- AFI's 100 Years... 100 Cheers: #93
- Dawson Casting: Russell Crowe was in his late 30s during the filming, which begins as Nash enters Princeton University. While his age is not stated in the movie, in reality this happened when Nash was 20 years old. Granted, Crowe plays him right up until he receives the Nobel Prize in his mid-sixties.
- Deleted Scene: A love scene with John and Alicia was cut from the film.
- Fake American: Russell Crowe as John Nash.
- Hey, It's That Place!: The Pentagon office scene was filmed in the basement of Keating Hall on Fordham University's Bronx campus (the same room was used in the filming of the Georgetown University language lab scene in The Exorcist).
- Playing Against Type: Russell Crowe was more associated with tough-guy action roles.
- Real-Life Relative:
- Bryce Dallas Howard can be seen after the math lecture when Nash is sedated by Dr. Rosen, looking into the car as it drives away.
- One of John Nash's sons plays the orderly on the right, in the scene where Nash is being dragged down the hall.
- Romance on the Set: Jennifer Connelly and Paul Bettany fell in love while filming this movie and later married.
- Throw It In!: Nash's rambling about different kinds of tea came from the man himself during one of Russell Crowe and Ron Howard's conversations with him. As they left, Crowe said to Howard "I'm using the tea shit."
- What Could Have Been:
- Robert Redford was originally going to direct, but withdrew due to scheduling conflicts.
- Alec Baldwin, Matthew Broderick, Nicolas Cage, Kevin Costner, Tom Cruise, John Cusack, Johnny Depp, Robert Downey Jr., Ralph Fiennes, Mel Gibson, Jared Leto, Guy Pearce, Sean Penn, Brad Pitt, Keanu Reeves, Charlie Sheen, John Travolta and Bruce Willis were all considered for John Nash.
- Salma Hayek was the original choice for Alicia Nash. Other candidates included Geena Davis, Teri Hatcher, Famke Janssen, Ashley Judd, Jennifer Jason Leigh, Brittany Murphy, Meg Ryan, Hilary Swank, Charlize Theron and Rachel Weisz.
Trivia / A Beautiful Mind