The precise nature of John Nash's illness is a matter of considerable debate to this day. At the time when he first started showing symptoms of his illness—delusions and hallucinations—he was way past the age when schizophrenia normally develops. Yet John was diagnosed as having schizophrenia anyway, and it was quite common in those days for psychiatrists to apply such a diagnosis to any patient deemed unsuitable for psychoanalytic treatment.
That John, like so many people at the time, was misdiagnosed is reinforced by his subsequent recovery. Schizophrenics tend not to recover, at least not in the way that John Nash did. He was able to go on and forge a successful career as a world-renowned economist and mathematician, and this would suggest that, whatever mental illness he experienced for so many years, it wasn't the paranoid schizophrenia with which he'd originally been diagnosed.