John F. Nash Jr., a mathematician who shared a Nobel in 1994 for work that greatly extended the reach and power of modern economic theory and whose long descent into severe mental illness and eventual recovery were the subject of a book and a film, both titled “A Beautiful Mind,” was killed, along with his wife, in a car crash on Saturday in New Jersey. He was 86.

Dr. Nash and his wife, Alicia, 82, were in a taxi on the New Jersey Turnpike in Monroe Township around 4:30 p.m. when the driver lost control while veering from the left lane to the right and hit a guardrail and another car, Sgt. Gregory Williams of the New Jersey State Police said.

The couple were ejected from the cab and pronounced dead at the scene. The State Police said it appeared that they had not been wearing seatbelts. The taxi driver and the driver of the other car were treated for injuries. No criminal charges had been filed on Sunday.

The Nashes were returning home from the airport after a trip to Norway, where Dr. Nash and Louis Nirenberg, a mathematician from New York University, had received the Abel Prize from the Norwegian Academy of Science and Letters.