January 2, 2002 -- "A Beautiful Mind" is a film based on the life story of John Nash, a troubled mathematical genius of soaring intellect and stunted emotions.

We first see John Forbes Nash Jr. (played well by Russell Crowe of "Gladiator") at the height of his powers in 1947 when he has just arrived at Princeton for graduate study in mathematics. He has no patience for classroom study, so he skips classes, bending his will to one task: finding an original idea. He is convinced this is the only way he will ever matter.

Incredibly, he comes upon the idea in a bar, based on a rare social insight, that when all the guys compete for the prettiest girl in a group, they all tend to lose, in part, because they alienate the other girls. His idea is called game theory, the mathematics of competition. He writes a paper on the subject. His theory that competition can be self-defeating flies in the face of 150 years of economic theory, contradicting some of the ideas of Adam Smith, the father of modern economics. Smith promoted the idea that economies are most effective when every individual pursues their own best interests. Game theory eventually causes a revolution in economic theory, and it is being applied to an ever-widening circle of fields.

At the same time, Nash becomes involved in breaking spy codes being used by the Soviet Union. A shadowy government agent, William Parcher (played by Ed Harris) calls Nash the greatest natural code-breaker he has ever seen. He recruits Nash for a top-secret project, to break codes hidden in newspaper and magazine articles. Nash also becomes involved with a lovely young student, Alicia Larde (played by Jennifer Connelly of "Requiem for a Dream"), and the two are married.

Just when it looks like Nash has the world by the tail, the center falls apart. He is diagnosed with paranoid schizophrenia. The drugs prescribed for his condition destroy his mathematical insights. Even when he was healthy, Nash was socially backwards. His mental condition causes him to be even more withdrawn. Nash faces an overwhelming personal and professional crisis. Alicia is determined to help him, believing that it might be possible for the heart to heal the mind.

Director Ron Howard ("Apollo 13") does a fine job with this film. He uses interesting visual techniques to show how Nash makes his amazing mathematical connections. He also does a good job of visually showing us what is going on in Nash's tortured mind when Nash is beset by mental illness. Crowe is excellent in the lead role, playing a very different character than the one he did last year in "Gladiator." He is nervous, introverted, confident and later, desperate. Connelly is solid in her role. The story, by Akiva Goldsman ("Lost in Space"), based on Sylvia Nasar's book, gives us a good idea of the challenges of mental illness, and the fierce battle waged by Nash to overcome his handicap. Production values are high with a rich production design, good cinematography and a solid musical score. This film rates a B.

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