It might be hard to imagine a mathematician as an exciting movie hero -- even a brilliant, mentally unstable mathematician. What's a director going to do with that? A dramatic zoom on the guy's calculator?

Yet Ron Howard's "A Beautiful Mind" is the fifth film in as many years focused on an off-kilter arithmetic genius -- and each one of them has been mesmerizing in its own way.

Fictionalized without seeming contrived, this biography of Princeton professor and Nobel Prize winner John Forbes Nash, Jr. is the story of a determined man overcoming madness on his own terms. It is a "let's make an Oscar movie" movie. It doesn't have "Good Will Hunting's" street-smart charm or "Pi's" jarring, visceral depiction of delusion. It's not intricately intellectual like "Conceiving Ada" (about Ada Byron King, great-grandmother of the modern computer) or deeply moving like "Infinity" (about Los Alamos bomb-designer Richard Feynman and his tuberculosis-afflicted wife).

But what it lacks in ingenuity, "A Beautiful Mind" makes up for in superb performances, potent emotions and graceful, emblematic (if safe and conventional) filmmaking.

Once again absorbing himself completely in his character, Russell Crowe stars as Nash, who begins the picture as a Princeton graduate student with "a chip on both shoulders" but practically no social skills. As he sits invisibly in the back of a lecture halls in 1947, you can see in Crowe's darting eyes that Nash's mind is constantly going 300 mph. He ignores class work and classmates on an obsessed quest to find "a truly original idea," scribbling elaborate formulae on the windows panes of his dorm room and looking for invisible algorithms everywhere. His goal is to make a discovery that will distinguish him. "It's the only way I'll ever matter," he says with an irrational fear of anonymity creeping across his face.

The film's conspicuously abbreviated timeline rushes through Nash's college years, pausing long enough to introduce his roommate, best friend and polar opposite, Charles Herman (Paul Bettany, "A Knight's Tale"), an outgoing party boy who has charisma in spades. Then comes one of screenwriter Akiva Goldman's bouts of creative license. Nash hits upon a revolutionary "game theory" -- which would transform 150 years of world economic reasoning and eventually win him the Nobel Prize -- while trying to hit on a beautiful blonde in an off-campus pool hall with some pals. "If we all go for the blonde, we'll cancel each other out," he reasons. "If none of us goes for the blonde, we all get lucky (with her friends)."

Exactly how this relates to Governing Dynamics -- and indeed what Governing Dynamics even means -- is never adequately explained. But Nash's breakthrough begets a job as a Cold War code-breaker with the government and a teaching position at Princeton, where he meets his wife Alicia (Jennifer Connelly). A confident, brainy beauty taking his class, she is attracted to him because he's the polar opposite of the average man. They turn each other on intellectually, and Crowe and Connelly have an affecting chemistry together, which is the one touchstone in Nash's life when his mind begins to unravel.

Paranoia sets in something fierce after his Pentagon work becomes dangerously, almost absurdly, cloak-and-daggerish under the guidance of a shadowy government agent played with highly focused intensity by the terrific Ed Harris. Crowe hints at Nash's mental instability in these scenes with increasingly overt behavioral tics. Meanwhile, director Howard -- who gives the whole film a bona fide 1950s Life Magazine sheen -- deploys his best Hollywood trickery in the codebreaking scenes, showing us what Nash sees on pages of endless data by having certain numerals begin to glow as he recognizes their patterns. It's a potent and visually stimulating effect.

Then Nash makes a horrifying discovery: All of this intrigue has taken place only in his head. The mysterious agent, the high-tech listening station in an abandoned government building, the complex Soviet codes he's been obsessed with finding in the text of magazines -- even his charismatic college roommate. None of it was real.

Crowe is subtly superb in the scenes that follow, as Nash endures months in an psychiatric hospital undergoing insulin shock therapy before returning home so heavily medicated that his mind becomes blunted, leaving an overwhelmed Alicia to become the family breadwinner. Connelly ("Requiem for a Dream," "Waking the Dead"), whose amazing talent has gone grossly under-appreciated for years, may finally get her just recognition for this performance of devotion, strength and perseverance.

Both the picture's stars shine most brilliantly in the third act as Nash deliberately abandons his medication, absolutely determined to defeat his paranoid schizophrenia using logic and willpower. He resolves to ignore his imaginary apparitions and focus on his wife and his mathematics, the only things he knows are veritable in his life.

"A Beautiful Mind" seems a little more focused on Academy-pandering than on storytelling. It's also hindered by less significant problems like its histrionic score and some bad age makeup that renders Connelly unrecognizable in later scenes (although Crowe looks great). But these flaws don't hurt the film as much as the lousy trailers and TV commercials -- which take some of the film's most moving moments out of context and make them look mawkish and trite.