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There are relatively few famous people with schizophrenia because schizophrenia is a brain disorder that typically strikes people when they are quite young - age 17 to 28.
People this age typically are too young to be famous, they are just starting out their professional lives after completing high school or college.
A recent Nobel Laureate in Economics, John Forbes Nash Jr., has a lifetime history of Schizophrenia but is now doing very well, as has been well documented in the book "A Beautiful Mind" and the academy award-winning movie of the same name.
Many "historical diagnoses" are frequently not entirely certain -- a "good guess" for schizophrenia includes Mary Todd Lincoln, wife of President Abraham Lincoln. Following is a list of famous people who have been diagnosed with schizophrenia, or are highly suspected of suffering (or who had suffered) from schizophrenia.
Here is another list that someone has developed - the NAMI list of famous people with mental illness.
Source: Schizophrenia.com
High impact articles: Schizophrenia Research and Treatment