Proof is the story of a famous mathematician's daughter, Catherine (Gwyneth Paltrow), trying to cope in the days after his death. She was also a math student, but dropped out of school when her father couldn't be left alone when he got more and more sick with schizophrenia. She seemed to have the same unorthodox methods of attacking mathematical proofs as her father (Anthony Hopkins); they both snuck around and took the back door instead of using popularly accepted methods.
After her father's death, she is afraid that she has inherited her father's illness. Catherine's out-of-touch sister sweeps into town for the funeral and gets too involved after years of not being involved enough. One of his father's grad students also enters the scene (Jake Gyllenhaal). He asks her permission to read through over 100 notebooks that her father complusively filled with proofs. He is hopeful that in his three years of illness, there were glimpses of lucidity where he might have written something important. The father worked obsessively on his notebooks, and believed he was producing groundbreaking scholarship, but his reality was severely skewed. In a heartbreaking scene that shows no doubt of her father's illness, her father forces Catherine to read aloud his new proof about which he is very excited:
"Let X equal the quantity of all quantities of X. Let X equal the cold. It is cold in December. The months of cold equal November through February. There are four months of cold, and four of heat, leaving four months of indeterminate temperature. In February it snows. In March the Lake is a lake of ice. In September the students come back and the bookstores are full. Let X equal the month of full bookstores. The number of books approaches infinity as the number of months of cold approaches four. I will never be as cold now as I will in the future. The future of cold is infinite. The future of heat is the future of cold. The bookstores are infinite and so are never full except in September..."
"Proof" was a play that Paltrow performed in London. Like Niel Simon's "The Goodbye Girl" adaption to screen, I like the tight dialogues, minimal scene changes, and economic storytelling. I was surprised by how much I liked this movie. I had read reviews that were lukewarm, saying it fell flat, but I didn't find that. Gwynnie was great. Her character was so angry. And Gyllenhaal played a great geek-chic grad student. For a long time, I wondered if I had a girly crush on this actor. When I wasn't watching him on-screen, I never thought he was all that great, but when I'm watching him, I'm always smitten. He has a great way of being present in a scene, but not out-shining other players. (I almost called him "The Gyllenhaal," but only The Clooney is great enough to be referred to with an article. Gyllenhaal gets no article. He's on the same greatness level as Depp. Depp and Gyllenhaal.) Anthony Hopkins was Anthony Hopkins. He sparkles in an Anthony Hopkins way. I am at a loss to describe him.