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From the writer of Batman & Robin, and the director of The Grinch, comes a film about... maths. Not an appetising prospect.

And yet, from its opening scenes of college boy rivalry at '40s Princeton, right up to the sight of a doddery Russell Crowe emoting in '90s Switzerland, A Beautiful Mind is never less than engaging, and frequently engrossing. Part love story, part Cold War thriller and all Academy friendly biopic, Ron Howard's drama proves the Pi/Good Will Hunting cinematic equation: maths genius + mental angst = entertainment. Squared.

From the instant Crowe appears, it's clear this is to be a performance of faultless verisimilitude. Here he is: the raging colossus of Gladiator, the scowling bruiser of LA Confidential, the middle-aged tobacco executive of The Insider; a burly 37-year-old movie star whose 'real' life profile couldn't be larger. And yet he totally convinces as an apprehensive 19-year-old yokel adjusting to life at an Ivy League university. He actually seems to shrink on screen, his massive frame dissolving into his suit, his eyes flitting nervously around the room, like a fly afraid of being squashed. But then this is a film of faultless performances.

Inspired by - rather than remaining faithful to - Sylvia Nasar's biography of Nobel Prize-winning mathematician John Forbes Nash Jnr, screenwriter Akiva Goldsman has shamelessly embellished the truth, hanging a largely fictionalised account of his life around certain key facts - the first being that the socially limited (that is, bloody rude) student revolutionised modern economic thought by challenging the theories of über-mathematician Adam Smith.

If that sounds dull - (and it does) - don't be put off, for while Howard's direction is typically conservative, his use of digital trickery to bring maths to life is extremely effective. The handling of the film's testing narrative shift, meanwhile, is impressive: what could have appeared a jaded cinematic gimmick engenders complete sympathy with the lead. In fact, it's only after Howard's successfully pulled off the difficult bit that he struggles at all, spending too long with Ed Harris' shady spy master, before picking up the pace for the final half hour.

Also, unusually for a Howard film, there is a feeling of genuine danger when Nash's government code-breaking activities unravel - a feeling that's exacerbated by a star-making supporting turn from Gangster No.1's Paul Bettany, and a suitably sly performance from Christopher Plummer as a sinister doctor. Most rivetting of all, though, are Nash's confrontations with his long-suffering wife (Jennifer Connelly). Crowe's feral quality induces a real sense of fear, while Connelly's heart-rending performance is Best Supporting Actress material, combining the glamour of an old school film star with the fearlessness of a butt-ugly character actor. Even the James Horner score can't screw things up. Go figure.