The taxi driver was injured in the crash and taken to the Robert Wood Johnson University Hospital in the town of New Brunswick. His injuries are reportedly not life-threatening. Nash received the Nobel Prize in economics for his work in "game theory" and his career as a Princeton professor, along with his struggle with paranoid schizophrenia, were portrayed by Russell Crowe in "A Beautiful Mind" which won four Oscars -- including Best Picture -- in 2002.
"Stunned... my heart goes out to John & Alicia & family. An amazing partnership. Beautiful minds, beautiful hearts," the actor tweeted on Sunday.
Nash pursued his academic career at Princeton and the Massachusetts Institute of Technology and received the Nobel for applying his revolutionary mathematical theories to the solution of economic unknowns.
He had battled mental health problems since his youth and became involved in assorted controversies during his life, including being accused of anti-Semitism, which he denied.
Along with his wife, who was of Salvadoran origin, he had campaigned for years to raise public awareness of mental illness.
This year, Nash, along with Louis Nirenberg, received the Abel Prize, considered to be the "Nobel Prize of mathematics" and awarded by the Norwegian Academy of Science and Letters, for his work in partial differential equations.