(Charles Rex Arbogast/AP)

This post has been updated.

Sylvia Nasar, the biographer of the late John Nash, has often said the Nobel-winning economist did not "will" himself out of schizophrenia, but instead "aged out" of the devastating mental illness. Research confirms that a small percentage of people diagnosed with schizophrenia can experience remissions, or at least diminishment in what are called the "positive" or active symptoms of schizophrenia -- hallucinations, paranoia, delusions. (Negative symptoms include social withdrawal, flat affect and problems with motivation.)

But while Nash, who was killed in a car accident Saturday along with his wife, Alicia, may have experienced relief from the more debilitating aspects of schizophrenia in later life, his greatest mathematical achievements occurred at an age when he was also the most mentally ill. Few people, including Nash, can function at a high level in the throes of psychosis, but was there a connection between Nash's breakthrough mathematical insights and his schizophrenia?

[Related: Q&A with John Nash's biographer]

Scientists have long been interested in the link between creativity and madness; the association has been made as far back as the ancient Greeks. Only in recent years, however, have scientists been able to study the neurological connection. There remains much debate, but researchers have determined that schizophrenia does involve hyperactivity in the prefrontal cortex, a region of the brain that helps people make unusual connections between seemingly unrelated ideas. Conversely, says Harvard's Alice Flaherty in a 2005 paper, "frontal lobe deficits may decrease idea generation, in part because of rigid judgments about an idea's worth." This is a brain region that is especially active during paranoid episodes of schizophrenia. It is also an area linked to high levels of the neurotransmitter dopamine, which is suspected of causing positive schizophrenic symptoms, but also, says Flaherty, "novelty seeking and creative drive."

Likewise, the density of dopamine receptors in the thalamus, the brain's relay center where information is filtered, is characteristic of schizophrenia. A lower degree of filtering means a higher flow of information, suggesting greater availability of information in problem-solving situations.

Few people would suggest a simply cause-and-effect relationship between mental illness and creativity. Not every mentally ill person, obviously, is creative. Two things were certainly clear in the case of John Nash:  The relationship between his illness and his mathematical insight was complex, and as he grew older his schizophrenia was at the very least more manageable and at best, in remission.

I was lucky enough to meet Nash about 10 years ago. It was at one of the legendary teas held by the Institute for Advanced Study in Princeton, after a public talk by Institute physicist Juan Maldacena. In truth, I attended the talk not only because I wanted to hear Maldacena, then a rising star in astrophysics talk about string theory and black holes, but because I guessed, accurately as it turned out, that Nash might be there, too. I was hoping to interview him about his current work in mathematics and he was easy to pick out at the tea in his sneakers and somewhat ruffled appearance, a look not uncommon around both Princeton University and the Institute, two separate entities.

Nash was polite but exceedingly shy and put off committing to an interview, which never did  happen. What he did want to talk about, however, was the Princeton town council meeting he and his wife would be attending after the tea. John and Alicia were both active participants in the community, something very few people outside the small insular world of Princeton knew at the time, and they were a frequent presence at town meetings when they involved discussions of zoning, widening roads or creating new traffic routes. What struck me that afternoon was Nash's enthusiasm about the mundane details of life in his town. It would have been easy to dismiss this as quaint, but what it told me was that a man who had long struggled with mental illness was fully engaged in the world and able to extract joy from that engagement in even the smallest of ways. Given the public and professional acclaim he found later in life, his happiness was richly deserved.