How do you convince someone of your superior intelligence when they lack the capacity to understand it and prefer to think of you insane?

Catherine (Gwyneth Paltrow) is having trouble coming to grips with the death of her father (Anthony Hopkins), a once-brilliant mathematician widely recognized in his field who later succumbed to dementia. With one of her father’s ex-students (Jake Gyllenhaal) pilfering through his old papers and her sister Claire (Hope Davis) trying to purge her father’s memory along with his property, Catherine has a fearful secret that might prove she has inherited her father’s genius, her father’s insanity, or both.

Who knew Gwyneth Paltrow could play haunted and tortured? Okay, everyone who’s seen any of her movies knows, but it isn’t hard to see why she’s perfect for the role of Catherine even if she sleeps through the part. And it isn’t the first time she’s played the part; the theatrical version of “Proof” ran in London’s West End in May and June of 2002 to positive buzz. It also shouldn’t be any surprise that the show’s director, John Madden, directed the stage version as well as Paltrow once before in Shakespeare in Love.

While the story itself sounds like a sequel pitch for A Beautiful Mind, Paltrow plays Catherine as someone fearful of making decisions for herself, a willing depressive rather than a raving lunatic; it works. Hope Davis plays her condescending, list-obsessed (let’s just say it: evil!) sister who was perfectly content letting Catherine care for their father but wouldn’t be above committing him to a home as she didn’t have to be personally involved with the day-to-day interruptions of her own life. Jake Gyllenhaal keeps everyone guessing as to what his true intentions are (contributing to Catherine’s mental state) while Sir Anthony Hopkins appears mostly in flashback, simultaneously filling the roles of father, mentor, and charge for Catherine.

While complex, cosmic-influencing mathematics are merely background (and the source of amusement at the expense of stereotypical intellectuals everywhere), the story escapes the Good Will Hunting melodrama of by centering everything around Catherine finding her place among family, friends, and fulfillment. Proof pushes the story beyond a mere romantic entanglement for a solitary woman and into one of finding a direction and the confidence to pursue it once it’s found; if a relationship happens to be part of the equation to achieve human fulfillment, so be it.

(a three skull recommendation out of four)