Director: Ron Howard
Stars: Russell Crowe, Ed Harris, Jennifer Connelly
Plot: After John Nash, a brilliant but asocial mathematician, accepts secret work in cryptography, his life takes a turn for the nightmarish.
The equations seen on the classroom chalk boards are actual equations written by the real life John Nash.
The film was shot in sequence in order to help Russell Crowe develop a consistently progressing manner of behavior.
The Riemann Hypothesis mentioned throughout the movie is a real and famous problem in mathematics that has gone unsolved (it has not been proved yet) for nearly 150 years. Many other important theories have been proved on the condition that the Riemann Hypothesis holds, hence its importance. In the year 2000, the Clay Mathematics Institute of Cambridge, Massachusetts listed the Riemann Hypothesis as one of seven "Millennium Prize Problems" and offered a $1,000,000 reward to the person that proves it.
John and Alicia Nash were killed in a car accident on May 23, 2015, when the driver of a taxi they were riding in lost control of the car and collided with a guard rail and a second car on the New Jersey Turnpike. The New York Times said that although the two drivers suffered only minor injures, the Nashes were "ejected from the cab and pronounced dead at the scene." John was 86 and Alicia was 82.
The scene towards the end of the film, where John Nash contemplates drinking tea, is based on a true event when Russell Crowe met the real John Nash. He spent fifteen minutes contemplating whether to drink tea or coffee.
Jennifer Connelly, who plays Alicia Nash, and Paul Bettany, who plays Charles, married shortly after the movie was released.
According to a 2001 Entertainment Weekly article on this film, the filmmakers originally wanted to mention John Nash's homosexuality, but they feared the film would make the wrong connection between homosexuality and schizophrenia, so they abandoned it. This connection, according to the article, was based on several now-discredited psychological studies that first appeared in the late 1950s.
Salma Hayek was originally considered for the part of Alicia Larde because Alicia Nash is from El Salvador.
John Nash is the co-inventor (independently from the Danish mathematician Piet Hein) of the strategy game Hex. This was caused by his frustration after he was defeated at Go, and he wanted to create a "perfect" game. The scenes where he does that were shot but then deleted from the final cut, and can be found in the DVD extras or online.
Professor Peyton Young was interviewed on the BBC radio programme "More or Less". He had dinner with John and Alicia Nash the night the movie opened and asked John Nash what he thought of it. He said "I liked it a lot. But it wasn't me."
The problem that John Nash writes on the blackboard in his lecture is a real one (unlike in other movies, where math on boards is usually either too simple or fake). There is an important theorem in mathematical physics that directly says the answer to this is 1. Later, when he discusses the problem with Alicia Nash, he makes additional restrictions for the solution, without which the problem is much harder, so he is pretty confident she didn't solve it.
Tom Cruise was considered to play John Nash.
In one scene, the imaginary roommate's niece runs through a field of birds. None of the birds move, proving she doesn't exist.
While this film is inspired by the life of John Nash, there were elements from his life that were deliberately omitted: 1) he was married twice, both to the same woman (Alicia Nash); 2) in the past, he had several affairs with both men and women; 3) he was arrested by the police by scandal; 4) He fathered a child out-of-wedlock in his twenties; 5) he believed that through his mental illness the extra-terrestrials spoke him, giving his advanced knowledge by means of cosmic connection with them; 6) he tried to renounce to his American nationality some times, in the belief that the USA government pursued him; and 7) he made numerous anti-Semitic comments during his period of extreme mental illness, most of which equated Jews with world Communism.
John Nash wasn't taking medication when he won the Nobel. When he is speaking to the man about whether or not he will embarrass himself at the award ceremony he mentions he is taking new medication but in fact he stopped taking his meds and was using pure mind over matter to handle his disease. The screen writers mother was a psychiatrist and mentioned that it might promote others with mental illness to stop taking their medications so that's why Nash says that in the movie.