He was in a different field, but Richard Feynman's mathematical genius is in dispute by nobody. However his measured IQ is widely quoted at 125.
IQ is somewhat correlated with intelligence, which is somewhat correlated with mathematical ability. You cannot be a mathematician without the mathematical ability. But your ability may or may not get fully reflected on an IQ test.
Physicist Steve Hsu on Feynman's alleged 125 IQ score:
"Feynman was universally regarded as one of the fastest thinking and most creative theorists in his generation. Yet it has been reported-including by Feynman himself-that he only obtained a score of 125 on a school IQ test. I suspect that this test emphasized verbal, as opposed to mathematical, ability. Feynman received the highest score in the country by a large margin on the notoriously difficult Putnam mathematics competition exam, although he joined the MIT team on short notice and did not prepare for the test. He also reportedly had the highest scores on record on the math/physics graduate admission exams at Princeton. It seems quite possible to me that Feynman's cognitive abilities might have been a bit lopsided-his vocabulary and verbal ability were well above average, but perhaps not as great as his mathematical abilities. I recall looking at excerpts from a notebook Feynman kept while an undergraduate. While the notes covered very advanced topics for an undergraduate-including general relativity and the Dirac equation-it also contained a number of misspellings and grammatical errors. I doubt Feynman cared very much about such things."
There is no surprise here. As http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/523.htm... makes clear, we consider someone "intelligent" because they possess many abilities of interest. But the possession of one ability (eg mathematical reasoning) is not well correlated with the possession of another (eg verbal ability). Unless you possess all of those, you won't score at the top in IQ.
But to excel in any specific field does NOT so much require top mental abilities of all kinds as exceptional ones required by that field. Not having a decent baseline of all abilities will be a handicap - you need that - but a Richard Feynman does not need to be a genius grammatically.
IQ tests are a very limited tool. They test a breadth of abilities and can indicate that you can do reasonably well at many things. (Indeed for a wide range of jobs, an IQ test is a better predictor of performance than your performance on the job interview!) However they can't recognize that you're truly exceptional at any particular thing.
Steve Hsu and his comments on IQ embarrass the actual research psychologists I know. Just in the last week a psychologist sent me a link to a take-down of Hsu's latest project.
The psychologist who sent me the link, and another psychologist colleague of his who was copied on the same email, are both experienced and astute human behavior geneticists (the other recipient was a math major as an undergraduate who became a psychology research after a mathematical career) and they don't agree with Hsu's conclusions about current data.
The sample size is indeed too low to have the statistical power to draw any solid conclusions. However it could be large enough to produce a set of candidate genes which reasonably might have small individual impacts on IQ. If you then could do a follow-up on a large population just looking at those genes, some of those candidates are likely to prove out.
It is a fishing expedition. You never know what you'll find. The odds that you come back empty handed are high. But it is still worth doing.
Hsu's claim in this matter is much easier to swallow than your contention that an IQ of 120 is sufficient for eminence in any field. Next you'll be telling us that anybody over five and a half feet tall can play for the Knicks.
He was in a different field, but Richard Feynman's mathematical genius is in dispute by nobody. However his measured IQ is widely quoted at 125.
IQ is somewhat correlated with intelligence, which is somewhat correlated with mathematical ability. You cannot be a mathematician without the mathematical ability. But your ability may or may not get fully reflected on an IQ test.