Matthew Good, a rock musician, suffers from bipolar disorder.
It's easy to see how this stereotype came about. Creating something new often means thinking of things which have little basis in reality, or are outside of what is considered normal. Something original is by definition not normal, since nothing like it has come before it. From there it's easy to make the transition to the abnormal, to mental illness. Mental illness can present itself as a disconnection from reality, or as a different way of thinking.
The Persistence of Memory (1931) by Salvador Dalí is known for its surreal imagery.
Is it true, or is the relation between the two just a romanticization of mental illness? The answer lies somewhere in between. According to a 40-year study of over 1 million people, there wasn't a strong correlation between mental illness and being in a creative profession. However, there was one between having a close relative with a mental illness and being in a creative profession. One conclusion to tentatively draw from this is that some traits of mental illness are beneficial for creativity, but that full blown mental illness tends to be either a neutral factor or a hindrance. Of course, this is just an average; there are plenty of anecdotal examples of artists who are "normal" and of ones who are "crazy."
As neuroscience advances we learn more and more about the way our brains work, such as how chemicals like serotonin and dopamine affect us, or how neuron links relate to memory and thoughts. We also create new medications. How will those influence creativity and art moving into the future? Only time will tell.
Maki-e Neurons (2012) by Greg Dunn.
Canadian Mental Health Assocation. "Bipolar Disorder, Manic Depression, Matthew Good Mental Illness." YouTube. Janwilkins2773, 21 Mar. 2009. Web. 15 May 2016.
Dalí, Salvador. The Persistence of Memory. 1931. Painting. Museum of Modern Art, New York City. http://www.dalipaintings.net. Web. 15 Mar. 2016.
Dunn, Greg. "Maki-e Neurons." Greg Dunn Design. 2012. Web. 15 May 2016.
Kaufman, Scott Barry. "The Real Link Between Creativity and Mental Illness." Scientific American Blog Network. Scientific American, 03 Oct. 2013. Web. 15 May 2016.
Kyaga, Simon, Mikael Landén, Marcus Boman, Christina Hultman, Niklas Långström, and Paul Lichtenstein. Mental Illness, Suicide and Creativity: 40-Year Prospective Total Population Study. Journal of Psychiatric Research, 14 Sept. 2012. PDF.