Russell Crowe's performance as John Forbes Nash, the American mathematician who overcame paranoid schizophrenia to receive the Nobel Prize for economics in 1994, is a tour de force.

We first meet him as a student at Princeton and last see him 47 years later and Crowe is utterly convincing throughout.

Meanwhile, what happens in those 47 years would be unbelievable if it weren't basically true.

The young Nash was arrogant, shy, odd and brilliant.

He invented a game theory, the Nash Equlibrium, which was to gain him the Nobel Prize, and became a codebreaker for the Pentagon.

He married one of his students, Jennifer Connelly, (also Oscar-nominated), and grew increasingly obsessive and alienated.

But by now the schizophrenia had kicked in and not all we are told is true.

The question, cleverly explored by Ron Howard¿s film, is: where does reality end and Nash's fevered imagination take over?

As time passes Nash, too, starts to wonder and to fight his illness with mathematical logic and the help of his long-suffering wife.

This is stirring and absorbing stuff and yet in some ways A Beautiful Mind falls short.

The supporting characters, apart from Ed Harris as a murky government agent, are underwritten and the ending, though heart-warming and triumphant, is heavily sentimental.

We know that Nash's story is deeply moving - we don't need the script to underline it for us.

Barry Norman