Parker crackled in the role, showing Catherine to be witty and feisty and still portraying her vulnerable side, but always grounded in her dignity and determination not to be cowed by her overbearing sister, who is played very impressively on screen by Hope Davis. Films should stand on their own, but the memory of Parker comes to mind as a way of defining what is wrong with the film version of David Auburn’s play, even though he collaborated on the screenplay with Rebecca Miller.

Paltrow is so whiny and hysterical that it is harder to imagine her as a math whiz. Also there seems to be less wit and sharpness than I recall in the stage version. “Proof,” directed by John Madden, retains its intellectual bent, but seems toned down from the way it was performed by Parker, with Catherine having given off more intellectual vibes in a much deeper performance than Paltrow delivers.

Anthony Hopkins plays Catherine’s father Robert. Although he is intermittently present, we soon catch on that he has died. This sort of device is easier to pull off successfully on stage where audiences, seduced by the magic of theater, more readily suspend disbelief, as opposed to the realism of film. Still, Hopkins is very good in the part, especially when we pity him for his mental condition in the flashbacks, all the more so because he acts as if he is perfectly sane and on a roll of mathematical discovery. Jake Gyllenhaal is effective as Hal, Catherine’s friend who is skeptical about her discovery and jealous of the possibility that she could overshadow him.