A young woman (Gwyneth Paltrow) fears that her late father (Anthony Hopkins), a brilliant mathematician, may have passed on to her not only his genius, but also the madness that blighted his declining years. Director John Madden’s film is an emotionally rich, intellectually exciting throwback to the days when Pulitzer Prize-winning plays routinely were made into movies. (Nowadays, Hollywood prefers to leave Broadway plays, with or without prizes, to PBS and cable television.) This one, adapted from David Auburn’s play, has a smooth script by Auburn and Rebecca Miller that only moderately opens up beyond the original four characters. Madden gets excellent performances from Jake Gyllenhaal as one of Hopkins’ former students and Hope Davis as Paltrow’s bossy sister, and a superb one from Paltrow herself.