Tyrrell_McAllister comments on Negative and Positive Selection - Less Wrong

71 Post author: alyssavance 06 July 2012 01:34AM

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Comment author: Tyrrell_McAllister 05 July 2012 09:46:48PM *  2 points [-]

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.

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):

The “two cultures” I wish to discuss will be familiar to all professional mathematicians. Loosely speaking, I mean the distinction between mathematicians who regard their central aim as being to solve problems, and those who are more concerned with building and understanding theories.

...

Let me now briefly mention an asymmetry similar to the one pointed out so forcefully by C. P. Snow. It is that the subjects that appeal to theory-builders are, at the moment, much more fashionable than the ones that appeal to problem-solvers.

Comment author: komponisto 05 July 2012 09:59:04PM 0 points [-]

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.

Comment author: Tyrrell_McAllister 05 July 2012 10:31:39PM 0 points [-]

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".

Comment author: komponisto 05 July 2012 10:45:36PM 0 points [-]

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.

Comment author: Tyrrell_McAllister 05 July 2012 11:31:01PM *  1 point [-]

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.

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