What do you mean by "diagnostic impression"? Do you want me to diagnose what his condition might be? Which character is "in question"? Please be more specific and more detailed.
John Nash, the subject of the movie "A Beautiful Mind" was a brilliant scientist. From seeing the movie, he is depicted as someone who falls into a delusional state of mind and can't escape. His delusional world is so real to him that he loses touch with the "real world." According to John Nash's own words, (which you can read at the Nobel site) he offers the explanation that his mental illness sometimes allowed him to see the impossible.
In other words, trying to solve the complex and unanswerable questions that he tackled somehow pushed him over the edge of reality. This was necessary in a way to allow him to reach deep into the recesses of his mind and find answers to impossible equations.
In my opinion, I would assess the character as an individual who got lost in his mind, trying to find answers to the universe and on occasion found his way back to reality and at other times remained a prisoner within his thoughts.
A sad and brilliant life, one that accomplished much. He was a victim of mental illness, Schizophrenia is a disease that has catastrophic consequences.