John Nash begins graduate school at Princeton in 1947, having received a prestigious scholarship for his mathematical genius. He’s annoyed to find he’s been given a roommate, literature student Charles Herman, despite having requested a private dorm, but over time the friendly and gregarious Charles grows on him. This pays off when Charles gets John to break out of his obsessive attempts to create a new form of economic theory and take a break at the local bar with some other students, in which applying the accepted economic theories to strategy in picking up girls causes him to realize there’s a better method and eventually create a groundbreaking new game theory.
John’s theory gets him a teaching job at MIT, where he’s especially impressed by his student Alicia Larde who demonstrates her lateral thinking skills in solving the problem of noisy construction outside the classroom. She eventually asks him out, and John also runs into Charles again, now raising his niece Marcie after her parents’ death. With Charles’ encouragement John proposes to Alicia who happily accepts, but he’s still unsatisfied with his job and questions if he’s making any difference in the world. This problem is also soon solved when he’s approached by William Parcher from the Department of Defense, who asks for his help in breaking Soviet codes to stop an imminent bomb attack.
As the mission continues with John searching for codes in newspapers and magazines, it also becomes more personally dangerous until Parcher forces him into a car chase with Soviet agents, and blackmails him into continuing to deliver his reports. Finally, he suspects more Soviets have tracked him down while presenting a speech and abruptly flees, only to quickly be caught and tranquilized.
John wakes up in a strange room where an old man introduces himself as Dr. Rosen. He also spots a shame-faced Charles in the corner and furiously accuses him of betraying him to the Soviets, only for Rosen to deny there’s anyone else in the room. It was actually Alicia who called Rosen after getting worried by John’s increasingly strange behavior, and Rosen diagnoses him with schizophrenia, with Charles, Marcie and Parcher all just figments of his diseased mind. John refuses to believe it at first, but when Alicia finds all his reports still at the drop spot unopened, he agrees to start treatment with electroshock therapy.
John continues taking medication, but quickly becomes unhappy with how the pills fog his mind and make it impossible to do his work, or even have sex. He stops taking them, and is soon seeing Soviet codes again and is even approached by Parcher who says Rosen really is a Soviet agent trying to stop him from finding the bomb. Charles and Marcie also appear, and Alicia eventually discovers his stash of pills and finds he’s left their baby alone in the bathtub, to which he claims Charles was watching him. Alicia starts to call Rosen, leading Parcher to arrive and put a gun to her head. John moves to save her and ends up violently knocking her and the baby to the floor, causing her to flee to their car and start to leave for good. However, John takes another good look at everything going on, and stops Alicia from leaving with his declaration that Marcie has never aged in the years he’s known her, and thus she and the others really are just in his head.
Despite accepting the truth of his schizophrenia, John refuses to go back on his meds and begins the long, hard process of overcoming his illness by sheer force of will, saying an emotional goodbye to Charles, Marcie, and Parcher. After enduring two decades of mockery and difficulty in thinking straight, he finally recovers enough to be allowed to teach again. In 1994 he’s presented with the Nobel Prize in Economics and devotes it to Alicia in his acceptance speech, saying “I’m only here because of you.” He takes one last look at the three imaginary figures, still lurking in his vision despite his refusal to acknowledge them, before heading back home with Alicia and their son.
