This post will have a spoiler, but the movie has been out a long time and it is impossible to talk about it any other way.
I had often heard that 'A Beautiful Mind' was a good movie, but I didn't know anything about it except the identity of the subject, John Nash. The movie opens with a scene in Princeton university in 1947, and one of the characters is wearing a tie that features a double helix pattern. Given that the structure of DNA was not actually found until 1953, there should be no reason for this pattern to be on a tie in 1947, so I assumed that this was a historical error in the movie. This primed me to expect further errors. So when more errors and strange occurrences started popping up, I assumed that it was just more Hollywood inaccuracy. Just when I was thinking that the movie was a piece of stupid Hollywood junk, it was revealed that none of these things were real; they were all Nash's delusions.
The movie is not about Nash*. It is about schizophrenia. And it is indeed a good movie, if for no other reason than it manages to force the audience to accept the reality of the delusions, which start small and keep growing, so that we understand the confusion of the main character as he must confront the fact that what he sees is not real. After I finished the movie, I semi-seriously ran an inventory of the people I know, to make sure that I had some proof that they were real: Had they been acknowledged by other humans, or interacted with physical objects, or otherwise shown that they had an actual connection with reality?
The movie also hints at how bad the state of mental illness treatment was in the 50's and 60's. The hospitals, treatments, and medicines were crude and barbaric. As the movie demonstrates, the best and perhaps only way of dealing with a mental illness is to really confront the problem yourself, aided by people who are close to you and love you. The real Nash stopped all medical intervention and medications in 1970, and learned to deal with the problems. The movie, however, says that he started taking 'newer medications' which was a lie put in for political reasons.
Even today, people have a lot of confusion about mental illness. The simple fact is that mental illness is whatever society says it is. Any behavior that makes you different, or less able to 'function properly' in our society, will be classified as mental illness. Behaviors that previous societies would consider normal, acceptable, or even admirable are now classified as mental illness.
The only strict biological definition of mental illness that makes any sense is 'any behavior that reduces the number of surviving, viable offspring' and by that criterion anyone who has sufficient resources to raise a child, and uses birth control or remains chaste, is insane.
At this point, you may be thinking, "Surely it must be mental illness if you accept as true something that is not found in reality." But this definition fails to exclude the majority of humanity. People's memories of events is almost always different from the literal truth. People lie to themselves all the time, inventing stories about events and motivations in order to fit their own narrative of the world. This is a standard psychological coping mechanism, we would not be able to function well without it. At some point, acceptance of unreal things becomes a problem, but that point is determined mainly by social convention.
I know a person, X, who sees fairies and ghosts, as well as a 'guardian angel' who talks to X and acts as an adviser. X knows that nobody else sees these things, and that most people react negatively when they are discussed. But X firmly believes that they are real, and considers the ability to see these things in general, and the angel in particular, to be a special gift from God. Because X trusted me, we were able to discuss these things. I asked a lot of questions, without making assumptions, and learned a lot.
X would almost certainly be diagnosed with schizophrenia, and possibly several other mental illnesses as well, but I do not consider X insane. The angel never tells X to do bad things, in fact the advice of the angel is always do things that are more rational and/or more moral than X would normally do. These visions do not cause any problems, and they may in fact help X function better. They are simply the way that X's mind perceives and deals with the world.
Neither I nor anyone else has any right to say that it is 'wrong' to see these things, and any medicine, even modern ones, would cause X far more problems than these visions. In another time or culture, X might easily be honored as a seer or prophet.
*There are a ton of inaccuracies; the person in the movie has almost nothing to do with the read Nash.