The film portrays Nash's mathematical genius and struggles with schizophrenia. However, it simplifies and romanticizes his life, omitting or altering certain aspects of his personal history and the nature of his illness.

Alicia Nash's support of John is a central theme. While she was indeed a crucial figure in his life, the film's portrayal of their relationship is somewhat idealized and omits some of the difficulties they faced.

Charles Herman is a fictional character representing John Nash's hallucinations. Nash never saw a character like Charles Herman.

William Parcher is another fictional character representing Nash's paranoid delusions. He adds a thriller element to the film, but is not based on any real person.

While Nash had academic rivals, Martin Hansen is a composite character. The film uses him to illustrate the competitive academic environment and Nash's early struggles.

Sol is a composite character, representing Nash's colleagues and friends. The film uses him to portray the social dynamics of the time.

John Nash was a genuinely brilliant mathematician who made groundbreaking contributions to game theory.

Nash was diagnosed with schizophrenia, significantly impacting his life and career.

While the film depicts Nash working for the Department of Defense breaking Soviet codes, there's no evidence this happened in reality.

The elaborate spy subplot involving Parcher and secret missions is entirely fabricated for dramatic effect.

While Nash's illness manifested in paranoia and delusions, accounts of violent behavior are exaggerated in the film.

The film romanticizes the relationship with Alicia, downplaying the challenges they faced due to Nash's illness.

The film omits significant aspects of Nash's life, including his relationship with Eleanor Stier and their son.

The film portrays Nash abandoning his child in a bathtub during a psychotic episode. This did not happen in reality.

Nash did undergo insulin coma therapy and electroconvulsive therapy, though their portrayal in the film is dramatized.

John Nash won the Nobel Prize in Economics in 1994 for his work on game theory.

The film captures the struggle and resilience of living with schizophrenia, though it simplifies the complexities of the illness.

While some colleagues were supportive, the film idealizes the academic community's response to mental illness.