PROOF

US, 2005, 99 minutes, Colour.
Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, Hope Davis.
Directed by John Madden.

Films about mathematics, especially at university level, are not the first titles that come to mind in wondering what would be most popular at the box-office.

However, during the 1980s, there was an interesting and challenging film about difficulties in schools in Hispanic East Los Angeles. The subject being taught was calculus. The film was Stand and Deliver with Edward James Olmos as a dedicated teacher who wanted to improve standards and possibilities in life for his students. It turned out to be quite popular.

More recently, a film about mathematics and the nature of intellectual genius won the Oscar for Best Film and was seen by millions. This was Ron Howard’s biography of Nobel Prize-winner, John Nash, memorably played by Russell Crowe. While there were many maths sequences, there was a great deal of plot beyond the maths. John Nash was diagnosed as schizophrenic. He lived part of his life in an interior world populated by espionage and code breakers as well as imaginary friends who dramatised other facets of his personality.

Proof is more in this vein.

It is based on a successful play by David Auburn which won awards on Broadway and was seen successfully around the world. In London, Gwyneth Paltrow played the leading character on the West End.
Proof is more of a specialist film and it would not be expected to be big box-office, despite Gwyneth Paltrow bringing her theatre performance to the screen.

But that does not mean that Proof is not worth seeing – and sitting back for some sequences where the talk about proofs and theorems and equations and prime numbers is more than a bit beyond most of us.

It is probably more accurate to describe Proof as a film about genius and about madness. Films about the mind and the psyche are often fascinating explorations of human nature, strengths and weaknesses.

The central character is 27 year old Catherine Llewellyn (Paltrow) whose mathematics professor father, Robert, has just died. She is grieving since she has been caring for him for three years, giving up her studies and her ambitions to tend him. A brilliant scholar in Britain and then in the US, he has been suffering from forms of madness for years, working away diligently at his studies but producing only notebooks of gibberish.

Her older sister, Claire, turns up, a practical woman wanting to interfere and control under the guise of taking care of Catherine. A maths teacher, taught by her father, Hal Dobbs, also turns up. Ultimately (but not without some severe tests of trust), he provides an alternative for Catherine’s life. She herself is like her father, a maths genius, but afraid that she too will descend into madness. An elaborate 40 page proof is at the centre of the crisis and the question of who wrote it, Robert or Catherine.

The credentials on this production are impeccable. David Auburn has adapted his play with the assistance of screenwriter and director, Rebecca Miller (Personal Velocity, Ballad of Jack and Rose – and daughter of Arthur Miller). Director John Madden guided Gwyneth Paltrow to her Oscar in Shakespeare in Love.

Gwyneth Paltrow herself brings a subtle poignancy to her quiet performance, suggesting vulnerability as well as determination, showing devotion but also deep apprehensiveness about her own mental condition. Hope Davis, often acting in lesser known independent films, is completely convincing as the ever-talking, list-making and busy Claire. Jake Gyllenhaal (Donnie Darko, Jarhead, Brokeback Mountain) is sympathetic as the do-gooding Hal.

As Robert Llewellyn, Anthony Hopkins gives an assured performance, appearing at times in his daughter’s imagination, seen in a series of flashback which show his mental deterioration, his determination and his sad acceptance of his condition.

Proof is a specialist film but it is interesting and thoughtful.

1. The impact of the film: the education background, mathematics, sanity and madness, family, father-daughter relationships?

2. The title, proofs as beautiful, like music? The fear of peaking at twenty-three for mathematicians? Mathematicians and their desire to have proofs, verifying theorems? The drugs? The conversation of culture with mathematics? Big ideas? Katherine’s comment that it is not big ideas, but working away, chipping away at a problem like her father? Coming from the side, weird angles, keeping to the grind? The film and the focus on the life of mathematicians?

3. The basis of the film as a play, the playwright adapting his play with Arthur Miller’s daughter, Rebecca? The intellectual background, the reliance on speech and speeches? Details of mathematics? The confined world of the university, academia, mathematics? The confined world of the play – and opening up the screenplay? Exterior scenes, close-ups? A successful adaptation? Performances?

4. The action in the present: Robert Llewellyn’s death, Katherine’s birthday, the preparations for the funeral? Hal’s visit, Claire’s arrival and her interactions and interference, the funeral, the aftermath, the issue of the proof, decisions about New York, the truth?

5. The flashbacks and their insertion? Robert as present to Katherine, the initial appearances to her, explaining his life, his death, his funeral? Her talking to her dead father? Her materialising her father and interpreting him? The development of the memories, the father as sane, talking about her birthday, at the university with Hal? His concern about Katherine’s going to school? The development of the proof, his exhilaration, their working together, his finally finishing, Katherine reading it, her dismay? His appearance at the end?

6. Gwyneth Paltrow and the portrait of Katherine: aged twenty-seven, clever, the younger sister, her difficult relationship with Claire, her love for her father, devotion to him? Living in the house, caring for her father and his madness for so many years? Cleaning house? Cleaning him? Coping with his madness? Claire and her absence in New York, having a life of her own? Her knowledge of maths, working with her father, wanting to go to school, North-Western? University and his comments about distance? Her love for maths? Her physical health, her fears of being like her father and mental breakdown? Claire and her interrogations? Her interaction with Hal, his coming on her birthday, the champagne, the discussions of his band, I As The Imaginary Number? His looking through the manuscripts, her discovering the manuscripts and her anger and calling the police? His wanting her father’s words to be a gift to her? Claire’s arrival, concern about her hair, going shopping, the discussion about the police and that she imagined Hal? Her reaction to the police, saying “I spat”, her swearing? Her explaining Hal? Her tantrums against Claire, buying the dress? Her moods? Her anger with Claire – and the vegetarian chilli? Meeting Hal in the street and his being real? The funeral, her nerviness, her getting up to make the speech, the bluntness of the speech about her father and his condition, about the friends who didn’t visit him? The social afterwards, going to her room, Hal and his being with her, playing in the band, going to her room, the books about maths, inhibited, the sexual encounter? Her feeling like an egg about to be cracked open? Giving Hal the key to the desk, saying that she wanted him to be the first to see the proof? The prospect of New York? The issue of the house, her arguments with Claire about the house? The proof, Claire’s anger, not believing that she wrote the proof, Hal and his doubts, not trusting her?

7. The portrait of Robert, his reputation, skills, lectures, Hal as his student, his lucid time and Katherine and her birthday? His study? Katherine’s speech about him and the aliens, how he stank? The description of his exhilaration? His madness, working, looked after by Katherine, watching television? His continued work, collaboration, urging her not to waste her life, counting the number of days wasted? His joy at having the proof? Her reading it aloud – and his collapse?

8. The contrast with Claire, overbearing, a currency analyst, absent from Chicago and making a life of her own? Arrival at the airport, phone calls, incessant talking? Her attacks on Katherine, interfering, calling her Katie? Her stories about Mitch, the plan to marry? Interrogating Katherine during the shopping, about Hal and the police? Meeting him? Claire’s reaction to Katherine’s eulogy? The party, laughing out loud at the band, the theoretical physicist, her hangover? Wanting Katherine to move, her plan, the selling of the house to the university? Defending her life? Suggesting that her father would have been better in an institution, arranging doctors in New York for Katherine, not believing her about the proof, urging her to go to New York, at the airport – and her explanation of her lists? Katherine leaving her?

9. Hal, his studies, dissertation? His supervision by Robert? The chance encounter with Katherine – and her remembering? Her birthday, the champagne, the manuscript, trying to smuggle it out, the truth that he wanted to give her a gift? His band? Wanting to go to the funeral, at the funeral and his concern, following her out? At the social, the band playing, her room, the kiss, the sexual encounter, saying that he wanted to spend time with her? Her giving him the key to the desk?

10. The funeral, the people arriving, the eulogy, the music, Katherine and her speech? The criticism of the friends and their absence? The social, people chatting, Katherine morose, the band playing?

11. Hal and the manuscript, his joy, willing to go through all to find the professor’s work? Katherine giving him the proof? The importance of the proof about prime numbers? Claire’s reaction, Hal’s reaction, the consequences – and Katherine announcing that she wrote the proof?

12. Katherine’s memories of the study, the professor and the discussions and her explaining to the professor about her homework, that she was involved in further research? His wanting her to do the ordinary work? The ordinary professor? Katherine’s concern, phoning, phoning Claire, the discussions with her father, the sadness in reading his gibberish? The meal and the professor saying that she was lazy, the thirty-three-and-a-quarter days, that she should stop moping? Her giving him the book? His not responding to her work?

13. The dispute about who wrote the proof, Hal’s reaction, the issue of handwriting? His not believing Katherine? Planning to take the proof to professors? His reasons for doubt? The verification? Claire and her attack? Katherine’s bitterness, wanting to tear up the proof?

14. Claire and her packing, Katherine tossing all away, weeping? The going to the airport – the talk at the airport, the lists?

15. Hal and the verification, the professors, his eagerness? Katherine’s bitterness? Their talk – and his running, tossing the manuscript into the taxi?

16. Katherine’s soliloquy, the image of searching the house, unable to get out? Hal coming, talking? Her fears that she was like her father? His offering to disprove negatively that she was insane?

17. The overall effect, understanding people’s lives, intellectual lives, imagination, emotions? Genius and the fear of madness?