There is a nice profile of mathematician Terence Tao in the New York Times magazine this week. Tao is astonishing in his breadth and depth. He could probably master any subject in any field if he just put his mind to it. The article plays up his “normality” in contrast to the stereotype of the eccentric asocial mathematician like Gauss, John Nash or Grigory Perelman, who proved the Poincare Conjecture. However, in my experience, most mathematicians, even the very best, are reasonably normal and sociable. My guess is that the rate of personality disorder among mathematicians is no higher than the general populace. It is perhaps true that mathematicians are more introverted and absent minded than average but rarely to a pathological degree. I think the myth persists because of a few very prominent examples but also that mathematics is a pursuit where having a personality disorder is not a major handicap. One could probably not be a great lawyer, physician or statesman if they were socially abnormal. Thus, if the rate of historically great eccentric mathematicians is high compared to other fields, it is because the sample is biased.
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Scientific Clearing House 
your last comment i think would be a reasonable ‘null hypothesis’—the ‘mad scientist’ (or mathematician) is a myth based on sampling error. however, it may also be one reason the myth exists is that its somewhat true in the sense that stereotypes often have a germ of truth. also it may exist becauase some of the most eccentric types also got some of the greatest or well known results. But, people can be eccentric or somewhat un-normal in many ways–b russel, poincare, godel, turing, feynman, nash, w pitts, jensen, various ones with political views seen as unnacetable now etc. Some also may be normal in one area and ‘cranks’ in another —i seem to come across many papers viewed as ‘cranky’ (eg hidden variable variable theories, anti-big bang, disproofs of Cantor and einstein, etc. ) done by people who may do valid work in other fields—usually more applied and seem to have academic jobs. .
i also am not a big fan of the concept of normal or normality. (now we live in the age of the ‘new normal i hear). the maxwell-boltzmann is distribution is normal (gaussian) but the boltzmann is exponential—and in a sense one is just dealing with different coordinates or representations (and i think the same could be said of spin glasses / ising models/ fitness landscapes.) The surface of the earth may be normally distributed in elevation looked at one way, but the sierra nevada is not the same as the geat plains. .
if one looks at income distribution (some say normal, lognormal, exponential, etc…) it is somewaht ‘normaly distributed’ but that is not the case geographically –bny neighborghood or country, etc. Also it runs in families, etc. as does IQ (which is closer to a bell curve apparently). Prison populations are not random samples of populations; skin color likely isnt, and animals are different though perhaps connected by ‘phase transitions’. I prefer symmetry breaking type conceptual models to explain why things are not normal—eg the old famous one on racial segregation by thomas shelling of U Md..
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Personality disorders primarily affect one’s ability to have relationships. However, I cannot think of any particular personality disorder that could actually enhance mathematical thinking. A brief description of the various personality disorders can be found here: http://psychcentral.com/personality/
That being said, surely there must be some psychological traits that enhance mathematical thinking. As you are a mathematician, do you have any insight into what some of those traits might be?
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@tom There are many traits that could enhance mathematical thinking. The ability to concentrate, to focus, to shut out distractions, to think logically, to visualize, to generalize, and so forth. I think someone who doesn’t worry about the niceties of human interaction could possibly devote themselves more to thinking about math problems. People like Newton, John Nash (even before the psychosis), Paul Erdos, and Alan Turing were socially awkward. This may not have contributed to their math greatness but it didn’t impede them either.
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I looked over your list, and I wouldn’t have a problem with anything that you listed. You had brought up the concept of personality disorders in your original commentary. However, I will suggest a phrase that might be more relevant. Instead of personality disorder, it might be more accurate to look for a particular type of cognitive processing style as helpful in mathematical thinking. Using the list of traits that you provided, I will suggest that a particular neurological condition incorporates such traits like:
*sticky attention (prolonged attention to a stimulus)
*improved visualization (the formation and manipulation of mental images in solving visualspatial tasks.)
*decreased need for social interaction
Individuals with this condition completely fail on the task of generalization and abstraction, and in general, do not excel at mathematical skills. Ironically, though, the parents of children with this condition are more likely to excel in the hard sciences, including mathematics. And if I told you that Terence’s brother had that condition, would you entertain the idea that small doses of this cognitive style may be intellectually advantageous as long as was not “too much”?
I realize that you probably know Dr. Tao, and you might even consider him a friend. Hence, you would probably be hesitant to say anything that might be perceived as disrespectful. Rest assured, I am not trying to be disrespectful. But I’m betting that you know of a number of colleagues in academia who have children with some degree of this condition. In fact, I could reference a study in which individuals in the highest 20% of academic achievement have the highest risk of having a child on the autism spectrum in comparison to the 80% with less academic achievement. And this means that such of a possible association cannot be dismissed out of hand.
And, of course, I’m referring to the condition of autism spectrum.
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@tom Actually, I don’t know of anyone personally that has clinically diagnosed autism or children with autism. Your hypothesis is a long standing one in the field of autism and one that has been pushed by Simon Baron Cohen. It is plausible but not validated.
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