John Nash arrives at Princeton University as a new graduate student. He soon becomes best friends with his roommate, Charles. Nash admits to Charles that he is better with numbers than people, which comes as no surprise to them after watching his largely unsuccessful attempts at conversation with the women at the local bar.
Nash is seeking a truly original idea for his thesis paper, and he is under increasing pressure to develop his thesis so he can begin work. A particularly harsh rejection from a woman at the bar is what ultimately inspires his fruitful work in the concept of governing dynamics, a theory in mathematical economics.
Five years later while teaching a class on Calculus at MIT, he places a particularly interesting problem on the chalkboard that he dares his students to solve. When his student Alicia Larde comes to his office to discuss the problem, the two fall in love and eventually marry.
On a return visit to Princeton, Nash runs into his former roommate Charles and meets Charles young niece Marcee, whom he adores. He also encounters a mysterious Department of Defense agent, William Parcher. Nash is invited to a secret United States Department of Defense facility in the Pentagon to crack a complex encryption of an enemy telecommunication. After being chased by the Russians and an exchange of gunfire, Nash becomes increasingly paranoid and begins to behave erratically. After observing this erratic behavior, Alicia informs a psychiatric hospital. He views the officials of the psychiatric facility as Soviet kidnappers.
When confronted with this evidence, Nash is finally convinced that he has been hallucinating. The Department of Defense agent William Parcher and Nash's secret assignment to decode Soviet messages was in fact all a delusion. Even more surprisingly, Nash's friend Charles and his niece Marcee are also only products of Nash's mind.
After a painful series of insulin shock therapy sessions, Nash is released on the condition that he agrees to take antipsychotic medication. However, the drugs create negative side-effects that affect his relationship with his wife and, most dramatically, his intellectual capacity. Frustrated, Nash secretly stops taking his medication and hoards his pills, triggering a relapse of his psychosis.
Caught between the intellectual paralysis of the antipsychotic drugs and his delusions, Nash and Alicia decide to try to live with his abnormal condition. Nash consciously says goodbye to the three of them forever in his attempts to ignore his hallucinations and not feed his demons.
Though Nash still suffers from hallucinations and mentions taking newer medications, he is ultimately able to live with and largely ignore his psychotic episodes. He takes his situation in stride and humorously checks to ensure that any new acquaintances are in fact real people, not hallucinations.
Nash eventually earns the privilege of teaching again. He is honored by his fellow professors for his achievement in mathematics, and goes on to win the Nobel Memorial Prize in Economics for his revolutionary work on game theory.
