Aspergers Syndrome in the Mathematician community

In source researching I am running across a common theme. There is a strong link between mathematicians and the aspergers syndrome side of the autism spectrum (think Dustin Hoffman in "Rain Man"). It brings up a suspicion in me that most mathematicians who are afflicted with any sort of mental illness would be more likely to be afflicted with aspergers syndrome than schizophrenia. People who are afflicted with aspergers suffer from an inability to interact with other people on a level that we consider to be "normal". They often withdraw into themselves and fixate on certain other things. Numbers and math in general are a popular fixation amongst aspergers patients. It would then make sense that the field of math and other sciences would contain higher levels of aspergers afflicted individuals simply because it is a disease that does not hinder their ability to do well in these areas. Schizophrenia, on the other hand, is tremendously inhibiting on a persons ability to understand systems and concepts required to be a mathematician or scientist. I think then that John Nash was not aided in his ability to do math by his mental challenges but rather the opposite. I also think that a character like Max in Pi is an unlikely type of number theorist.