The adaptation differs greatly from the original biography, in the aspect that real-life John Nash never had visual hallucinations. He only have auditory hallucinations, but the filmmakers said that the purpose of this depiction is to make sense of the story. Sylvia Nasar, the writer of the book said that while the film is not to be taken as a literal depiction of Nash's life, but it carries the spirit of his struggles with the illness.
Additionally, Nash never worked at Department of Defense in MIT, instead he commutes regularly between Princeton and MIT, where he worked in RAND Corporation as a consultant.
His hallucinations, while in the film is depicted to start when he entered Princeton University, isn't actually true. It actually started some years after he graduated.