Nash was born on June 13, 1928, in Bluefield, West Virginia. His father, John Forbes Nash, was an electrical engineer for the Appalachian Electric Power Company. His mother, Margaret Virginia (née Martin) Nash, had been a schoolteacher before she was married.

Nash attended kindergarten and public school, and he learned from books provided by his parents and grandparents.[9] Nash's parents pursued opportunities to supplement their son's education and arranged for him to take advanced mathematics courses at a local community college during his final year of high school. He attended Carnegie Institute of Technology (which later became Carnegie Mellon University) through a full benefit of the George Westinghouse Scholarship, initially majoring in chemical engineering. He switched to a chemistry major and eventually, at the advice of his teacher John Lighton Synge, to mathematics. After graduating in 1948 (at age 19) with both a B.S. and M.S. in mathematics, Nash accepted a scholarship to Princeton University, where he pursued further graduate studies in mathematics.

Nash earned a Ph.D. in 1950 with a 28-page dissertation on non-cooperative games.

Nash, John Forbes (1950). "Equilibrium Points in N-person Games". Proceedings of the National Academy of Sciences of the United States of America.
Nash, John Forbes (1950). "The Bargaining Problem". Econometrica. Basel, Switzerland: MDPI.
Nash, John Forbes (1951). "Non-cooperative Games". Annals of Mathematics. Princeton, New Jersey: Princeton University.
Nash, John Forbes (1953). "Two-person Cooperative Games". Econometrica. Basel, Switzerland: MDPI.

Although Nash's mental illness first began to manifest in the form of paranoia, his wife later described his behavior as erratic. Nash seemed to believe that all men who wore red ties were part of a communist conspiracy against him. He mailed letters to embassies in Washington, D.C., declaring that they were establishing a government.

In 1951, the Massachusetts Institute of Technology (MIT) hired Nash as a C. L. E. Moore instructor in the mathematics faculty. About a year later, Nash began a relationship in Massachusetts with Eleanor Stier, a nurse he met while admitted as a patient. They had a son, John David Stier, but Nash left Stier when she told him of her pregnancy. The film based on Nash's life, A Beautiful Mind, was criticized during the run-up to the 2002 Oscars for omitting this aspect of his life. He was said to have abandoned her based on her social status, which he thought to have been beneath his.

Nash did groundbreaking work in the area of real algebraic geometry, His work in mathematics includes the Nash embedding theorem, which shows that every abstract Riemannian manifold can be isometrically realized as a submanifold of Euclidean space. He also made significant contributions to the theory of nonlinear parabolic partial differential equations and to singularity theory.

In Santa Monica, California in 1954, while in his 20s, Nash was arrested for indecent exposure in a sting operation targeting homosexual men.[47] Although the charges were dropped, he was stripped of his top-secret security clearance and fired from RAND Corporation, where he had worked as a consultant.

Not long after breaking up with Stier, Nash met Alicia Lardé Lopez-Harrison, a naturalized U.S. citizen from El Salvador. Lardé graduated from MIT, having majored in physics. They married in February 1957; although Nash was an atheist, the ceremony was performed in an Episcopal church. They had a son together, John Charles Martin Nash, who earned a Ph.D. in Mathematics from Rutgers University.

Nash's psychological issues crossed into his professional life when he gave an American Mathematical Society lecture at Columbia University in 1959. Originally intended to present proof of the Riemann hypothesis, the lecture was incomprehensible. Colleagues in the audience immediately realized that something was wrong.

He was admitted to McLean Hospital in April 1959, staying through May of the same year. There, he was diagnosed with paranoid schizophrenia. According to the Diagnostic and Statistical Manual of Mental Disorders, or DSM, a person suffering from the disorder is typically dominated by relatively stable, often paranoid, fixed beliefs that are either false, over-imaginative or unrealistic and usually accompanied by experiences of a seemingly real perception of something not actually present. Further signs are marked particularly by auditory and perceptional disturbances, a lack of motivation for life, and mild clinical depression.

Nash was admitted to the New Jersey State Hospital at Trenton. Over the next nine years, he spent periods in psychiatric hospitals, where he received both antipsychotic medications and insulin shock therapy.

Although he sometimes took prescribed medication, Nash later wrote that he did so only under pressure. After 1970, he was never committed to a hospital again, and he refused any further medication.

In 1978, Nash was awarded the John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called Nash Equilibria.

Nash has suggested hypotheses on mental illness. He has compared not thinking in an acceptable manner, or being "insane" and not fitting into a usual social function, to being "on strike" from an economic point of view. He advanced views in evolutionary psychology about the value of human diversity and the potential benefits of apparently nonstandard behaviors or roles.

In 1994, he received the Nobel Memorial Prize in Economic Sciences (along with John Harsanyi and Reinhard Selten) as a result of his game theory work as a Princeton graduate student. In the late 1980s, Nash had begun to use email to gradually link with working mathematicians who realized that he was the John Nash and that his new work had value. They formed part of the nucleus of a group that contacted the Bank of Sweden's Nobel award committee and were able to vouch for Nash's mental health ability to receive the award in recognition of his early work.

Nash received an honorary degree, Doctor of Science and Technology, from Carnegie Mellon University in 1999

A Beautiful Mind is a 2001 American biographical drama film based on the life of John Nash, a Nobel Laureate in Economics. The film was directed by Ron Howard, from a screenplay written by Akiva Goldsman. It was inspired by a bestselling, Pulitzer Prize-nominated 1998 book of the same name by Sylvia Nasar. The film stars Russell Crowe, along with Ed Harris, Jennifer Connelly, Paul Bettany, Adam Goldberg, Judd Hirsch, Josh Lucas, Anthony Rapp, and Christopher Plummer in supporting roles. The story begins in Nash's days as a graduate student at Princeton University. Early in the film, Nash begins to develop paranoid schizophrenia and endures delusional episodes while watching the burden his condition brings on wife Alicia and friends.

Nash received an honorary degree in economics from the University of Naples Federico II on March 19, 2003

He was also a prolific guest speaker at a number of world-class events, such as the Warwick Economics Summit in 2005 held at the University of Warwick.

Nash received an honorary doctorate in economics from the University of Antwerp in April 2007

Nash received an honorary doctorate of science from the City University of Hong Kong on November 8, 2011, and was a keynote speaker at a conference on game theory.

He was elected as a fellow of the American Mathematical Society In 2012.

A few days before his death, Nash, along with Louis Nirenberg, was awarded the 2015 Abel Prize by King Harald V of Norway at a ceremony in Oslo On May 19, 2015.

On May 23, 2015, Nash and his wife died in a car accident on the New Jersey Turnpike near Monroe Township, New Jersey. They had been on their way home from the airport after a visit to Norway, where Nash had received the Abel Prize, when their taxicab driver, Tark Girgis, lost control of the vehicle and struck a guardrail. Both passengers were ejected from the car upon impact. State police revealed that it appeared neither passenger was wearing a seatbelt at the time of the crash. At the time of his death, the 86-year-old Nash was a longtime resident of West Windsor Township, New Jersey. He is survived by his two sons, John Charles Martin Nash who lived with his parents at the time of their death, and the older, John Stier.