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 married. He was baptized in the Episcopal Church. He had a younger sister, Martha (born November 16, 1930).

Not long after breaking up with Stier, Nash met Alicia Lardé Lopez-Harrison (January 1, 1933 – May 23, 2015), 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.

Nash's later work involved ventures in advanced game theory, including partial agency, which show that, as in his early career, he preferred to select his own path and problems. Between 1945 and 1996, he published 23 scientific studies.

Nash attended kindergarten and public school, and he learned from books provided by his parents and grandparents. 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. degree in 1950 with a 28-page dissertation on non-cooperative games.

In 1951, Nash was hired by the Massachusetts Institute of Technology (MIT) 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.

In Santa Monica, California in 1954, while in his 20s, Nash was arrested for indecent exposure in a sting operation targeting homosexual men. 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.

In the Nash biography A Beautiful Mind, author Sylvia Nasar explains that Nash was working on proving Hilbert's nineteenth Problem, a theorem involving elliptic partial differential equations when, in 1956, he suffered a severe disappointment. He learned that an Italian Mathematician, Ennio de Giorgi, had published a proof just months before Nash achieved his proof. Each took different routes to get to their solutions. The two mathematicians met each other at the Courant Institute of Mathematical Sciences of New York University during the summer of 1956. It has been speculated that if only one had solved the Problem, he would have been given the Fields Medal for the proof.

In 1958, Nash earned a tenured position at MIT, and his first signs of mental illness were evident in early 1959. At this time, his wife was pregnant with their first child. He resigned his position as a member of the MIT mathematics faculty in the spring of 1959 and his wife had him admitted to McLean Hospital for treatment of schizophrenia that same year. Their son, John Charles Martin Nash, was born soon afterward. The child was not named for a year because his wife felt Nash should have a say in the name given to the boy. Due to the stress of dealing with his illness, Nash and de Lardé divorced in 1963. After his final hospital discharge in 1970, Nash lived in de Lardé's house as a boarder. This stability seemed to help him, and he learned how to consciously discard his paranoid delusions. He stopped taking psychiatric medication and was allowed by Princeton to audit classes. He continued to work on mathematics and eventually he was allowed to teach again. In the 1990s, Lardé and Nash resumed their relationship, remarrying in 2001.

Nash dated the start of what he termed "mental disturbances" to the early months of 1959, when his wife was pregnant. He described a process of change "from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as 'schizophrenic' or 'paranoid schizophrenic'". For Nash, this included seeing himself as a messenger or having a special function of some kind, of having supporters and opponents and hidden schemers, along with a feeling of being persecuted and searching for signs representing Divine revelation. Nash suggested his delusional thinking was related to his unhappiness, his Desire to feel important and be recognized, and his characteristic way of thinking, saying, "I wouldn't have had good scientific ideas if I had thought more normally." He also said, "If I felt completely pressureless I don't think I would have gone in this pattern". He did not draw a categorical distinction between schizophrenia and bipolar disorder. Nash reported he did not hear voices until around 1964, and later engaged in a process of consciously rejecting them. He further stated he was always taken to hospitals against his will. He only temporarily renounced his "dream-like delusional hypotheses" after being in a hospital long enough to decide he would superficially conform — to behave normally or to experience "enforced rationality". Only gradually on his own did he "intellectually reject" some of the "delusionally influenced" and "politically oriented" thinking as a waste of effort. By 1995, however, even though he was "thinking rationally again in the style that is characteristic of Scientists," he said he felt more limited.

In 1961, 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. According to Nash, the film A Beautiful Mind inaccurately implied he was taking what were the new atypical antipsychotics of the time period. He attributed the depiction to the Screenwriter who was worried about the film encouraging people with the disorder to stop taking their medication. Journalist Robert Whitaker wrote an article suggesting recovery from illnesses like Nash's can be hindered by such drugs.

In 1978, Nash was awarded the John von Neumann Theory Prize for his discovery of non-cooperative equilibria, now called Nash Equilibria. He won the Leroy P. Steele Prize in 1999.

At Princeton, Nash became known as "The Phantom of Fine Hall" (Princeton's mathematics center), a shadowy figure who would scribble arcane equations on blackboards in the middle of the night. He is referred to in a novel set at Princeton, The Mind-Body Problem, 1983, by Rebecca Goldstein.

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.

Sylvia Nasar's biography of Nash, A Beautiful Mind, was published in 1998. A film by the same name was released in 2001, directed by Ron Howard with Russell Crowe playing Nash; it won four Academy Awards, including Best Picture.

Nash received an honorary degree, Doctor of Science and Technology, from Carnegie Mellon University in 1999, an honorary degree in economics from the University of Naples Federico II on March 19, 2003, an honorary doctorate in economics from the University of Antwerp in April 2007, an honorary doctorate of science from the City University of Hong Kong on November 8, 2011, and was keynote speaker at a conference on game theory. He has also been 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. In 2012, he was elected as a fellow of the American Mathematical Society. On May 19, 2015, 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.

In 2011, the National Security Agency declassified letters written by Nash in the 1950s, in which he had proposed a new encryption–decryption machine. The letters show that Nash had anticipated many concepts of modern cryptography, which are based on computational hardness.

On May 23, 2015, Nash and his wife were killed in a vehicle 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 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.