Trivia: Right at the end, in fact the very last frame, you can see a face in the snow as the shot fades out.
Trivia: There are more than a few Hitchcock references in this movie. Most notably Harrison Ford's character - Norman (Psycho), suspecting the neighbour of murdering his wife (Rear Window), Michelle Pfeiffer falling in the shower and pulling the shower curtain down with her (Psycho). There are many others if you watch for them.
Trivia: When Claire goes to Madison's house, there is a framed picture of Madison and underneath it, there is a newspaper clipping from "The Guardian" that is very prominant. This certainly signifies what Madison was to Claire.
Trivia: There are quite a few close-up scenes filmed through glass, on the floor, with the camera on the bottom side and the actors on the top side. For example, when Claire is paralysed, Norman bends down and talks to her before picking her up and carrying her upstairs - when they are downstairs, Claire is lying on glass with the camera filming her from below.
Chosen answer: Spencer's theorem was Norman's father's theorem. Norman wants to be greater than his father was, so to be accidentally complemented on something that his father did would be bad enough. To say that the guy knows that his father is dead is to imply that the guy probably insulted him intentionally.
Myridon