However the original definition of IQ was in tests for children, and it was measured as mental age divided by physical age. Those tests are still used for children, and it IS possible for a 6 year old to get an official IQ of 230 on a test like the Stanford-Binet.
Which is exactly what Terry Tao did at the age of 6. Comparisons to adult tests may be problematic. But it remains an officially recorded IQ from a standard test.
I haven't checked the maths, but I know the Gaussian distribution is falling fast past a few standard deviation, so such a result would not surprise me.
IQ stands for "intelligence quotient".
It was developed as a ratio between mental age and physical age, times 100. So if you performed as expected, your IQ was 100. It was originally developed as a way of finding people who were behind, literally "retarded". However it also proved useful as a way of finding people who are intelligent as well.
After IQ tests were adopted in school systems, we found that they were approximately normally distributed with a mean of 100 (by definition), and a standard deviation of 15-16. For a variety of reasons (including identifying military recruits to train for specialized roles), there was a desire to have ability tests aimed at young adults. We developed those and scaled them to be explicitly normal with a mean of 100 and standard deviation of 15 or 16 (depending on the test). We also found that childhood IQ is a fairly good predictor of your later adult abilities, and therefore many of those tests are ALSO called IQ, even though there is no quotient involved.
On the adult tests, the tests do not scale out to IQ 230, nor is it likely that anyone is that many standard deviations out. But on the child tests, there is no problem scaling it. And it turns out that, in practice, the tails are heavier for the original type of IQ test. Which means that it is more common to find a 6 year old who performs at a 14 year old's ability, than a person who is over 8 standard deviations out.
Terry Tao had his IQ officially measured on a childhood test, not an adult one. However there has been no test since that is able to reliability measure his ability, particularly in math.
Consider, at 7, his SAT score put him well within the top 1% of college-bound kids.
At 10, his performance on the International Math Olympiad meant that he was literally in the top handful of high school students in the world.
Yeah, we don't have properly scaled tests for that.
That's why my above comment was explaining why the 230 figure couldn't possibly make sense under the modern definition.
However the Stanford-Binet test is still used for children. And in young children can still produce extremely high IQ scores.
Also note that while usually the standard deviation is made to be 15 these days, there are still tests, like the Binet and OLSAT, where the standard deviation is 16. That's why I said that the standard deviation depends on the test.