Starring Gwyneth Paltrow, Anthony Hopkins, and Jake Gyllenhaal. Rated PG. Opens Friday, September 30, at the Cinemark Tinseltown and the Park Theatre

Math geeks and theatre buffs can rejoice, in their tweedy way, at the arrival of Proof, yet another Quality Product that revels in the life of the mind without actually causing the audience to use too much grey matter.

In this version of David Auburn's Pulitzer Prize-winning play, adapted by the author and Rebecca Miller, Gwyneth Paltrow impressively plays Catherine, a kind of numeral-happy Sylvia Plath having trouble finding her place since the death of her famous mathematician father (Anthony Hopkins). Her dad is such a force of nature he refuses to leave her alone even after he's buried. It turns out that the old man was long ensconced at a big old house on the campus of a Chicago university (although interiors were shot largely in the U.K.) through the years of his declining mental health.

"I believe you have some of his talents," says Catherine's pushy older sister (a misused Hope Davis), "and some of his inclinations towards instability." As movie lines go, it's not exactly up there with "put your lips together and blow", but the filmmakers feel strongly enough about its encapsulation of their main theme to put it in the trailers.

From what we can see, this skinny, surly gal could use some prime rib before tackling another prime number, but she has inherited a dizzying fixation on sums. Eventually, she finds some red meat in the form of Hal (an okay Jake Gyllenhaal), a grad student ready to plow through her dad's many nutty-looking notebooks, and maybe through Catherine herself, to get to some undigested math nuggets. Naturally, our heroine isn't quite ready to give up her tatty cardigans to reenter a life outside the mind, so there's quite a bit of fighting about people's motivations, integrity, intellect, and other things that don't really matter to most people who buy popcorn.

There are a few interesting issues raised here, especially in the implications of a young woman in an old-boy's world. But like Hopkins's character, these are not really developed past what's needed to set a problem in motion. And, in the end, the approach of John Madden-who also directed Paltrow in the London run of Proof-doesn't do more than chalk this problem on the board. We're supposed to marvel at the sheer smartness of it, but there's no sense that anyone has really done the math.