That’s very interesting to me – thanks for sharing.
. When he says “exceptional” here, I think he means it in the ordinary sense of the word—the sense relevant to most of the readers he’s addressing—which would include not only himself but also almost all of his UCLA colleagues (for example).
Thanks for pointing out a possible alternative explanation. Can you elaborate? I think that I might understand what you’re saying, but I’m not sure. Are you saying that UCLA math professors would be considered to be exceptional mathematicians but not exceptionally intelligent? It’s not clear to me that this is the case – you seem to be breaking symmetry by interpreting his two uses of ‘exceptional’ in different ways.
UCLA math professors are as a group more intelligent than UCLA math grad students, who are in turn as a group more intelligent than UCLA math majors. His remarks in the article that I linked suggests that he adheres to the threshold theory – that after a certain point intelligence doesn’t yield incremental returns. I think that this is wrong whatever reference class one is using.
Can you elaborate? I think that I might understand what you’re saying, but I’m not sure. Are you saying that UCLA math professors would be considered to be exceptional mathematicians but not exceptionally intelligent?
I think what Tao means is something like: among the total population of those intelligent enough to eventually become senior faculty at a UCLA-level department, variables other than intelligence are much better predictors of (the binary variable of) whether a given individual achieves (at least) that level of status (as opposed to, say, the level of more typical state universities).
This is not inconsistent with intelligence being the best predictor of Tao-like status conditional upon UCLA-level status. In terms of intelligence, ordinary universities might contain a large percentage of could-have-been-UCLA’s even if UCLA-level places contain only a small number of could-have-been-Tao’s.
I also suspect you and Tao (or at least, his public “voice” as reflected in his writings) may disagree somewhat about the relative contribution to mathematics of Tao-level and merely-UCLA-level mathematicians.
That’s very interesting to me – thanks for sharing.
Thanks for pointing out a possible alternative explanation. Can you elaborate? I think that I might understand what you’re saying, but I’m not sure. Are you saying that UCLA math professors would be considered to be exceptional mathematicians but not exceptionally intelligent? It’s not clear to me that this is the case – you seem to be breaking symmetry by interpreting his two uses of ‘exceptional’ in different ways.
UCLA math professors are as a group more intelligent than UCLA math grad students, who are in turn as a group more intelligent than UCLA math majors. His remarks in the article that I linked suggests that he adheres to the threshold theory – that after a certain point intelligence doesn’t yield incremental returns. I think that this is wrong whatever reference class one is using.
I think what Tao means is something like: among the total population of those intelligent enough to eventually become senior faculty at a UCLA-level department, variables other than intelligence are much better predictors of (the binary variable of) whether a given individual achieves (at least) that level of status (as opposed to, say, the level of more typical state universities).
This is not inconsistent with intelligence being the best predictor of Tao-like status conditional upon UCLA-level status. In terms of intelligence, ordinary universities might contain a large percentage of could-have-been-UCLA’s even if UCLA-level places contain only a small number of could-have-been-Tao’s.
I also suspect you and Tao (or at least, his public “voice” as reflected in his writings) may disagree somewhat about the relative contribution to mathematics of Tao-level and merely-UCLA-level mathematicians.