See my comment here. I agree to some extent, but the correlation between cognitive ability and math SAT scores is positive for all levels of cognitive ability and SAT math scores, including the highest ones (even if it becomes substantially smaller).
Added: To operationalize the situation, I would guess that the frequency with which mathematicians who have won famous prizes (Abel Prize, Fields Medal, etc.) would miss no questions at all (say, as 18 year olds) would be noticeably higher than the corresponding frequency for professors at top 50 math departments. I’ll give evidence in subsequent posts.
To operationalize the situation, I would guess that the frequency with which mathematicians who have won famous prizes (Abel Prize, Fields Medal, etc.) would miss no questions at all (say, as 18 year olds) would be noticeably higher than the corresponding frequency for professors at top 50 math departments.
I agree that I expect it would be higher, though I would describe my expectation as “modest,” which probably overlaps with “noticeable.”
See my comment here. I agree to some extent, but the correlation between cognitive ability and math SAT scores is positive for all levels of cognitive ability and SAT math scores, including the highest ones (even if it becomes substantially smaller).
Added: To operationalize the situation, I would guess that the frequency with which mathematicians who have won famous prizes (Abel Prize, Fields Medal, etc.) would miss no questions at all (say, as 18 year olds) would be noticeably higher than the corresponding frequency for professors at top 50 math departments. I’ll give evidence in subsequent posts.
I agree that I expect it would be higher, though I would describe my expectation as “modest,” which probably overlaps with “noticeable.”