The film, of course, is a fictionalized account of his life, but he was undoubtedly one of the greatest mathematicians of the 20th Century. He made critical contributions to the field of Game Theory (modeling how people rationally make decisions), which explains a lot about why his Nobel was in Economics, not Mathematics. He was also schizophrenic, and thinks that he got better without the aid of modern pharmaceuticals.
Well, it turns out that his work anticipated modern cryptography by decades, as shown in his recently declassified 1955 letter to the National Security Agency:
The National Security Agency (NSA) has recently declassified an amazing letter that John Nash sent to it in 1955. It seems that around the year 1950 Nash tried to interest some US security organs (the NSA itself was only formally formed only in 1952) in an encryption machine of his design, but they did not seem to be interested. It is not clear whether some of his material was lost, whether they ignored him as a theoretical professor, or — who knows — used some of his stuff but did not tell him.Fittingly, the declassified letter was "discovered" (well, popularized on the Internet) by Ron Rivest, the "R" in the RSA encryption algorithm that your computer uses every day.
Even more interesting, he is active today in economics, working on ideas for sounder currency in this day of Quantitative Easing and hidden inflation. Ron Paul should get him on the team.
But enough crypto-geekery. He was played in the film by Russell Crowe. As a service to my Lady Readers, here's some of Russell Crowe's beautiful, err, mind: