As a movie fan, I make my viewing choices based upon a film's lead actors just as much as upon its subject matter. A strong cast can often help make a boring film interesting or simply strengthen the story altogether. That's why I decided to watch the 2005 film Proof despite the fact that one of its main subject matters is mathematics. I figured that Gwyneth Paltrow, Jake Gyllenhaal, and Anthony Hopkins were well worth the risk of a potentially boring movie.
Paltrow stars as Catherine, a young woman whose father Robert (Hopkins) has recently died. Robert was an award-winning mathematician who did groundbreaking work before he was 25, but who had been in something of a mental decline ever since then. The last few years of his life were marred by dementia and brightened by only a few occasional lucid moments.
Catherine basically put her education, career, and life on hold in order to move back home to take care of her father during his decline so that he wouldn't have to be institutionalized. During that time, she starts to wonder if perhaps she might inherit Robert's madness at some point in her life. Indeed, in the opening scenes of the movie, Catherine sees a vision of her already-dead father and even has a conversation with him. Catherine then wrestles with the question of whether she's just going through a natural grieving process or whether she's slipping into the same blackness that enveloped her father's final years.
Catherine receives input and offers of assistance from two different people who come around after Robert's death. One is her sister, Claire (played by Hope Davis), who carried on with her life in New York and didn't share Catherine's burden of caring for Robert. Catherine is more than a little bitter about this, but Claire brushes Catherine's feelings aside, saying that Robert belonged in an institution and that no one forced Catherine to give up so much. Claire tries to convince her sister to come back to New York and start a new life there.
The other person involved in the story is a University of Chicago mathematics professor named Hal (Gyllenhaal). Hal used to be a student of Robert's and would like to go over the hundreds of notebooks Robert left behind after his death. Hal hopes that he can find some interesting material in the notebooks, public the information, and basically launch his career from that. He openly explains all this to Catherine because he doesn't think there's anything crass about that plan. Catherine, who remembers Hal from when Robert was well, at first doesn't want anyone to have access to the notebooks, but then reluctantly agrees. It should also be mentioned that Hal and Catherine have a bit of a fling. Hal would like it to become much more, but Catherine keeps him at a distance.
As the film progresses, Hal discovers a notebook containing a mathematical proof so innovative that it could have profound effects on the entire field. At first, he thinks it must be Robert's work, but then comes to realize that Catherine could very well be the author. A good part of the film is devoted to trying to identify the author and verify the proof.
Overall, I found that the great cast couldn't save Proof from being a boring movie in the end. In fact, I thought that the cast actually detracted from the film somewhat. For example, I didn't think that Jake Gyllenhaal was the right actor to play a mathematics professor because he simply doesn't look the part, and I thought Gwyneth Paltrow was way too brooding and despondent in her role as Catherine. Was she really supposed to be crazy or was she actually sane? I think the filmmakers took the angle that she was sane, but from the way she moped around, I would have tried putting her in an institution too!
I have to say that Hope Davis was a pleasant surprise as Claire, and positively stole all the scenes she was in. Hopkins was good, but didn't appear in enough scenes to make a real difference in the film.
Due to these factors, I wouldn't recommend watching Proof. I think it could have been a good movie, but ends up falling flat because of the execution.

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