In addition to inspiriting the classics with her warm breadth of intelligent characterization, such as in a movie derived from the bard, Shakespeare in Love, Gwyneth Paltrow has demonstrated her ability, if not proclivity, for the super-intelligent subject. After her accomplished researcher in 19th century literature for her 2002 pic, "Possession" (only 4 movies ago), she does it now for theoretical math, and she pulls off the illusion of an advanced mind well enough. Or, is it an illusion?

Catherine (Paltrow) is an enigmatic woman living with and caring for her genius of a father Robert (Anthony Hopkins) who, in his late twenties, wrote a theorem that set the math world on its ear. Now, after a stroke and mentally unstable, the professor is cheerless and difficult with intermittent moments of clarity. The dutiful daughter dedicates her life to his care, a strain that leads to forms of depression as well as to her own mathematical secrets. When Robert dies, the strains she's been under take new forms.

While Robert's assistant and former student Hal (Jake Gyllenhaal) respects and admires Catherine, and searches among his mentor's notebooks for the possibility of hidden work of high value, Catherine is less than trusting about his motives. Above all, she's foundering in a sea of confusion after being cut loose from her dad, her anchor. Haunted by his lingering influence, her harbor of refuge is confrontation while she sorts sorrow out from fear.

In the meanwhile, she's enigmatic and incapable of sound judgement. Her training as a mathematician and its demand for complete objectivity is swamped by the overriding power of her emotions, including the sexual tension that hangs over encounters with Hal. In this state of mind, she's quick to misjudge Hal's motives and rejects his advances. But hasty emotional reactions slowly give way to the reasoning of her intellect and she comes to realize her fears for what they are--a transition that Paltrow delivers skillfully.

Less respectful of Catherine and her potential is sister Claire (Hope Davis) who has arrived for dad's funeral and with an agenda to "improve" Catherine's life. Nothing to her is sacred, not her father's house, not Catherine's preferences, and certainly not her sister's romantic involvement.

When that romance flowers into a consummation, Catherine musters enough trust in Hal to give him the key to an upstairs drawer in which a certain notebook has lain locked and ignored for years. In it, Hal discovers a formula for what may be the next whole evolution in math theory. "You knew about this?" she's asked in a three way confrontation. "Yes," she replies. "When did you discover it?" Catherine ponders the question for a moment. "I didn't discover it," she says... "I wrote it."

This brings the curtain down on act one in a movie based on David Auburn's play "Proof" premiered at the Manhattan Theater Club in May, 2000 before it went to Broadway. It became the longest running play there since "Amadeus" and, Paltrow played it in a production on London's West End. The movie brings it alive with enough skill and scope to conceal its stage origins. Giveaways include a cast essentially limited in number and a similarly limited number of major sets. But one can easily take it for the reasoned and intelligent movie that it is.

Which shouldn't suggest it's without its difficulties. Hopkins tends toward the overly theatrical in his articulation of the grand man enfeebled, the genius who has "lost it" and who imagines he can reattain it. Paltrow, while playing somewhat lost and unstable herself, fulfills the enigmatic pattern of her character with suitable mental drift and depression. But it's so sustained a note that sympathy for the ambivalence of her mental state is strained. Strained, but not quite demolished.

In the other spectrum, Davis is pitch perfect as the coldhearted sister, so sure of her own correctness and the total negation of another person's individuality and choice. Her rendering of the family villain can't be faulted. Hsssss.

Gyllenhaal is delightful, cool, cute, warmly insistent and supportive, a cuddly leading man. Females in the audience are likely to want to throw their arms around this charming rescuer of genius theoreticians.

A few theatrical devices linger and could be the cause of bother, as they were for me. [Warning: Don't read the rest of this paragraph if you haven't yet seen the picture.] When Catherine ends her funeral oration about her dead father by proclaiming that she's glad he's dead, it comes off as an over-the-top stage device. How does she mean it? Does she regret saying it? If she truly feels that way, is it likely to change when the immediate grief subsides? With these questions left unanswered, one can only carry away the feeling that this is a writers trick to get attention as the final act approaches. A curtain dropping exaggeration.

But after all that is said, I add that the movie is, for a prime audience, quite splendid in dramatizing an esoteric and brainy subject--and it engages you without testing your knowledge of math theorems. Is Catherine the genius daughter of a genius? There's more than one proof being called for here and Proof proves it can raise the questions. I'll take a dramatization of math theory over a sports movie anytime, but that's just me.

                                      ~~  Jules Brenner