This is really a microcosm of one particular problem that AI presents to the world: what do people do when their labour is not required any longer?
Here the worry is the social structures of mathematics are eroded such that fewer humans become able to do the work and less well, similarly to how juniors are being recruited less in software engineering, breaking the ladder and leading to fewer seniors in the years to come.
The answer to this really depends strongly on what AI can actually accomplish, but I’ll assume the maximal case and say that AI can do everything economically necessary, and further even those things just desired, such that human labour isn’t required for anything that anyone wants in a practical sense.
Here, we don’t need a human understanding of mathematics to give people a perfect standard of living. We also don’t need humans involved with anything else.
Everything therefore becomes a hobby or a game. People do things because they enjoy them for their own sake, or because they are endeavours used as vehicles to socialise and enjoy others’ company, or because a shared social belief exists and is cultivated such that doing such and such a thing confers social status.
And I think that’s more or less it. I predict we may see some fairly strange sorts of things, such as games where the team structure looks like the descendant of a company org and they compete in an artificial economy. Likewise we may see gamified versions of universities and academia. All of these would be “tamed” such that the rougher parts of the experiences were sanded off.
Sort of like how we evolved in an ancestral environment, and we have certain drives and expectations driven by that environment even though they no longer matter for survival. Our social structures may be derived similarly from those of today, even after they have ceased to serve a real purpose, but changed and repurposed to give meaning and community.
> 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.
[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..
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
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
Chance-Device · · focus · HN ↗
Here the worry is the social structures of mathematics are eroded such that fewer humans become able to do the work and less well, similarly to how juniors are being recruited less in software engineering, breaking the ladder and leading to fewer seniors in the years to come.
The answer to this really depends strongly on what AI can actually accomplish, but I’ll assume the maximal case and say that AI can do everything economically necessary, and further even those things just desired, such that human labour isn’t required for anything that anyone wants in a practical sense.
Here, we don’t need a human understanding of mathematics to give people a perfect standard of living. We also don’t need humans involved with anything else.
Everything therefore becomes a hobby or a game. People do things because they enjoy them for their own sake, or because they are endeavours used as vehicles to socialise and enjoy others’ company, or because a shared social belief exists and is cultivated such that doing such and such a thing confers social status.
And I think that’s more or less it. I predict we may see some fairly strange sorts of things, such as games where the team structure looks like the descendant of a company org and they compete in an artificial economy. Likewise we may see gamified versions of universities and academia. All of these would be “tamed” such that the rougher parts of the experiences were sanded off.
Sort of like how we evolved in an ancestral environment, and we have certain drives and expectations driven by that environment even though they no longer matter for survival. Our social structures may be derived similarly from those of today, even after they have ceased to serve a real purpose, but changed and repurposed to give meaning and community.
freehorse · · focus · HN ↗
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 · · focus · HN ↗
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..
<a href="https://youtu.be/svl_1upFpQo" rel="nofollow">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
<a href="https://en.wikipedia.org/wiki/Negative_capability#Reception" rel="nofollow">https://en.wikipedia.org/wiki/Negative_capability#Reception
<a href="https://www.poetryfoundation.org/education/glossary/negative-capability" rel="nofollow">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? Lolfreehorse · · focus · HN ↗
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 · · focus · HN ↗
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