Ron Howard's witless and smarmy 2001 pop-math soap opera A Beautiful Mind (2001) won an Oscar for Best Picture and brought in close to $200 million at the U.S. box office, proving that the subject of mathematics does not equal certain failure at the cineplex. The same year that Howard's driveling effort began collecting its abundant fortunes, David Auburn's play Proof also about pioneering mathematicians struggling to retain their sanity picked up the Pulitzer Prize for drama, further arguing that the science of numbers was not, culturally, a negative integer. However, John Madden's excellent 2005 film version of Auburn's play failed to reproduce A Beautiful Mind's stunning popularity, proving that quality direction, acting, and writing were not necessary components to the equation of success. Gwyneth Paltrow stars as Catherine, the disheveled daughter of a revered math genius (Anthony Hopkins) who changed the landscape of mathematics as a young man and descended into madness and delusion thereafter. Having dropped out of school and forsaken her own promising career to care for her ailing dad during his final five years, after his death Catherine fears that she, too, is losing her grip on reality. Catherine's organized sister, Claire (Hope Davis), arrives for the funeral determined to contain her younger sister's spiraling mood by whisking her away to New York, where she can be more closely monitored. More likely to reconnect Catherine to reality, however, is Harold (Jake Gyllenhaal), a young professor scouring the deceased's largely incoherent papers for scraps of cogent ideas. Unlike the bombastic award-magnet A Beautiful Mind, Proof is intimate, intelligent, efficient, respectful, and honest, aching with pain and glazed with knowing wit. It's a terrific piece of carefully controlled, emotionally charged writing, tightly directed by Madden, and the cast couldn't be better. Paltrow reprises her role from the London stage version and effortlessly inhabits the vulnerable Catherine, whose repressed strengths flail for control of her overwhelming depression. Davis, whose character is initially too stagy, is Catherine's perfect antagonist, always doubting and prodding, but never with malice. Hopkins gives a powerful supporting turn, brimming with brilliance, ego, and embarrassment worthy of haunting Catherine's self-image. Gyllenhaal is eminently sympathetic as an outsider passionately attempting to survive the family drama and faithfully uncover truths that cannot be proven. Despite its meager $7 million domestic box office and dearth of ribbons, Proof is the perfect antidote to its bizarro blockbuster counterpart in showing what beautiful minds can do when they really apply themselves to filmmaking. Buena Vista/Miramax's DVD release includes a terrific anamorphic transfer (2.35:1) with Dolby Digital 5.1 audio. Madden provides a commentary track, and the disc also includes two deleted and one extended scene (with optional Madden commentary), as well as the featurette "From Stage to Screen: The Making of Proof." Trailer, keep-case.