Once upon a time, Catherine (GWYNETH PALTROW) was a promising if unfocused mathematician who seemed likely to follow in the footsteps of her brilliant father Robert (ANTHONY HOPKINS). Yet, when he eventually slipped into progressively worsening dementia, she gave up everything to care for him in his Chicago home, always worried that she might have somehow inherited his mental condition.
Now that he's recently died, her mental state has only worsened. Compounding the matter is that Robert's former student and now teacher Hal (JAKE GYLLENHAAL) wants to go through his mentor's prolific if mostly deranged writings in hopes that there might be some mathematical nugget hidden somewhere among the nonsense.
When Catherine's efficient sister Claire (HOPE DAVIS) arrives from New York wanting to help her settle their father's estate, things only become tenser. With the discovery of a potentially groundbreaking mathematical proof, Catherine claims that it's actually hers. Yet, as the others question that claim, she only sinks deeper into questioning her own sanity, all as she recalls her previous interactions with her father.