Factual error: In a scene that takes place in 1956 or 1957, Alicia Nash places an orange Tupperware container in the refrigerator. Although Tupperware first became very popular in the mid-50s, the particular model of Tupperware used in the film was not introduced until the late 60s or early 70s.
Nash is a paranoid schizophrenic. His college roommate(Paul Bettany), his roommate's niece, and the Defense Department agent(Ed Harris) were all imagined. Nash is hospitalized, and undergoes intense experimental treatment with mixed results. In his later years, he's able to control his illness and goes on to win a Nobel Prize for his economic theories.
Nash: In competitive behavior someone always loses.
Charles: Well, my niece knows that, John, and she's about this high.
Nash: See if I derive an equilibrium where prevalence is a non-singular event where nobody loses, can you imagine the effect that would have on conflict scenarios, arm negotiations...
Charles: When did you last eat?
Nash: ...currency exchange?
Charles: When did you last eat? You know, food.
Nash: You have no respect for cognitive reverie, you know that?
Charles: Yes. But pizza - now, pizza I have enormous respect for. And of course beer.
Nash: I have respect for beer. I HAVE RESPECT FOR BEER!
Trivia: When Saul comes to visit John, John plays a joke on him by pointing to an empty chair and saying, "You've met Harvey." This is a reference to a play by Mary Chase titled "Harvey" in which Harvey is an imaginary rabbit seen by the main character.
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