Catherine (Gwyneth Paltrow) is a clever yet confused young lady who has given up a seemingly bright future in order to take care of her ailing father, Robert (Anthony Hopkins). Robert is a ‘formerly’ brilliant mathematician who has unfortunately gone somewhat crazy, however this does not make Catherine love him any less. After he dies Catherine's closed off world is interrupted by Hal (Jake Gyllenhaal), a young mathematician who closely followed Robert, and Claire (Hope Davis), her successful sister. Claire has fears that Catherine is too much like their father, a very talented, supremely intelligent person who has unfortunate severe mental problems. The girls know that during the last years of his life, Robert filled over a hundred notebooks with his writings, but one of them, written during a brief period of clarity, could turn the math world on its head, while also threatening Catherine's already uncertain sanity.

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