John Nash was just a young man in the beginning of the movie, but he was already a genius. He was accepted and got a scholarship to Princeton University. The movie starts with his first day at the University, where he clearly already shows himself as antisocial and quiet. He meets his roommate Charles, who becomes his closest friend. However, it is important to highlight here that as the movie will reveal further, Charles was just a hallucination projected by him due to his schizophrenia.
Some time later, John develops one of his most famous theories, the Game Theory that refuted Adam Smith’s theory, showing his genius mind, and then he began to get noticed. His friend Charles occasionally appeared in some of the scenes and nothing can makes us even imagine that something was abnormal. 5 years later, he is shown helping the U.S government to decrypt numbers of codes that had been sent by the Soviet Union. He is also a teacher at MIT, and in the first class he has to teach at the movie, he meets for the first time the young woman who will further become his wife. Soon, he meets with a man that takes him to an office full of highly technological equipment; where he starts working as a code breaker. Again, whoever is watching does not have an idea that this office, the work or even the man do not exist, it is only one more thing created by John’s mind, that not even he knows it is not real. As the movie goes, he goes on a date with Alicia, his student, and during the date he starts to feel followed and observed.
John starts to look for codes at all kinds of papers, from magazines to newspapers, and it starts to become an obsession. A series of events that make us believe that he is really working for a “spy” company starts happening, even though it’s nothing more that his only imagination. And he also continues going out with Alicia, and she shows to be the only woman that likes and is attracted to his weird behavior towards females. His friend Charles shows himself again in the movie, this time with his niece. Even though the audience does not notice, Charles has not changed anything since 5 or more years ago, and during all the movie he, along with his niece do not change. That will be a way for John to realize that they are hallucinations and understand that he really has schizophrenia.
John and Alicia get married and other episodes deepen us in the idea that John is really working for a secret company. And then, when they move in together, Alicia starts noticing his strange behavior. Not only her, but also his students, and some of his friends as soon as he behaves really weird. When John freaks out at home, his wife calls the psychiatric hospital, where he is taken during a mathematician’s conference and John thinks the Russians have taken him. While the doctor was talking to him, John sees Charles at the room and guessing he was helping the Russians, starts scream at him. Then, the doctor asks him whom he is talking to; assuring that there is no one there. That’s when, the audience starts being suspicious about what is happening and also confused if the doctor is telling the truth. Right after, Alicia shows herself asking the doctor what is wrong with John while both are observing him. The doctor then says that John has schizophrenia and he is dealing with paranoia. Everything that has been made by John’s mind during the movie starts being revealed, all his hallucinations. Alicia finds out that her husband really has a mental issue and need to be treated and then, reveals to John that everything related to the secret company he has been working for, was created in his mind and were not actually true. He denies that and leaves, to realize right after that she was telling him the truth and he was really having hallucinations. He starts the treatment that was, at the time, believed to treat the schizophrenia, a sequence of electroshocks and medicines that induced him to have seizures, and that was years later considered a failed treatment.
1 year later, they moved back to New Jersey, close to Princeton. John is taking his medicines and Alicia takes care of him and their baby, although the situation is really hard for her. Some time later, after seeing his wife suffering with his condition, he secretly stops taking his medicine, because it does not allow him to reach mathematical solutions, to help with the baby and leaves him with no sexual desires at all. And he starts having hallucinations again. He finds a small house close to his house where he starts working on breaking codes and finding hidden messages on newspapers and magazines, and his mind finds excuses to persuade him that everything was real. His wife finds out when she finds the house, and after he almost accidentally killed their son and hurt her, she calls the psychiatric hospital and goes away, leaving him alone. Then, he finally realized, on his own, that everything was and is not real, when he notices that Charles’ niece never gets old. He stops Alicia and tells her.
After a visit from the doctor, she decides to give John one more chance for him to get better without medicine or treatment. She believes something extraordinary can happen. And it does. He starts “getting better”, he learns to deal with the hallucinations. He goes back to work in the Princeton library. Then, he freaks out again and tells Alicia he decides to go back to the hospital, but she asks him to try one more time. And he does. This time, he ignores his hallucinations, and finally gets better. He starts giving classes and developing new theories. When his friend asks him if his hallucinations were gone, he answers him that they were not, and probably they would never be, but he learned to ignore them, and that way they gave up on him.
In the end of the movie, years later, he wins the Nobel and receives a standing ovation by all. It is not surprising to say that the movie later on, in 2002, received the Oscar for Best Picture.