It certainly isn't necessary to be well-versed in mathematics to enjoy this movie, but it does help, if only to identify with the personalities that inhabit this most arcane "science." This story is told in the "present" and via flashbacks, and the editing facilitates it very nicely. In the present, in Chicago, the mathematician and father Robert (Anthony Hopkins) has just died, his at-home daughter Catherine (Gwyneth Paltrow) prepares for the arrival from NY of her somewhat estranged older sister Claire (Hope Davis). The sisters always seem to be at odds, and this is magnified several times when Catherine finds out that Claire is also planning on selling the family residence right away, at the same time hoping to convince Catherine to move to NY with her. See, Robert did his ground-breaking work in his early 20s and shortly thereafter began to go mad, spending the last 40-odd years of his life scribbling nonsense in notebooks. Claire is afraid her sister is following in dad's mental steps.
Jake Gyllenhaal is a 20-something mathematics post-graduate Hal who understands Robert's contributions, and seems to have come to accept that he (and most others) will never have a hope of contributing at that very high level. But he is both romantically attracted to Catherine, and also realizes she may have inherited Robert's gift for ground-breaking mathematics. He wants to help her realize that too.
This movie is not about mathematics, it isn't really about Robert. It is about Catherine, afraid she is becoming mad like her dad, but also realizing that she may have talents that she must develop. In a great sense, the future of our world depends on the occasional genius coming up with striking advances, so what happens if one of them "breaks the chain" and refuses to use their gift? Catherine is torn between retreating, giving up, and letting herself go insane without struggle. But is that her path? Maybe she only inherited the genius, and will NOT go insane. The movie is about her inner struggle to cope with both possibilities.
May 2009 edit: Saw it again last night, it was as good and fresh as when I watched it 3 years ago. Good movie.
SPOILERS FOLLOW. In the heat of the sister/sister friction after the funeral services, and when Catherine is talking to Hal, who had been going through the 103 notebooks of gibberish Robert had written, looking for a spark of genius, Catherine gave him a key to an upstairs desk. In it he found one notebook which contained an elegant "proof" of a long-standing problem regarding prime numbers. Catherine said she wrote it, but Claire doesn't think she is capable. Hal says the handwriting looks like Robert's. He has two groups of mathematicians examine it and, while they didn't grasp all the transformations, they could NOT find anything wrong with it. A flashback shows us, the audience, that Robert could not have written it, indeed it was Cathernie's. On the verge of leaving for NY with her sister, that flashback in her mind made her go back, and the movie ends with her back on campus, willing to explore her mathematical mind. As Hal says, he can't prove she won't go mad eventually, but he also can't prove she will. So she might as well work as if she will not!
Jake Gyllenhaal is a 20-something mathematics post-graduate Hal who understands Robert's contributions, and seems to have come to accept that he (and most others) will never have a hope of contributing at that very high level. But he is both romantically attracted to Catherine, and also realizes she may have inherited Robert's gift for ground-breaking mathematics. He wants to help her realize that too.
This movie is not about mathematics, it isn't really about Robert. It is about Catherine, afraid she is becoming mad like her dad, but also realizing that she may have talents that she must develop. In a great sense, the future of our world depends on the occasional genius coming up with striking advances, so what happens if one of them "breaks the chain" and refuses to use their gift? Catherine is torn between retreating, giving up, and letting herself go insane without struggle. But is that her path? Maybe she only inherited the genius, and will NOT go insane. The movie is about her inner struggle to cope with both possibilities.
May 2009 edit: Saw it again last night, it was as good and fresh as when I watched it 3 years ago. Good movie.
SPOILERS FOLLOW. In the heat of the sister/sister friction after the funeral services, and when Catherine is talking to Hal, who had been going through the 103 notebooks of gibberish Robert had written, looking for a spark of genius, Catherine gave him a key to an upstairs desk. In it he found one notebook which contained an elegant "proof" of a long-standing problem regarding prime numbers. Catherine said she wrote it, but Claire doesn't think she is capable. Hal says the handwriting looks like Robert's. He has two groups of mathematicians examine it and, while they didn't grasp all the transformations, they could NOT find anything wrong with it. A flashback shows us, the audience, that Robert could not have written it, indeed it was Cathernie's. On the verge of leaving for NY with her sister, that flashback in her mind made her go back, and the movie ends with her back on campus, willing to explore her mathematical mind. As Hal says, he can't prove she won't go mad eventually, but he also can't prove she will. So she might as well work as if she will not!