It requires more motivation than most people usually feel -- and more time and effort that most people are prepared to devote to it. Which is especially odd, when you reflect that, with this particular form of wealth as with all others, you can't take it with you.
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Replying to @MathPrinceps @DRMacIver
OK, here’s the plan. We deploy elite special forces units to capture all the Fields Medalists and take them in black helicopters to a purpose-built underground fortress on Svalbard, and use secret CIA psy-op interrogation techniques to force them to reveal what they know
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Replying to @Meaningness @DRMacIver
Honestly, what impresses me most is how profoundly the attitudes of great masters vary from art to art. Itzhak Perlman, Emanuel Ax, Midori -- all have put a great deal of effort into transmitting their tacit knowledge. The number of great mathematicians who do likewise?
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Replying to @MathPrinceps @DRMacIver
Zero, I think. Rota and Thurston are partial exceptions. Any others?
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Oh, and Terry Tao.
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Replying to @Meaningness @DRMacIver
The thing is, they become more common, the further back in time you go. This is what worries me most: the practice of apprenticeship itself seems to be decaying. Once there were giants: Lefschetz, Zariski, Chern, Bott. Fewer and fewer great mentors now.
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yes, this is my sense too! something very strange seems to have happened to mathematics sometime in the last ~50 years and i wish i knew what
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It's a gradual process of decay, I think, that was for a time largely masked by the unusual longevity of those great masters directly connected by intimate personal ties to the last generation of mathematicians whose education took place largely outside of modern institutions.
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Replying to @MathPrinceps @QiaochuYuan and
Another point worth emphasizing, though, is that there are two parties to an apprenticeship, and each must understand the purpose of the practice, and how each contributes to its success. It's not just great mentors, but also keen apprentices, who've grown gradually scarcer.
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Replying to @MathPrinceps @QiaochuYuan and
This is no great surprise, of course, and no one is to blame; as cultural practices come to seem obsolete and irrelevant, people forget how to engage in them. A few decades ago, every physics student knew how (and why) to use a slide rule. Now, most can't even recognize one.
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Similarly, there was a time not so very far removed from ours in which many young people took dancing lessons, and learned to waltz (and even to tango, and to cha-cha-cha.) Mathematics students today want to be apprentices about as much as they want to learn to waltz.
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