Proof is a movie about a mentally unbalanced mathematician (Anthony Hopkins), based at the University of Chicago, who has, it seems, passed on his genius (and perhaps his madness) to his daughter Gwyneth Paltrow. It’s the old ‘genius = madness’ equation with a genetic inheritance twist. The father was a brilliant mathematician whose genius was crippled by mental instability. Upon his death, Paltrow has to face her fears and emotions via flashbacks with his ghost.
While recognising that his genius, which she seems to have inherited, may come at a painful price, her estranged sister (Hope Davis) arrives to settle their father’s affairs. Paltrow adjusts to the death with the help of one of her father’s former mathematical students (Jake Gyllenhaal), a supportive character who plays the part of a geek rock band member. They enjoy romance and he then begins a search through the father’s notebooks in the hope of discovering a fragment of brilliance. On her advice, he inspects a notebook with a handwritten proof of a ‘prime number’ theorem that may shake the academic world. But there is a possibility it may be the work of the daughter not the father. They were both working on a problem though, in her memories, Gwyneth sees his role as crazy. Indeed she claims the work as her own to the disbelief of others.
The issue: Can the insistence of an unstable young woman be taken as its own proof? Or do matters of trust enter into the picture? This is the human ‘proof’ issue addressed in the film and seemingly more difficult than the mathematics of proof.
It is interesting that Hollywood likes mathematicians (think of movies like Straw Dogs, Rain Man, Drowning by Numbers, Die Hard With a Vengeance, Good Will Hunting, Pi, A Beautiful Mind) . But, in the popular mind, mathematicians are nerds – people of ‘above-average intelligence’ whose interests (in science and mathematics) are not shared by mainstream society. Maybe mathematicians are appealing because they are a bit weird.
If you like Paltrow you will enjoy this film. She provides a moving performance and her fiendishly direct rationality does suggest eccentricity at least. She is the centre of the show. Hopkins does not play a central role and the sister comes on as the tough, not overly-bright New Yorker.
The film is based on a play with the same title by David Auburn which won the 2001 Pulitzer Prize for Drama and the 2001 Tony Award for Best Play. In the play the startling math result is revealled to be a new proof on the infinity of the number of Germain primes although this is not revealled in the movie. Paltrow starred in the play as well.