The plot alternates between events immediately following the death of Robert (Anthony Hopkins), a brilliant mathematician whose genius was undone by crippling mental illness, and flashbacks revealing the life he shared with his daughter Catherine (Gwyneth Paltrow). Catherine is also a mathematician, but she struggles with living in her father's shadow, with balancing her demanding studies with caring for her father and also with the fear that she may have inherited his mental illness. At home, Robert clings to sanity by constantly bombarding Catherine with complex mathematical problems.