This probably won’t come as a huge surprise, but I was never all that good at math in high school or college. Not that I was bad, not to toot my own horn but I could manage a high “B” to a low “A” if I put my mind to it, it was just that the subject never completely held my interest. It was okay, I guess, I just personally got far more excitement out of reading Grapes of Wrath or researching the murderous exploits of French revolutionary Robespierre.

So I’m not shocking anyone by saying an enigmatic time-jumping love story mystery about mathematical proofs might not be at the top of my must-see list. But that’s exactly what the long-delayed “Proof” (another Miramax entry being thrown out of the vaults) is, and as such it is most definitely a highbrow unabashedly intellectual puzzle box full of secrets, lies and sometimes annoyingly cranky binds tying families together. But whereas in math anything that is unknown can be theoretically solved by using the right combination of numbers, life isn’t so easy to negotiate. Many of the things we hold dear; love, friendship, even sanity; cannot be proved they can only be felt, the solution to whether they are true or not resting in some unknown crevice of the human heart.

Those are some of the problems vexing Catherine (Gwyneth Paltrow). The daughter of famous mathematical genius Robert (Anthony Hopkins), Catherine not only has his funeral to prepare for, but also the arrival her estranged busybody older sister Claire (Hope Davis). If that wasn’t enough, budding mathematician Hal (Jake Gyllenhaal) is rummaging upstairs, going through all of her father’s notebooks in furious search of the next great numerical advance. To top it all off, it’s her 27th birthday, and as it begins the young woman is starting to think she might be going insane.

Why? Well, because for all of Robert’s brilliance his faculties had departed at far too early an age and he was, for lack of a better term, crazy. That’s why the notebooks upstairs are such a mystery. Who knows what mad mathematical thoughts were running around his noggin’ before he died? But then, that’s the worry, too, because Catherine was the one that dropped everything to take care of their father, living day in and day out with his wavering mental state. Worse, what Robert had is hereditary, and Claire suspects her younger sister might be going as nuts as dear old dad. The thing is, it might not be madness but brilliance that Catherine has inherited, but the only way to prove that isn’t through numbers, but through the heart.

Based on the Pulitzer Prize-winning play by David Auburn, and working from a screenplay by Auburn and Rebecca Miller (“The Ballad of Jack and Rose”), John Madden (“Shakespeare in Love”) has crafted a picture that’s every bit as vexing as it is intoxicating. At times dry, stilted and strangely bland, it also has moments where it takes off into the stratosphere, unleashing torrents of emotion and heart so strong most other pictures would kill to have it. It doesn’t work, at least not completely, but it resonates strongly in both the heart and in the head leaving plenty to think about and ponder long after the curtain closes.

I find it interesting that Paltrow has given her best performances under Madden’s direction. But were she was sunny and full of rapturous life in “Shakespeare in Love,” here’s she’s a tortured mess unsure of her own sanity. Paltrow looks worn and haggard, the pain of caring for her father and putting her own dreams on hold making the young woman look far older than her 27 years. But when she does smile, when Catherine actually does take the time to give into hope, the moment is blissful, Paltrow shimmering like the morning’s first rays of sunshine sparkling in the morning dew.

Not that the rest of the cast doesn’t hold their own. If anything, this is the first time I can recall Gyllenhaal staying so positive and upbeat, smiling even, for an entire picture. Davis is also good providing a wonderful counterpoint to Hal narcissistically beating her sister down and refusing to believe genius could strike twice inside her own family. Only Hopkins falters, overplaying his hand time and time again until I just didn’t care if he was insane or not, happy when he finally disappeared and left the picture for good.

Speaking of insane, Madden over-directs himself into a corner and as consistently reliable a filmmaker as he is (“Captain Corelli’s Mandolin” and “Golden Gate” notwithstanding) this is a great surprise. But the elliptical structure of Auburn’s play eludes him, Madden’s ability to maintain focus through shifting time and place a little beyond his reach. He also can’t quite escape the staginess of the story, too many scenes feeling as if they were filmed on an Off-Broadway stage and not on a Hollywood set.

What Madden does know, however, is drama and director manages to pull the heartstrings magnificently every time he has to. For me, two scenes stick out allowing elevating “Proof” to grand levels. The first comes during the late-night party for Robert where Catherine actually allows Hal to open up her heart a little and finally start living. The next comes the following morning upstairs in her father’s study, both Claire and Hal heartbreakingly unable to find it within to believe Catherine when she most needs them to.

It’s scenes like these that make the movie so perplexing. For one scene that bores that is one right after that soars. If there is a moment that just doesn’t quite cut it there will be one just a few beats latter that’s Oscar worthy. The only constant in all of this is Paltrow, so good it’s hard to imagine another actress making the part their own so easily (but then, I never saw Mary-Louise Parker do this on Broadway so maybe I’m wrong). I guess, in the end, “Proof” is just like the mystery at its core, only in its case I’m not exactly sure its problems are going to be ones audiences are going to want to take the time to solve.

Film Rating: êê1/2  (out of 4)