There are three major mental illnesses associated with autism: depression, ADHD, and anxiety. So maybe.
As for the overlap between schizophrenics and geniuses, I believe I know why this is. The dopamine hypothesis that was the basis of mainstream treatment of schizophrenia for many years was partially true but incomplete; that is, it was believed that the problem was excess levels of the neurotransmitter dopamine being released in the brain, and the treatment was anti-psychotic drugs to lower dopamine levels. While it's true that excess release of dopamine does cause psychosis and hallucinations, it didn't explain the "negative symptoms" such as flat affect. It was eventually discovered that in schizophrenics, the process of converting glutamate (an amino acid and excitory neurotransmitter) to GABA (an inhibitory neurotransmitter) was defective. The dopaminergic neurons were being overstimulated.
Now consider what these neurotransmitters actually do: dopamine is associated with rewards such as food, sex, learning, and drugs (in fact, stimulants release a flood of dopamine, which is why stimulant psychosis can happen). GABA helps suppress questionable outputs from neural networks as well as helping to reduce anxiety. There is a personality disorder called schizotypal personality disorder that tends to occur in people whose families have schizophrenics; essentially, it's a low-grade form of schizophrenia with mostly negative symptoms and few or no positive symptoms (note that in this context, "positive symptom" means the presence of something abnormal, such as delusions, and "negative symptom" means the absence of something normal, such as normal social interaction). Schizotypals are eccentric, asocial, heavily introverted people with a strong tendency to chronic maladaptive daydreaming: they tend to spend a lot of their time engrossed in fantasies that they share with few or no other people, which can become incredibly elaborate. They don't seem to need other people because they generate their own internal reward stimuli, generating dopamine through the activities of their own constantly active minds. Meanwhile, the low GABA prevents unusual interpretations of ambiguous internal and external stimuli from being suppressed; this can be a spur to creativity and novel solutions to problems.
Essentially, then, the brain of a highly intelligent schizophrenic is constantly active, capable of coming to highly unusual conclusions, and needs no validation from others. With such a brilliant mind, working all the time, freed from the constraints of conventional world views or the need to socialize, is it any wonder that such people have the potential to be unbelievably brilliant, creative, and productive, even when they are also insane?
www.audible.com
www.bbc.co.uk
www.reuters.com
