The math genius is a well-explored Hollywood fixture. From “Pi” to “A Beautiful Mind” to “Good Will Hunting,” there is something strangely compelling about number savants furiously scribbling long strings of gibberish on blackboards. Even more so if they’re crazy.

Bonus points if the madness is hereditary, as it is in “Proof.” Katherine (Gwyneth Paltrow), the long-suffering daughter of a celebrated and very mentally ill mathematician (Anthony Hopkins), finds herself grappling with the possible insanity of her own math genius. It’s more than your typical daddy issue. Katherine all but abandoned her own schooling to take care of him in his sickness, witnessing firsthand the startling tragedy of a crumbling mind. She fears such a fate, and for good reason – her father’s mental decline began in his late 20s, Katherine’s current age. In the wake of his eventual death (from a brain aneurysm, no less), Katherine plummets headlong into mourning – as much for the loss of his mind as it is for the question of whether she will also lose hers.

It’s an operatically emotional process, one that Paltrow really sinks her teeth into. As Katherine, she plays injured to excellence, glaring like a wounded dog at anyone who dares offer a caring hand. This is not a woman who entertains sympathy – not from teachers, not from love interests and certainly not from Claire (Hope Davis, “About Schmidt”), her efficient, businesswoman sister who flies in for the funeral. Claire needs but to recommend her favorite conditioner and Katherine sets in with narrow-eyed ridicule, heartlessly diffusing Claire’s happy praise of jojoba extract with a scrutiny that far overextends the subject.

In fact, Katherine is so mercilessly logical that she’s virtually unrelatable. Like a stubborn kid who repeatedly asks “why,” she won’t accept societal niceties, and it’s only to Paltrow’s great credit that she doesn’t end up coming off as an archetype of sheer belligerence. She whines, glowers and rolls her eyes like a confrontational teenager, yet she remains believable, as caustically unlikable as she is desperate to be respected. Jake Gyllenhaal makes a fair attempt as the requisite love interest, though in the end he’s left with little to do but mince about like a lovesick puppy.

Paltrow’s fine performance should come as no surprise, though – she knows the territory well. “Proof” is a screen version of the recent play by David Auburn, in which Paltrow played Katherine for several months on London’s West End to high praise. It’s that very critically proven source material, however, that ultimately makes the film’s biggest stumbling block – for what might have resonated on the stage falls rather flat on the screen. The careful scene-crafting so crucial to theater gives the movie an over-structured feel; the story is so painstakingly plotted that it’s isolated, even cold.

As a result, the film rings hollow. Directed with little imagination by John Madden (“Shakespeare In Love”), “Proof” hits every expected note of the typical high-art drama. With the exception of Paltrow’s notable character work, “Proof” ends up certainly strong – but, unlike its pioneering protagonists – far from memorable.

Rating: 3 out of 5 stars

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