Other mistake: When Nash is put into the car and is being taken away to the hospital, there is a line of people watching him drive away. Two of the spectators are the imaginary roommate and the little girl. They are standing in front of rest of the spectators. As the car is driving away you see a female student look around the imaginary roommate to see the moving car. If the roommate can only be seen by Nash why did she need to look around the roommate to watch the car drive away?
Real-life mathematician, John Nash (Russell Crowe) was branded at an early age as a genius. After winning a prestigious scholarship to Princeton University, he develops his ultimate theory "Governing Dynamics." This earns him a professorship/research position at MIT. There he meets his future wife, Alicia (Jennifer Connelly) who is not only both bright and beautiful, but who loves him deeply. Meanwhile, he is called upon to serve his country in a secret mission, but the task takes an emotional toll on him.
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!
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