JonahSinick comments on Innate Mathematical Ability - Less Wrong

40 Post author: JonahSinick 18 February 2015 11:11AM

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Comment author: komponisto 18 February 2015 08:06:17PM 3 points [-]

Very interesting, thanks!

I'll have more to say about the role of verbal reasoning ability in math later on

When you do, I hope you'll mention Paul Halmos, one of my favorite mathematicians (and the author, among many other things, of Naive Set Theory, which is on the MIRI reading list), who famously began his autobiography with the sentence "I like words more than numbers, and I always did."

People who are able to pick the correct choice at all can usually do so within 2 minutes – the questions have the character "either you see it or you don't."

Contrary data point here: I eventually figured out the "correct" answer (in the sense of the answer that everyone else came up with), but it took me something like 15-20 minutes (including interruptions by various distractions, such as reading subsequent paragraphs -- which I'm glad I did, because it allowed me to discover that the test was untimed, which is what gave me the confidence to try to figure it out!).

A reasonable amount of intelligence is certainly a necessary (though not sufficient) condition to be a reasonable mathematician. But an exceptional amount of intelligence has almost no bearing on whether one is an exceptional mathematician.

It's not entirely clear to me how somebody as mathematically talented as Tao could miss the basic Bayesian probabilistic argument that Scott Alexander gave, which shows that Tao's own existence is very strong evidence against his claim.

I think this is uncharitable to Tao. 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).

Comment author: JonahSinick 18 February 2015 08:34:54PM *  2 points [-]

Contrary data point here:

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.

Comment author: komponisto 19 February 2015 01:08:58AM 3 points [-]

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.

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