> what do people do when their labour is not required any longer

I don't think this is the main issue (if at all) discussed here or in the field medalist letter. If anything, the majority of pure mathematics graduates are absorbed from the industry and a lot of exodus happens along the different scales of academia to there (though industry is also dealing with this issue but that's not what's concerned here). The issue discussed is what mathematics itself will be, which is much deeper. AI finding proofs to open problems does not solve at all the question of how to produce new problems, and there is no indication imo that there is way to go with that with AI.

Pure mathematics is not like applied sciences, as it is only tangentially influenced by external applications. Deciding which problems to tackle is a social process and a matter of taste/aesthetics, and is built largely through the exact friction that is more and more removed with AI. This is what makes it unclear how one can find problems without this friction, and none of these posts/letters have an answer really. Each one seems to describe just different standpoints than concrete, practical ideas.

▲ oliculipolicula 12 hours ago | parent [-]

[Sorry that none of the following is concrete, but perhaps elucidating the paradox contained within might open our minds to .. the shape of the paths to action ?]

Your productive friction (eutripsis? ~ negentropy? Viscosity!!!???) seems like a wonderful concept that the original letter should have flagged to rally the community ( Gowers might not have missed this point if they had a new name for it!)

Tao had a relevant talk about the paradox of efficiency..

https://youtu.be/svl_1upFpQo

It's not clear to me that AI necessarily removes this eutripsis. The threat though, might become real if users don't see the threat :)

Also reminiscent of Keat's

https://en.wikipedia.org/wiki/Negative_capability#Reception

https://www.poetryfoundation.org/education/glossary/negative...

Still abstract, but nearer to quantitative (mathematical anthrop(ic)ology even?): ordinary, bad friction is, eg, "size-consistent"

   Coasean Ceiling: organizational size limit where the internal friction of managing a firm consumes all of its energy, leaving nothing left for actual production

So.. for eutripsis, Coasean Floor? Lol

▲

freehorse 11 hours ago | parent [-]

That's a good point. And yeah I got the term from Tao, as I had not described it this way before but I think it elucidates well the issue.

The problem imo is that, from a purely psychological/phenomenological perspective, there is not always a perceivable difference between "eutripsis" and "dystripsis" (just made it up but "dys" is the opposite of "eu") as experienced. There is some reward coming from learning through friction (depending on personal interests, environment etc), but mostly it is effort and humans usually try to reduce or avoid effort.

Moreover, even if one tries to be fully mindful and choose where to employ friction and where not, there could be systemic factors to optimise away any kind of friction. Imo we already see that in software engineering, judging from a lot of different anecdotes, where increasing the pace of generating code sacrifising human understanding is already taking place. It is not like these forces are not already in place widely in academia too even before AI (eg optimising for paper output quantity), so AI reinforcing this direction sounds a reasonably probable scenario, unless some other action is taken.

	▲	oliculipolicula 11 hours ago \| parent [-]
		Ah, contrary to what I mused elsewhere, concreteness can also lead to bad friction Eg, KPIs, metrics, but of productivity, of "veracity", not understanding Anecdotes--> better friction than data, sometimes, though :) How about Inverse Metrics. of simplicity? Parsimony? Shortness of code? (Efficiency/compressibility is a sort of "intensive" metric, so it might not be especially relevant, thermodynamically speaking) Just taxidermy, stamp collecting, and vibe-anthropologizing here TT