David Auburn’s Pulitzer Prize-winning play “Proof,” like most Pulitzer Prize-winning plays, is better as a play than as a movie. Few things get better when they are removed from their original medium and shoehorned into a different one, after all. But “Proof” is brilliant enough as a play that even if you only capture SOME of the genius on film, as John Madden has done, you’re still left with a pretty good movie.

Auburn wrote the screenplay, too (aided by Rebecca Miller), including a few new scenes aimed at making the film feel, well, less like a play. (More locations, more characters, and so forth.) And Gwyneth Paltrow, who played the lead role in London’s West End, reprises it to great effect here, contributing her best dramatic work since … what, “Shakespeare in Love”? Which was also directed by John Madden? There may be a lesson there, Gwynnie.

Paltrow plays Catherine, the 27-year-old daughter of a legendarily brilliant University of Chicago mathematician named Robert (Anthony Hopkins). Dad has just died after many years of declining lucidity and usefulness, during which Cathy put her own life on hold to care for him, her mother being dead and her sister Claire (Hope Davis) living in New York.

Cathy continues to talk to Robert despite his being dead. Robert points out that this is not a good sign, a joking reference to something Cathy has begun to fear: that she will inherit the professor’s insanity along with his genius for math.

Claire, a well-organized, fussy gal, blows into town for the funeral and is worried about her sister, insisting she come live with her and her fiancé in New York. Does she have reason to worry? Well, Cathy hasn’t done much lately, puttering around the family’s old house and talking to her deceased father. You can’t blame Claire for thinking she might be losing it. But at the same time, Cathy shows an awareness of her situation, the realization that something must be done to get her life in order now that Dad is gone.

Also in the mix is Hal (Jake Gyllenhaal), one of Robert’s students and a budding math geek himself. He has taken the task of sorting through Robert’s notebooks, all written since he officially retired, to see if there’s anything worthwhile — heck, anything coherent — in them. He finds one that seems to include a brilliant new proof, a monumental event if it’s true. But did Robert write it? Or did Cathy?

Madden favors an unadorned storytelling method, letting the words of Auburn’s smart (but not inaccessible) script speak for themselves. The complicated world of higher math is a backdrop for the film, but the core remains the characters and their relationships to each other.

That said, it makes little sense to cast someone like Gyllenhaal as a math nerd, given his physical muscularity and renowned teen-idol good looks. Not to disparage real-life math geniuses, but come on. Next we’ll have Ashton Kutcher as a young Albert Einstein?

Hopkins’ Britishness is a mild distraction at first — what’s a Brit doing as a U of Chicago math professor? — but once you settle into it, you see he’s doing solid, albeit unspectacular, work as Robert (seen in flashbacks as well as in Cathy’s mind). The moment when his mind proves itself to be irreversibly gone is a sad, painful one.

But the central dynamic is between Paltrow and Davis, believable as sisters and both reliable actresses in their own right, especially when given the right material (a luxury that has evaded Paltrow the past few years). Claire’s concern hidden under a layer of efficiency, Cathy’s common sense lost under all that instability — it’s all here in these two very sharp performances. The movie is surprisingly funny but surprisingly tender in its drama, too. It’s no longer playing on Broadway or in the West End, but the movie is a reasonable second-best option.

B (1 hr., 40 min.; PG-13, some brief sexuality, very mild profanity; a very 'soft' PG-13.)