Nash had read the classic "Men of Mathematics" by E.T. Bell by the time he was in high school. He planned to follow in his father's footsteps and studied for three years at the Carnegie Institute of Technology in Pittsburgh — now Carnegie Mellon University — but instead followed his passion for math.
He then went to Princeton, where he worked on his equilibrium theory and, in 1950, received his doctorate with a dissertation on non-co-operative games. The thesis contained the definition and properties of what would later be called the Nash equilibrium.
But it was while teaching at the Massachusetts Institute of Technology in 1959, when his wife, Alicia, was pregnant with their son, that schizophrenia began to emerge, a yearslong fight that was chronicled in the Academy Award-winning blockbuster "A Beautiful Mind." The Nashes died in a car accident late Saturday on the New Jersey Turnpike. He was 86; she was 82.
"John's remarkable achievements inspired generations of mathematicians, economists and scientists who were influenced by his brilliant, groundbreaking work in game theory, and the story of his life with Alicia moved millions of readers and moviegoers who marveled at their courage in the face of daunting challenges," Princeton President Christopher Eisgruber said in a statement.
In an autobiography written for The Nobel Foundation website, Nash said delusions caused him to resign as a faculty member at MIT. He also spent several months in New Jersey hospitals on an involuntary basis. However, Nash's schizophrenia diminished through the 1970s and 1980s as he "gradually began to intellectually reject some of the delusionally influenced lines of thinking," he wrote.
2001's "A Beautiful Mind" was based on an unauthorized biography by Sylvia Nasar, who wrote that Nash's contemporaries found him "immensely strange" and "slightly cold, a bit superior, somewhat secretive." Much of his demeanour likely stemmed from mental illness.
"A Beautiful Mind" won four Academy Awards, including best picture and best director, and generated interest in John Nash's life story.
Russell Crowe, who was nominated for best actor for playing Nash, tweeted that he was "stunned" by news of the couple's death.
"An amazing partnership," he wrote. "Beautiful minds, beautiful hearts."
Jennifer Connelly, who won the Oscar for best supporting actress for her portrayal of Alicia Nash, called the couple "an inspiration," and the film's director, Ron Howard, tweeted that "it was an honour telling part of their story."
The Nashes split in 1963 then resumed living together several years later and remarried in 2001.
John Nash held a research post at Brandeis University before eventually returning to Princeton. Known as brilliant and eccentric, he was associated with Princeton for many years, most recently serving as a senior research mathematician.
He was awarded the Nobel Prize in economics for his work in game theory, which offered insight into the dynamics of human rivalry. It is considered one of the most influential ideas of the 20th century.
Just days before his death, Nash received a prize from the Norwegian Academy of Sciences and Letters in Oslo with New York University mathematician Louis Nirenberg, who called Nash a truly great mathematician and "a kind of genius."
Nirenberg said he had chatted with the Nashes for an hour at the airport in Newark, New Jersey before they'd gotten into a taxi to return home to Princeton Township.
New Jersey State Police say the Nashes were thrown out of the taxi when it crashed around 4:30 p.m. Saturday in Monroe Township, about 12 miles from their home. The cab driver was hospitalized.
Associated Press writers Geoff Mulvihill in Trenton and Jeff McMillan in Philadelphia contributed to this report.