner, 86, and his 82-year-old wife, Alicia, were riding in a taxi on Saturday when the incident happened, police said.

“The taxi passengers were ejected,” Sergeant Gregory Williams said, adding that they were both killed.

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Nash and his wife were involved in the deadly crash at 4.30pm on the New Jersey Turnpike near the town of Monroe, after their taxi attempted to pass another vehicle, lost control and struck a guard rail and car.

US media reported the couple were possibly not wearing seatbelts.

The taxi driver was airlifted to the hospital with non-life-threatening injuries.

A passenger in the other car was taken to hospital with neck and back pain.

The Princeton University and Massachusetts Institute of Technology mathematician was best known for his contribution to game theory – the study of decision-making – which won him the Nobel economics prize in 1994.

Russell Crowe as John Forbes Nash Jr in A Beautiful Mind.

His life story formed the basis of the Oscar-winning 2001 film A Beautiful Mind in which Russell Crowe played the genius, who struggled with mental illness.

“Stunned…my heart goes out to John & Alicia & family. An amazing partnership. Beautiful minds, beautiful hearts,” Crowe posted on Twitter.

The film’s director, Ron Howard, also tweeted his tribute to the “brilliant” John Nash and his “remarkable” wife.

Nash’s life story took a twist in early 1959 when he began suffering from “mental disturbances” that caused him to resign from his faculty position at MIT.

Eventually diagnosed with schizophrenia, Nash faced a lifelong struggle with delusions, which affected his career and marriage to Alicia, whom he wed in 1957.

The couple would divorce in the early 1960s but remained in contact and remarried decades later in 2001. By the time Nash received his Nobel Prize, his delusions had decreased.

Earlier this month, Nash and mathematician Louis Nirenberg received Norway’s prestigious Abel Prize for their contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.

– with AAP