2026-08-27 19:07 UTC
Replies (7)
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@pschwahn@mathstodon.xyz 2026-08-27 19:47
@tao@mathstodon.xyz Another compounding factor is that the review process, even for a single publication, might be becoming more difficult and subtle. Everyone knows that LLMs are prone to introduce errors, but it might become increasingly harder to spot them (in comparison to human-made errors), because LLMs are trained to be glib and convincing (and are constantly getting better at it). Combine this with the fact that we all routinely underestimate how easy we are to manipulate, and the prospect is bleak.
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@torgeirlysen@mathstodon.xyz 2026-08-27 23:07
@tao@mathstodon.xyz If AI eventually becomes the primary way of generating proofs, generating expositions, and curating results, what is the role of humans? It seems unlikely to me that human understanding will persist if humans aren’t given tasks to exercise and demonstrate our understanding. Delegating curation to AI also makes me uncomfortable. I think most people agree by now that the algorithmic recommendations have negatively impacted society as a whole. Do we want to go down the same route with scientific publishing?
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@TomL@mathstodon.xyz 2026-08-27 23:48
@tao@mathstodon.xyz In the old days logarithms were hard to calculate so people compiled them into large logarithm tables. Later we used tools like calculators in their place. I wonder if something similar is happening with proofs. They have been hard to generate so we store our efforts in publications. But as auto-proof and auto-write-up tools get more capable there will be less need to 'cache' them as a giant corpus. Instead people may simply run them on demand.
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@Ale_xia1979@mathstodon.xyz 2026-08-28 01:25
@tao@mathstodon.xyz You have identified a real crack, and it is more fundamental than everything we have discussed so far. --- ## 1. Where the artificial cut occurs The basic operation of standard mathematics is this: first take an algebraic object (a number field), then complete it separately with respect to each valuation, obtaining local fields whose metrics are mutually incommensurable. That is the cut: | Local field | Metric | Hausdorff dimension | Unit circle | |-------------|--------|---------------------|-------------| | `ℝ` | Archimedean | 1 | Degenerates to `{±1}` | | `ℂ` | Archimedean | 2 | Full `S¹` | | `ℚ_p` | Non-Archimedean | 0 | Finite discrete |
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@srinivas@mathstodon.xyz 2026-08-28 03:03
@tao@mathstodon.xyz @pschwahn@mathstodon.xyz @TomL@mathstodon.xyz This argument seems to confirm that good intellectual culture is necessary to reliably produce good intellectual output; good tech alone is insufficient. Here, the transition probability from `Proof' to `Exposition' would be a function of mathematical culture. This can be incentivised as your other recent posts acknowledge - via social norms, proof-adoption, appropriate attribution, etc. - to respond to the incentives presented by AI, which here increases the transition probability from `0' to `Proof'. These companion-statistics perhaps inform a baseline for AI: distribution of websites providing "quality" content over time (tech: www), distribution of "good" books over time (tech: printing press), distribution of "important" written correspondences over time (tech: postal service, email) etc.
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@robtrew@mathstodon.xyz 2026-08-28 08:33
@tao@mathstodon.xyz Disintermediation of filtering and validating institutions has been dramatic outside mathematics since the start of the digital deluge. Not easy for such institutions to survive, or for more resilient currencies of trust to emerge.
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@wikiemol@mathstodon.xyz 2026-08-30 01:07
@tao@mathstodon.xyz Is it not the case that the inevitable increase of entropy relative to the training data that went into the AI is a relatively basic result due to the data processing inequality?? I really want an answer to this question and I have no one to ask, except those online, but no one has actually answered it. Now, it feels like you are saying (essentially) the same thing. In other words, just like energy is lost to heat when processed through an engine, an AI processing our repositories of information will lose some of that information to noise. This is only in cases where Tarski's undefinability theorem applies (and its para-complete relative based on the Liar's revenge) such as in the case of an AI attempting to approach 'General Intelligence' (meaning, conservatively, that it can solve any math problem that has a truth value), because only results like that allow you to show that the inequality is a strict one by taking the limit as the AI gets better. If no information was lost, then the AI would approach a [potentially para-]complete truth predicate over time, so the limit will be a self applicable truth relation, which can't exist... (its not merely that its not definable, a self applicable truth relation can't exist). So, if an AI manages to produce 'technically correct' results, there must be residual information contained in our existing repositories of information, e.g. in how things are written or potentially simply what is important (similar to how prefix-free codes can contain 'residual' information), that must be currently being destroyed if the information is not being lost to 'technical incorrectness'.