https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/#comment-22648

It is strange that IQ has such a hold over the popular imagination, because as far as I can tell it plays no role in academia whatsoever. In professional mathematics, at least, we don’t brag about our IQs, put them in our cv’s, or try to find out other mathematician’s IQ when trying to evaluate them; it has about as much relevance in our profession as the Meyers-Briggs Type Indicator.

More generally, the skills and traits that are popularly associated with “intelligence” or “genius” become largely decoupled, after a certain point, to those that are needed to do good mathematics. For instance, a very creative person may have a hundred innovative ways to attack a mathematical problem, but what one really needs is the rigorous thinking, comparison with existing literature, intuition and experience, and knowledge of heuristics in order to winnow these hundred ways down to the two that actually have a non-zero chance of working. Indeed, being overly creative at the expense of true mathematical skill may in fact impede one’s progress on a mathematical research problem, due to all the time wasted on the ninety-eight hopeless avenues.

Similarly, a very intelligent person may be very comfortable with abstract concepts and abstruse reasoning, and a certain amount of this can indeed be an asset when learning some of the more theory-intensive portions of mathematics, but at some point one has to be able to digest this theory and connect it with more mundane, “common sense” concepts (e.g. geometry, motion, symmetry, information, etc.); there is a risk of an excessively intelligent student getting overly enchanted with the formalism and esotericism of a subject, and neglecting to keep his or her knowledge grounded in reality (and to communicate it effectively with others).

In a third direction, a very quick thinker may be able to pick up new ideas rapidly, to find snappy rejoinders to any question, and to complete tests and examinations in a remarkably short amount of time, but these attributes may in fact lead to excessive frustration when such a student encounters a genuine research problem for the first time – one that requires months of patient and systematic effort, starting with existing literature and model problems, identifying and then investigating promising avenues of attack, and so forth. In athletics, the best sprinters can often be lousy marathon runners, and the same is largely true in mathematics.

To summarise: as I said in the main article, a reasonable amount of intelligence is certainly a necessary (though not sufficient) condition to be a reasonable mathematician. But an exceptional amount of intelligence has almost no bearing on whether one is an exceptional mathematician.