If this were the only argument in support of the thesis, it would be easy to discount. After all, there's nothing in the single case study of Newton to suggest that his neuroticism was a cause of his contributions to Calculus, mechanics, gravity, and cubic-plane curves. Newton's quote suggests that he had great powers of concentration and grit (passion and perseverance for especially long-term goals), not that his nervous breakdown was somehow a positive contributor to his groundbreaking work.
But Perkins and colleagues do go on, bringing in past research to support their claim. Among the papers they cite is a study of advertising-industry employees showing that those working in creative roles tend to score significantly higher on neuroticism than employees in "noncreative roles." They also cite a study showing that people in creative professions have a higher risk of psychiatric illness and suicide.
But here's the thing: One can be creative in any field. There are a heck of a lot of uncreative artists and a lot of creative accountants (far too many, in fact). And for the most part, the relationships between neuroticism and creativity are pretty weak.
In a reply, a group of psychology researchers published a response to the opinion piece reviewing the existing literature on the link between neuroticism and creativity. Their review found only very weak (and sometimes even negative) correlations between neuroticism and a host of creativity-related variables, including IQ, creative thinking, insightful problem solving, creative achievement, everyday creative behavior, and self-assessed creativity.
Along the same lines, my colleagues and I recently administered a battery of cognitive and personality tests to three demographically diverse samples, totaling 1,035 participants. The average correlation between neuroticism and creative achievement was zero. In fact, we found that the only personality trait that consistently predicted creative achievement across the arts and sciences was openness to experience.