Comment by freehorse
1 day ago
> 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.
I disagree.
> 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.
This has not yet been explored with AI only because solving hard problems is where everyone, practicing mathematician or layperson, understands 99.99% of the prestige to be.
AI's attention will not be directed towards generating interesting new conjectures until all the low-hanging prestige-rich fruit of famous decades-old conjectures have been mined, because it makes no economic sense for frontier AI companies to do so.
There won’t be anybody around to understand and care about the new open problems if the AI companies proceed with totally destroying the culture of mathematics. Gowers doesn’t care, apparently because it’s just about winning for him. Same with Tsimerman.
[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"
So.. for eutripsis, Coasean Floor? Lol
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.
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