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In 1947, mathematics graduate students at Princeton University are reminded that mathematics built the atomic bomb and won the war, and now needs brave, publishable advances. Entering student John Forbes Nash, Jr. takes the admonition to heart and immediately alienates his competitive classmates, Martin Hansen, Ainsely, Bender and Richard Sol, by declaring that they have yet to produce any innovative ideas. Throughout the term, John sequesters himself with his studies, often scribbling formulae on his dorm window. One day, John's personable British roommate, Charles Herman, convinces him to take a break, and John admits that work is all he has in life. Weeks later, after John spends forty-eight hours straight in the library tracing the algorithms of pigeons and footballers on the windows, Charles encourages him to visit the local bar. There the other students challenge John to approach a blonde co-ed, but she responds to his disconcertingly direct proposition by slapping him. Soon after, Professor Helinger warns John that his lack of progress and refusal to attend classes are jeopardizing his future placement, and points out a professor in the faculty room receiving pens from fellow teachers, an honor bestowed for "the achievement of a lifetime." John's dismay is tempered only after Charles throws his desk out the window, and they both break down in laughter. Later at the bar, while analyzing the most expedient way to win over a blonde, John formulates an idea that leads to a breakthrough paper on game theory, and Helinger awards him a position at the Wheeler Laboratories at "MIT," the Massachusetts Institute of Technology. There, Bender and Sol work as his assistants while John gains fame as one of the most promising scientists of his time. In 1953, Pentagon officials call on John to break a Russian code, and his brilliance attracts the attention of government agent William Parcher. Later, John reluctantly teaches a class at MIT, where student Alicia Larde impresses him with her resolve and intelligence. Parcher then visits John's office and reveals a vast secret workforce defending America against Russian-held bombs. After implanting an identifying radium diode in John's arm, Parcher engages him to scan American publications for embedded codes. Soon after, Alicia asks the shy professor on a date, and he brings her to a governor's ball, where he charms her by showing her how to trace shapes against the stars. Over the next few weeks, he leaves envelopes of deciphered codes in a secret drop box for Parcher and dates Alicia, who responds favorably to his direct approach. John grows nervous about his secret work, seeing men in the shadows, but is cheered when one day Charles visits with his new charge, his orphaned niece Marcee. That night at dinner, John asks Alicia for empirical evidence of love, which she says takes the same kind of faith as does believing that the universe is infinite. They marry, and at the wedding, John spots Parcher watching from a parked car. One day in 1954, John drops off a package, and this time Parcher speeds up, commanding him to get into the car. They are chased by Russians, whom Parcher eventually kills, leaving John shaking in terror. He later tells Parcher that the work is too dangerous, especially as Alicia is now pregnant, but Parcher threatens that if he quits he will be killed, and John grows increasingly paranoid. At a conference, John is pleased to see Charles attending, but during his speech, he sees men in black suits and flees in panic, then is trapped outside and drugged. He awakens in a psychiatric hospital run by Dr. Rosen, but John believes the psychiatrist is a Russian interrogator and that Charles has turned him in. Rosen reveals to Alicia that John suffers from schizophrenia, a hallucinatory mental disorder, and that neither Charles, Marcee nor Parcher and his whole department exist. Uncertain, Alicia insists on gaining entry to John's office, and is shocked to find it in chaos, with scribbled-on magazine pages tacked to every surface. Following a tip from Sol, she finds the drop site and discovers dozens of John's envelopes sitting untouched in a mailbox. When she tries to inform John of his delusions, however, he turns away, afraid that she is part of the conspiracy against him. After John tears his arm apart looking for the implant, Rosen prescribes an intensive regimen of insulin shock therapy. A year later, the Nashes move to Princeton, where John's medication reduces his ability to reason, care for their son or have sex. Alicia grows depressed and frustrated, and in response, John stops taking his pills. Soon Parcher reappears, urging John to continue his work in the barn, and when one day Alicia discovers the barn walls covered with paper, she realizes that John is sick again and barely saves the baby from drowning in the bath John is drawing for him. When she calls Rosen, Parcher, Charles and Marcee command John to stop her, and after he pushes her down, Alicia runs away in fear. A stricken John races out to Alicia's car, but when she stops, he tells her that he has realized that Marcee never ages, and thus cannot be real. Although Rosen later advises them that schizophrenia is degenerative, John and Alicia agree to work together to find a solution not reliant upon medication. Hoping that a familiar community will help him chase away his delusions, he returns to Princeton, where Martin now heads the math department, and awkwardly asks his former rival to allow him access to the campus resources. Martin agrees, even after some minor stress causes John to have a breakdown outside the library, during which Parcher reviles him for his cowardice. Over the years, John continues to work and manages to ignore Parcher, Charles and Marcee, who nonetheless always remain nearby. Although most of the students ridicule John, one day in 1978, student Terry Kellum approaches him with a theory, and soon after, Alicia is proud to see John surrounded by students in the library. Martin agrees to allow him to lecture, and by 1994 he is a popular teacher. In March, Thomas King visits to inform John that he is being considered for the Nobel Prize in economics. King, who is there to ensure that John is competent enough to receive the award, insists on eating in the faculty room, and John reluctantly agrees. There John is shocked and pleased as, one-by-one, the other professors place pens at his table in honor of his achievements. In Stockholm, Sweden, John accepts the 1994 Nobel Prize in economics, and in his speech states he has discovered that "only the mysterious equations of love hold logic." After crediting Alicia with his accomplishments, John escorts her home, with his demons accompanying them.