The subtype of schizophrenia that John Nash is presenting with is Paranoid Schizophrenia. .
Paranoid schizophrenia is a preoccupation with one or more delusions or frequent auditory hallucinations. In the beginning of the movie, we are introduced to the peculiar character of John Nash. A strange and somewhat socially inept man that is a genius. He is dubbed "the mysterious West Virginia genius." John Nash attends Princeton University, and he is in search of his "original idea." His goal is to "Find a truly original idea. It is the only way I will ever distinguish myself. It is the only way I will ever matter." The viewers of the movie are unaware of his illness at this time. We only get to see the socially withdrawn man with very peculiar ways. He does not fit in easily. "I don't like people much, and they don't like me." We are introduced to Nash's roommate at the beginning of the movie, Charles Herman. .
It is very interesting as to how the movie only allows the viewer to see that Charles Herman, Charles' niece Marcie as well as William Parcher, who works as a spy for the department of defence, are all hallucinations that John Nash is experiencing after we have been introduced to them. Before we know that Charles is a delusion, there is dramatic irony in what Charles says to Nash: "Nothing's ever for sure, John. That's the only sure thing I do know." Only once Dr Rosen intervenes and takes Nash to a psychiatric hospital do we find out that Nash's peculiar behaviours are due to the schizophrenia and some of the people that he has met, are in fact, delusions and hallucinations.
As we find out that he has the illness, one can start putting the pieces together slowly. The fact that only Nash speaks to Charles and that he does not feature in any conversations with the other university members such as Martin. John Nash does not realise that he has the illness even though he is admitted to a psychiatric hospital.