The entire film was filmed in sequence. Meaning that each shot you see in the movie is the order in which the filmmakers filmed it. This is unusual for films as filming in sequence can be very inefficient, as the filmmakers have to keep revisiting the same sets and setting them up more than once rather than just filming all their scenes while they have the set ready for it.
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Quotes
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!
Mistakes
Near the end of the movie, when Prof. Nash goes back to Princeton, he is wearing a checkered brown and green shirt. The next day, he is wearing a light blue shirt, but when the scene changes, he is wearing the brown with green shirt again. See more...
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Directed by Ron Howard, starring Adam Goldberg, Christopher Plummer, Ed Harris, Jennifer Connelly, Judd Hirsch, Paul Bettany, Russell Crowe (add more)
The entire film was filmed in sequence. Meaning that each shot you see in the movie is the order in which the filmmakers filmed it. This is unusual for films as filming in sequence can be very inefficient, as the filmmakers have to keep revisiting the same sets and setting them up more than once rather than just filming all their scenes while they have the set ready for it.
Another indicator that the people weren't real: The little girl runs among some pigeons on the ground and none of the pigeons fly off.
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.
As mentioned in the errors, Nobel Prize winners do not make an acceptance speech. In the DVD commentary the directors acknowledge this, but state that they wanted one for the dramatic benefit of the film. Still a mistake, but there's why.
Paul Bettany and Jennifer Connelly are married in real life.
According to a 2001 Entertainment Weekly (American entertainment magazine) article on this film, the filmmakers originally wanted to mention Nash's homosexuality, but they feared the film will make the wrong connection between homosexuality and schizophrenia, so they abandoned it. This connection, according to the article, was based on several now-discredited psychological studies that first appeared in the late 1950s.
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