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Ha! Unmarked math puns! (Or, well, one. It's in the Windmill Crusader spoiler.)
This film was my introduction to the concept that the visual part of a film — the part we see — could have an Unreliable Narrator.
Let me explain. Since this film is Inspired by... a true story, it was decided that my first viewing of this film would be with the DVD Commentary instead of the main soundtrack. This didn't last long. The commentator started talking, when Charlie first appeared, about Nash's hallucinating him. Mind you, when Charlie first appears, if you go into this film unspoiled, there is no hint that he is anything less than real.
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How well does it match the trope?