In 1947, John Nash arrives at Princeton University as co-recipient, with Martin Hansen, of the Carnegie Scholarship for mathematics. He meets fellow math and science graduate students Sol, Ainsley, and Bender, as well as his roommate Charles Herman, a literature student.

Determined to publish his own original idea, Nash is inspired when he and his classmates discuss how to approach a group of women at a bar. Hansen quotes Adam Smith advocating "every man for himself", but Nash argues that a cooperative approach would lead to better chances of success developing a new concept of governing dynamics. Publishing an article on his theory, he earns an appointment at MIT where he chooses Sol and Bender over Hansen to join him.

In 1953, Nash is invited to the Pentagon to study encrypted enemy telecommunications, which he deciphers mentally. Bored with his regular duties at MIT, including teaching, he is recruited by the mysterious William Parcher of the United States Department of Defense with a classified assignment: to look for hidden patterns in magazines and newspapers to thwart a Soviet plot. Nash becomes increasingly obsessive in his search for these patterns, delivering his results to a secret mailbox, and comes to believe he is being followed.

One of his students, Alicia Larde, asks him to dinner, and they fall in love. On a return visit to Princeton, Nash runs into Charles and his niece, Marcee. With Charles' encouragement, he proposes to Alicia and they marry. Nash fears for his life after surviving a shootout between Parcher and Soviet agents, and learns Alicia is pregnant, but he is forced to continue his assignment. While delivering a guest lecture at Harvard University, Nash tries to flee from people he thinks are Soviet agents, led by psychiatrist Dr. Rosen, but is forcibly sedated and committed to a psychiatric facility.

Dr. Rosen tells Alicia that Nash has schizophrenia and that Charles, Marcee, and Parcher exist only in his imagination. Alicia backs up the doctor, telling Nash that no "William Parcher" is in the Defense Department and takes out the unopened documents he delivered to the secret mailbox. Nash is given a course of insulin shock therapy and eventually released. Frustrated with the side effects of his antipsychotic medication, he secretly stops taking it and starts seeing Parcher and Charles again.

In 1956, Alicia discovers Nash has resumed his "assignment" in a shed near their home. Realizing he has relapsed, Alicia rushes to the house to find Nash had left their infant son in the running bathtub, believing "Charles" was watching the baby. Alicia calls Dr. Rosen, but Nash accidentally knocks her and the baby to the ground, believing he's fighting Parcher.

As Alicia flees with the baby, Nash stops her car and tells her he realizes that "Marcee" isn't real because she doesn't age, finally accepting that Parcher and other figures are hallucinations. Against Dr. Rosen's advice, Nash chooses not to restart his medication, believing he can deal with his symptoms himself, and Alicia decides to stay and support him.

Nash returns to Princeton, approaching his old rival Hansen, now head of the mathematics department, who allows him to work out of the library and audit classes. Over the next two decades, Nash learns to ignore his hallucinations and, by the late 1970s, is allowed to teach again.

In 1994, Nash is awarded the Nobel Memorial Prize in Economic Sciences for his revolutionary work on game theory, and is honored by