On the other hand, it would be worth asking how many (if any) great mathematicians had high but non-exceptional intelligence
Some of my candidates (who, perhaps not coincidentally, also happen to be among my “favorite” old-time mathematicians, in the sense of stylistic identification):
Hilbert
Weierstrass
Lie
Cantor
Noether
All of these violate (what I think of as) the “math genius” stereotype in some way. None of these were considered child prodigies; in many cases they took up mathematics relatively late (Lie), had some competing interest (Cantor), or stood in contrast to a prodigy they knew (Hilbert, the prodigy being Minkowski).
Expanding the scope to physicists (and in the category of “widely held cultural beliefs that are probably wrong”), I will also nominate:
Einstein
whom I suspect of possessing significantly less Tao-style ability, and being more akin to the above-listed mathematicians, than is commonly assumed.
Tao’s abstract pattern recognition ability would seem to mark him as an outlier amongst mathematicians of similar accomplishment, whose relatively lower abstract pattern recognition abilities are counterbalanced by other abilities (some innate and others developed).
Some of my candidates (who, perhaps not coincidentally, also happen to be among my “favorite” old-time mathematicians, in the sense of stylistic identification):
Hilbert
Weierstrass
Lie
Cantor
Noether
All of these violate (what I think of as) the “math genius” stereotype in some way. None of these were considered child prodigies; in many cases they took up mathematics relatively late (Lie), had some competing interest (Cantor), or stood in contrast to a prodigy they knew (Hilbert, the prodigy being Minkowski).
Expanding the scope to physicists (and in the category of “widely held cultural beliefs that are probably wrong”), I will also nominate:
Einstein
whom I suspect of possessing significantly less Tao-style ability, and being more akin to the above-listed mathematicians, than is commonly assumed.
Tao’s abstract pattern recognition ability would seem to mark him as an outlier amongst mathematicians of similar accomplishment, whose relatively lower abstract pattern recognition abilities are counterbalanced by other abilities (some innate and others developed).