Miramax | USA | 100 mins

Love is impossible to calculate, or solve. It comes about and lasts, or fades away, rather inexplicably. In one, short, sloppy but completely true sentence is explained John Madden’s Proof, a small little gem full of performances that ache in the aftermath of a first viewing. Gwyneth Paltrow plays Catherine, the tortured genius daughter of a tortured genius father, who’s played by Anthony Hopkins. Her father has just passed away, but Catherine continues to speak to him, hallucinating his presence throughout the film.

David Auburn, who adapted the film from his play, handles this father-daughter interaction nicely, relying solely on the conversation between the two people and ignoring the mortal aspects Catherine’s hallucinations ignore as well. This is not a film about special effects, after all, but rather about the oddity of human relationships.

Adding the word “oddity” to the above sentence is Jake Gyllenhaal‘s turn as ambitious math student Hal, who is determined to solve a complicated proof Hopkins’ Robert left unsolved at his death. He turns for Catherine for help with the proof, and one thing leads to another (notice the above photo).

Sure, it’s a simple equation, but one worth experiencing, thanks to the expert execution. Madden, after all, is at his absolute best when dealing with the trials and tribulations of love (see Ethan Frome, Shakespeare in Love). The camera is calm throughout, never cutting anxiously, certainly not as flashy as Shakespeare in Love but far less meandering than Captain Corelli’s Mandolin (everybody makes mistakes guys).

The acting on display here is a wonder. In many ways, Proof is a performance showcase, not offering much in the way of setting or even plot but everything in the way of line delivery and line reaction. It is based on Auburn’s play, remember, and it seems the writer was keen to maintain the base of the original work, which hinges on character interaction.

Paltrow’s Catherine struggles with the idea of living a life versus living her dream, which is mathematics. Like many dreams, it can (and does) become a nightmare, forcing social sacrifices that leave her comatose in a world without proofs and logarithms. Hal becomes the antidote Catherine needs to break free of her obligations, to her dream and her father. Of course, the curing process is far from easy, and Paltrow does a great job bringing her audience into Catherine’s struggle, which at first feels tepid but soon feels real and tragic. This is a great artist who, like so many great artists, can’t step out of her own way. It takes the help of a good-not-great mathematician (i.e. Hal) for Catherine to do so.

All of this begging the question so many artists must ask of themselves: is it better to achieve great work at the sacrifice of a life? Is it worth constant suffering for a name that will last centuries past its death?

The mathematics here might as well be literature or film. Proof leaves the question unanswered, completely aware of its irony and of the importance for each viewer to answer the questions themselves.

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