Near the end of her article in the July-August issue of the Atlantic magazine, Nancy Andreasen describes a colleague’s hospital visit to famed mathematician and schizophrenic John Nash, subject of the 1998 biography “A Beautiful Mind.” “How could you . . . a man devoted to reason and logical truth, believe that extraterrestrials are sending you messages?” the colleague asked. To which Nash replied: “Because the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”

That link between genius and mental illness has been the focus of study for decades for Andreasen, a psychiatrist and neuroscientist, and she describes what she has learned and how she learned it in readable detail. She begins with her early work at the University of Iowa, where she used her association with its well-known Writers’ Workshop to study 30 gifted writers and their families and established that both creativity and mood disorders were overrepresented in the writers’ families.

Which raises other questions: “What differences in nature and nurture can explain why some people suffer from mental illness and some do not? And why are so many of the world’s most creative minds among the most afflicted?” She examines the problem of how to define creativity: The basic criterion for most tests has been “divergent thinking,” or the ability to come up with many responses to questions, as opposed to “convergent thinking,” which is the ability to come up with the correct answer to problems that have only one answer. (Her example of the former: How many uses can you think of for a brick? Construction material, bludgeon, bookend . . .) And can creativity in the arts be equated with creativity in science or business?

Andreasen also describes her current study using brain-imaging technology to try to identify the unique features of a creative brain, particularly the unconscious processes. This involves using 13 people recognized for unusual creative ability via such standards as Pulitzer, Nobel and Oscar awards. The study compares their brain scans as they perform mental tasks — for example, free association, which has long been recognized as a window on the unconscious — with those of a control group. Her subjects include filmmaker George Lucas, writer Jane Smiley and mathematician William Thurston, and six Nobel laureates in the sciences.

Some of the ideas here don’t seem groundbreaking. What’s interesting is the process as well as some of the side issues she uncovers along the way.