2026-07-25 01:07 UTC
Replies (3)
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@MaloTarpin@mathstodon.xyz 2026-07-25 08:45
@tao@mathstodon.xyz thank you for submitting yourself to this exercices. Albeit one could regret you kept it very self-referential by not seeking a ferocious technical human journaliste to interview you, one must recognize that the LLM questions were rather surgical. One angle which was glaringly absent in my eyes (and maybe for good reason because I feel you are usually silent about it) is the huge environmental cost of AI. How do you compound it with the current state of the world and where we are headed? Do you hope that more parsimonious use of lighter models could fit into a zero CO2 emission world? I feel like as a society we are extremely bad at cutting back on established habits so right now we are hurtling down a slope which will be very hard to come back up from.
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@wikiemol@mathstodon.xyz 2026-07-25 13:18
@tao@mathstodon.xyz Your recent blog post on the Jacobian Conjecture + these slides + your answers in this AI "interview" have done a fantastic job of painting a more hopeful picture of the future of AI use in mathematics (at least for me). I think this hope is especially kindled by finally seeing this topic of "foundations of practice" being taken up in earnest. You have talked about this in the past, but this is the first time I have seen it taken up with some eye towards being partially tractable with the tools of logic/math (instead of relying solely on empiricism). I personally think this will increasingly become more precise and more than a heuristic analogy. Explicitly stating the "Working Hypothesis" in a precise way is a great thing to do. This sort of clarity is extremely important and I think will help guide the discussion in more helpful directions. Like you mentioned, this shouldnt take away from your overall points, (which I think are absolutely fantastic), but I have one comment about this hypothesis. The analogy I might give is with the previous crisis in foundations. Classical geometry was "solved" by the notion of computability, but new problems arose that made the equivalent of the "working hypothesis" false anyways. Similarly, what is meant by "Research level mathematics" now could change and render the "working hypothesis" false in the future, even if it is true right now. This has been my primary issue with this hypothesis and I haven't had the chance to state this objection clearly since it is rarely explicitly stated. I.e. if even a small subset of problems are not AI tractable but are tractable by humans, then the "reasonably strong" form is likely to collapse to the "weak" form.
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@wikiemol@mathstodon.xyz 2026-07-25 15:09
@tao@mathstodon.xyz I realized that my last comment on the "Working Hypothesis" may seem more pedantic than useful. So let me describe why I think it is important, even if it may seem like its not. The important point is "value" being analogous to work in classical physics. The "value" of an AI may go down as its "information" is "digested", in the same way that the work an engine is capable of doing will go down as its energy is extracted, and if the energy is completely extracted then the engine stops being useful entirely. I think this is the fundamental principle behind the erdos problem submission issue that was faced. The value of these submissions has drastically decreased as previous uses in this area were digested, making AI use more unhelpful than helpful in these specific areas. But this has only happened over some (in this case small, but in general potentially larger) time scale, and is not apparent immediately without more detailed investigation. Then, in this specific area, the problems easily solvable by AI are no longer really considered "research level", rendering the Working Hypothesis false in this area. The "digestion" of its answers might be, but the AI cannot help as much with this, and in the hardest cases may not be able to help at all.