Continuity mistake: The second time Nash sees his old roommate's niece he drops his briefcase to hug her. A couple of shots later as he is walking away, his briefcase is back in his hands, without him having picked it up. Later in the film we see him from another man's point of view, and he is kneeling down, stroking the face of a girl who isn't there. He moves like he's really interacting with the imaginary people, so it can't be that he never really dropped his case.
Factual error: The scenes where Nash is home, recuperating, feature a radio that he listens to, first on the porch, then later in his den. The timeframe, according to the movie titling, is 1956, whereas the radio is a transistorized Zenith TransOceanic (Royal 1000), introduced in late 1958.
Factual error: At the Nobel Prize Ceremony, Nash is giving a speech. During a wide-shot right before he leaves the stage, you can see a few girls wearing white military style caps (to the right of the screen). Hats are in fact worn by Swedish students at the Nobel Prize Ceremony, however the style is completely different. The caps should have a much smaller, soft crown and not the wide crown of a military hat.
Continuity mistake: During Nash's first lecture at Wheeler Labs, he writes a mathematical problem on the blackboard. However, you can see that the dimensions of spaces change between shots - first there is R^3, then R, and finally R^3 again.
Factual error: John Nash enters Princeton as a graduate student (Ph.D.) candidate in 1947. By that time the Graduate College had already been built (1913) and is about three miles from the main campus. At that time, all graduate students had to live at the Graduate College building, and not where Nash is shown living with his imaginary roommate at the center of campus.
Answer: There was always a basis of reality for his delusion. As I recall it, early on, Nash was actually recruited by the Pentagon to study encrypted telecommunications of foreign enemies. Nash's association with the government appears to have been limited, but it became a springboard for his extreme fantasy of working for the U.S. Department of Defense and with the unreal Agent Parcher.
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