John Madden’s adaptation of David Auburn’s stage play examines the situation of a young woman (Gwyneth Paltrow) living under two long shadows cast by her recently deceased father (Anthony Hopkins). Robert, the father, was a unparalleled math genius and Catherine, the daughter seems paralyzed by the pressure to follow in his footsteps. Robert was also crippled by severe schizophrenia that virtually ended his teaching career and Catherine fears the genetic legacy of her father’s mental illness.
Catherine has been caring for her father for the last several years, neglecting her studies and exasperating both her instructors and her father in his more lucid moments. Her isolated life has left her socially awkward and more than a bit anti-social. You would think that her father’s death would liberate her from the prison she’s created for herself, but in Catherine’s view it only draws the walls in tighter, since it brings her sister Claire (Hope Davis) into the picture.
Claire is something of a control freak, one of those people who thinks everything can be fixed and then proceeds to attempt to fix everything. For someone like Catherine, who simply wants to be left alone, this sort of person is an unwelcome intrusion. Catherine also seems to project onto Claire her fear of her own potential for mental illness. Her paranoia about her sister’s intentions almost seems to be a self-fulfilling prophecy. Catherine’s erratic behavior leads Claire to insist that she come to New York rather than continuing to live in their father’s house, which Claire wants to sell back to the university.
The other player on this stage is Hal (Jake Gyllenhaal), one of Robert’s former graduate students. Catherine distrusts him at first, thinking he’s there just to plunder her father’s work for something he can claim as his own, but he’s likeable and supportive and a bond forms between them based on their common interest in Robert’s theories.
A tug of war starts to build between Hal and Claire and the conflicting impulses they represent within Catherine’s own mind. She always shied away from pushing herself and possibly falling short of people’s expectations for her. The conflict comes to a head when Hal discovers a revolutionary new proof on the nature of prime numbers among Robert’s writings. Did Robert manage to come up with this in one final burst of lucidity? And if he didn’t write it, who did?
While the film’s characters live and work in the rarified world of higher mathematics, the film doesn’t drown us in theoretical minutiae. The focus is on the character of Catherine and what the proof means about her relationship with her father. Gwyneth Paltrow gives a raw, wounded performance as Catherine, showing range that people who only know her lighter work never give her credit for. Jake Gyllenhaal’s Hal is just geeky enough to be believable as a math grad student without being any kind of nerdy caricature. Together they create a rarity among film characters, highly intelligent individuals who are allowed their full range of human flaws. Being super-bright does not solve everything for these people.
Hope Davis’s Claire could have a been a stock villain, who’s only purpose in the story was to stand in the way of Catherine’s goals, but she emerges as a fully realized person whose goals and desires are fully understandable. She doesn’t want to drag Catherine off to New York just to be mean to her sister but because she honestly thinks that it’s for the best.
As Robert, Anthony Hopkins is not given as much to work with as the other actors. His character exists mostly in Catherine’s memory and those memories are occasionally sketchy. We see him mostly as his daughter chooses to remember him, which means we see him in his more lucid moments.
Far removed from the frothy comedy of director Madden’s and Paltrow’s last collaboration, Shakespeare in Love, Proof is highly affecting human drama about taking responsibility for her own gifts and making the best use of your life.