A lot of talent and energy have gone into this adaptation of David Auburn’s play about the charged relationship between a troubled young woman (Gwyneth Paltrow) and her father (Anthony Hopkins), a brilliant but mad mathematician. As in many Miramax pictures, the source material has undergone some sentimental softening, though Hope Davis, as the heroine’s sister, does a swell job of making sanity seem obnoxious. It’s set and partly filmed around the University of Chicago, and John Madden directs the actors with sensitivity. Auburn and Rebecca Miller collaborated on the script. With Jake Gyllenhaal. PG-13, 99 min. (JR)