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Tyrrell_McAllister comments on Negative and Positive Selection - Less Wrong
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That'd be a much harder question to answer; my talent is specialized toward figuring out the shape of the right theorem to be proved, not the actual proof which is where most modern math concentrates its prestige. (This is an objectively verifiable form of mathematical talent; it means that sometimes Marcello would prove something and I would look at it and say, "That doesn't look right" and at least half the time there'd be a mistake.) I feel insecure about not being an expert in the tools by which most modern mathematicians measure basic competence; I can also apparently make "well, if that's your problem, try transforming it this way" suggestions to someone doing graduate mathematical research at Yale that are accepted as brilliant. I confidently depose that, even taking unusual talents into account, I am not in the literal top tier of mathematical potential - if I can explain basic Bayes better than anyone or was first to state the Lob problem or invented TDT, those outputs drew on at least some non-mathematical high-percentile sections of my brain (explanatory ability in the first case, or what's somewhat vaguely referred to as "philosophical" talent in the other two). I'm also reasonably confident that, given a hundred modern mathematicians, an average of zero will pick the right problem to solve.
I think I'm comfortable at this point with saying that I'm in the top 99+% of writers - I've been picking up "real" books and trying to read them and finding that they seem visibly badly-written to me now that I've written HPMOR. Though I'm still not in the literal top tier; there are basic things in writing that I still don't do too well, despite being outstanding in others, and my new level of skill is just enough to start noticing that Neil Gaiman and Terry Pratchett are doing things way the hell above me.
Being able to give some actual proofs is a prerequisite of prestige. But it's not clear to me that it's right to say that mathematics concentrates its prestige there. See, for example, Fields Medalist Timothy Gower's article The Two Cultures of Mathematics (pdf):
I suspect the distinction Eliezer is making is more akin to the controversial "theoretical vs. experimental" one proposed by Jaffe and Quinn than the traditional "theory-builder vs. problem-solver" one discussed by Gowers.
It's been years since I read the Jaffe–Quinn article. But, as I recall, it was more about the methods used to answer questions, and about how rigorous human-verifiable proofs might give way to heuristic/probabilistic and computer-aided proofs. Eliezer, on the other hand, seemed to be saying that mathematicians concentrate prestige on answering questions (by whatever means the community considers to be adequate), as opposed to "figuring out the shape of the right theorem to be proved".
Jaffe and Quinn mainly advocate that labor should be divided between people who make conjectures ("theoreticians") and people who prove them ("experimentalists"). I don't think there is much of anything about probabilistic or computer-aided proofs.
You are right. Looking at the Jaffe–Quinn paper again, it is closer to the distinction that Eliezer was making. (However, I note that the mathematical "theoreticians" in that article are generally high-prestige, and the "rigorous mathematicians" have to fight the perception that they are just filling in details to results already announced.)
My mischaracterization of Jaffe and Quinn's thesis happened because (1) Thurston replied to their article, and he discusses computer-aided proofs in his reply; and (2) even more embarrassingly, I conflated the Jaffe–Quinn article with the Scientific American article The Death of Proof, by John Horgan.