As far as I can tell, the whole job of mathematics professors is to obfuscate the fact that this is a thing.
@DRMacIver is a computer scientist and hasn’t been forced to take the sacred vows of silence. Yet. They won’t let him go much furtherhttps://twitter.com/DRMacIver/status/1189827287748927488 …
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Replying to @Meaningness @DRMacIver
The sentiment here expressed is no doubt somewhat tongue-in-cheek, so it's unclear how seriously to respond to it. But, for the record, obfuscation is not the whole job of any mathematics professor. Most strive ceaselessly to make themselves clear. (And usually fail, alas.)
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What is true is that few mathematics professors are willing to confess publicly their private heuristics and intuitions; as Grothendieck once famously lamented, a perverse taboo among them seems to seal their lips on these matters, which, as Leibniz correctly argued, matter most.
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Replying to @Meaningness @DRMacIver
An interesting justification for silence on these matters -- and, curiously, one more common among the best elder mathematicians -- is that keeping mum prevents talented young people from wasting their time in hero-worship-motivated yet doomed and misguided attempts at imitation.
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Replying to @MathPrinceps @Meaningness
My suspicion is that it is more commonly just vanilla curse of knowledge and people not consciously knowing things that they have very heavily internalised.
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Replying to @DRMacIver @Meaningness
This of course plays a major part in the phenomenon. But I don't think it can account for everything. One still sees this perverse embarrassment/diffidence in elder masters, who have spent decades reflecting on their practice, and know a great deal about why they do what they do.
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Replying to @MathPrinceps @Meaningness
Yeah, it's probably also true that people who can don't, but I don't think that accounts for most teachers of mathematics.
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Replying to @DRMacIver @Meaningness
Most mathematics professors are, of course, selfish. They prefer to pursue their own research, and are incentivized to do so. And if the only audience to whom they are required to address themselves consists of their own colleagues, then of course communication skills atrophy.
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But it is truly extraordinary how far the atrophy can go. For decades, Atle Selberg's office at the IAS was directly across the hall from Robert Langlands'. Hard to imagine two men with more to talk about -- yet in all that time, they seem to have had exactly one conversation.
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