Gwenneth Paltrow plays the daughter of a famous mathematical genius who may, or may not, have written the proof that a certain mathematical theory exists. Sound boring? Not at all! The great performance by Paltrow as a woman lacking confidence in her own potential, and who may be just a little bit nuts, really makes the film. Gyllenhaal plays a sincere and noble love interest who helps her to realise her potential. Davis is believable as the dominating, controlling sister who breezes in telling Paltrow what to do, but is really just jealous of her brilliant sister. If you enjoy films like Good Will Hunting, you will probably enjoy this too.
So this was an enjoyable and well acted film. Hopkins' acting seemed a little stilted in a way which wasn't fully accounted for by the kind of wooden quirkiness which sometimes marks insanity in both films and real life. Yet the film managed to approach the topic of mathematical genius with script which was neither unintelligible nor providing a total cliche of inspirational innovation. What it lacked, however, (and I've no idea if this was inherited from the play), was a true depth and inter-penetration of the key themes of: self-doubt, trust, inspiration, insanity, solitariness, relatedness, care and control. This meant that the characters needed a little more work, background, context, to make their emotional reactions and interactions more compelling, believable and revealing.