The New York Times magazine reports:
By the spring of 1985, with a 9-year-old Tao splitting time between high school and nearby Flinders University, Billy and Grace took him on a three-week American tour to seek advice from top mathematicians and education experts. On the Baltimore campus of Johns Hopkins, they met with Julian Stanley, a Georgia-born psychologist who founded the Center for Talented Youth there. Tao was one of the most talented math students Stanley ever tested — at 8 years old, Tao scored a 760 on the math portion of the SAT — but Stanley urged the couple to keep taking things slow and give their son’s emotional and social skills time to develop.
On page 422 of the book The Bell Curve it’s estimated that if virtually all American 17-yea-olds had taken the SAT in 1983 (not just the college bound ones), the mean math score would have been 411. On page 425 a graph estimates that if all American 17-year-olds had taken the SAT in 1983, only about 0.7% would have scored 700+.
Assuming a roughly normal distribution, these two statistics imply that in 1983, if all 17-year-olds took the SAT, the math standard deviation would be 117.
Thus Tao at about age 8.8, scored 2.98 standard deviations above the average U.S. 17-year-old.
I don’t know where this would put him compared to U.S. 8.8 year-olds on the math SAT, but on the WISC-R IQ test, U.S. 8.67-8.997 year-olds who score in the top 37% of U.S. 16.67-16.997-year-olds on Arithmetic (the subtest most similar to the math SAT) narrowly make the top 0.4% among their own age group. This suggests an age bonus of 2.33 standard deviations.
Thus Tao, was likely 5.31 standard deviations above the U.S. mean for his age, suggesting a math IQ of 180 (U.S. norms) and also 180 (U.S. white norms). Assuming roughly normal distributions, only about one in 21 million Americans should have math IQs this high or higher.