GWYNETH, GWYNETH, GWYNETH! Not having been overly impressed with any of her previous performances, in Proof, Gwyneth Paltrow brings a highly emotional, nuanced, and so finely-tuned performance, I must say this movie this movie a stand-out.

She inhabits her character so fully, I was pulled in and so completely entranced the entire time. In fact, certain words or phrases are reused and have an uncanny allusion to when they were previously said. The effect as that you experience and follow the moments, and the thoughts of the characters, even though they are so deeply imbedded within. I credit Gwyneth and the director with making this work so well. I've never experienced such an organic link between phrases separated in time in a movie before. Wow!

This is a movie about how a daughter, her sister, and a grad student deal with the passing of a great mathematician. While there may be similarities with 'A Beautiful Mind' and even 'Good Will Hunting', knowing there are any such links didn't help me with this movie and I think actually does a dis-service. This movie stands on its own. Ignore any such comparisons.

Acting-wise, there were strong performances all around with Anthony Hopkins giving a top-notch performance. Jake Gyllenhaal's was strong, but perhaps not to the level of his rather awesome performance in Brokeback Mountain.

Good things aside, the one thing that irked me about this film, was that given the strong link to mathematics, how unbelievable some of the dialogue was regarding the 'math. While Gwyneth's and Hopkins' characters pulled off a sense of mathematical intelligence, Jake's character hardly said anything mathematically competent and even came across as flustered in expressing himself mathematically leaving me feeling cheated. In my view, this is chiefly the fault of the screenplay but to a lesser extent in the actor's portrayal. Ignore this rather small point, and this movie passes with flying colours. Q.E.D.

"Proof", the excellent play by David Auburn, was one of the best things in the New York stage in recent memory. Part of the attraction was the intelligent subject matter, math science, and how it connected the four characters one got to meet. The casting was an ideal one, Mary Louise Parker, Larry Briggman, Johanna Day and Ben Shenkman, playing Cahterine, Robert, Claire and Hal, respectively.

Mr. Auburn and Rebecca Miller, a movie director, herself, took the task of adapting "Proof" for the screen. The result, directed by John Madden, opens the play in cinematic terms, no small undertaking in presenting the movie to a wider audience who might not be interested in science, and much less in the advanced math that plays an important role in the proceedings.

If you haven't seen the film, please stop reading here.

Catherine, the 27 year old, at the center of the film, is a woman who has stayed behind to take care of her aging father, a man much esteemed in academic circles, who is suffering from, perhaps, a neurological illness that is killing him slowly. Catherine has, in a way, sacrificed her life in order to see that Robert spends his last days at home instead of at an institution.

The death of the father brings Claire home. This woman, who lives in New York, wants to get rid of everything connected with her father. She even has made plans for Catherine to move from Chicago to be near each other in New York, where things are much better. To complicate things, Harold, the nerdy math student, finds a hidden notebook that might contain a discovery that will revolutionize math. The only problem is the proof might not have been the dead man's own creation.

"Proof" works as a film because of Mr. Madden's direction. We are kept involved in what is going on because we have been won by Catherine, the wounded woman trying to live her life without having to tend to a sick man. Catherine love for math, in a way, makes her realize her place is in the same institution where her father made mathematical discoveries as she will be following his steps.

Gwyneth Paltrow makes an excellent Catherine, a role she had played on the London stage. Ms. Paltrow is a welcome presence in the movie because of the intelligence she projects when working with a good director like John Madden. In fact, it has been a while since we saw this actress in a film.

Hope Davis, another excellent actress, plays Claire, the materialistic sister who has arrived and who wants to transform the frumpy Catherine and mold her to her own taste. Ms. Davis has accustomed us to expect a valuable contribution to any film in which she plays. As Claire, she clearly understand who this character she is portraying really is.

Anthony Hopkins has only a few good moments on the screen. Jake Gyllenhaal's character Harold is not as effective as Ben Shenkman's was on the stage. In fact, Mr. Gyllenhaal, with his dark good looks, seems to be someone who would not be interested in math at all.

"Proof" is an immensely rewarding film thanks to what John Madden's vision.

Catherine Llewellyn (Gwyneth Paltrow) is struggling to deal with the death of her genius math professor father Robert (Anthony Hopkins). He deteriorated mentally in his last years which forced her to quit school and take care of him. His former student Hal (Jake Gyllenhaal) is working through a mountain of Robert's incoherent notebooks to find anything worth saving. Catherine's sister Claire (Hope Davis) arrives for the funeral and seeks to bring Catherine back to New York for treatment. When Hal discovers a notebook filled with a ground-breaking math proof, Catherine claims it to be written by her.

This is a compelling portrayal of the mathematical obsession. It's not as flashy or romantic as cinema tries to dress up math sometimes. It is a bit sad. Paltrow does great work following Hopkins. She shows that she's not simply a romantic lead. It's a compelling character study.