2026-08-19 20:02 UTC
Replies (9)
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@kangmeister@mathstodon.xyz 2026-08-19 20:46
@tao@mathstodon.xyz This seems predicated on the notion that the Companies (who have little to no intrinsic interest in the mathematics itself) would continue to invest their resources in producing theorems. Do you see that continuing indefinitely? Maybe it's my own lack of imagination, but I'm struggling to envisage any long-run founts of theorems having no intrinsic mathematical motivation, which would necessitate such a regime. (I somehow prefer not to phrase this comment in terms of the analogy.)
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@wikiemol@mathstodon.xyz 2026-08-19 20:55
@tao@mathstodon.xyz I am probably a bit of a thorn with all of my comments on your posts at this point, but it is one of the only ways I can see myself having any modicum of input into the future that I will be mostly inheriting (as opposed to shaping). These analogies are being stretched too far: we desperately need more precision. You have framed the 'crisis' we are facing today as being primarily about values, rather than the truth status of what you called the (family) of capability conjectures (cc). I don't disagree with this. However, I believe you called the cc a "distraction", and called for mathematicians to redirect their focus towards values. This is where I disagree: right now there is a huge problem with framing the current 'crisis' in terms of values. Framing the crisis in terms of something so subjective has created an environment where we have a small group of mathematical oligarchs, and they are enforcing their values on everyone else, with absolutely no recourse for others (with less 'clout') to influence the direction of our field (unless the oligarchs say so). Personally, I believe these oligarchs to have mostly benevolent intentions. But thats not the point: this is not what mathematicians are meant to do or how mathematics is meant to work. I do not inherently disagree with framing things in terms of values. However, there is no (current) standard of quality or correctness with regard to these discussions in the context of mathematics. And without that standard, there will always be pushback.
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@bradheintz@mathstodon.xyz 2026-08-19 22:52
@tao@mathstodon.xyz The parenthood analogy has some utility, but I think you're reaching the limits of it. In the case of parenthood, a vulnerable human life is the driver of all the concerns that necessitate all the alternatives to a problematic or unavailable traditional parenting model. This does not apply to mathematical proofs. I'm just a master's student in mathematics, and no one is going to ask me to review a non-trivial proof, at least this week. That said, I have thirty years of experience building software, and I think an analogy to software engineering might be informative. A program does what it is supposed to, or not; a proof is correct, or not. Just as proofs require expert review to be accepted into the mathematical canon, most software teams (whether internal to a company, or a widely distributed open source project) require review by an expert for any change to the software to be accepted. If someone submitted a code patch for me to review, along with the information that they did not understand the code they had submitted, I would reject it out-of-hand without review. In this case, the odds that the patch introduced a subtle bug not covered by tests, or exploited an existing undetected bug to appear correct, or just generated values that passed the test, or had disastrous performance characteristics would be intolerably high. "Intolerably", because I'd be the one debugging what should have been debugged before it came to me, which wastes my time. I am far from alone in this attitude, as many open source projects inundated by superficially correct but bogus AI slop pull requests have started taking a hard line on AI usage and pull request quality. 1/
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@OndrejDvorak@mathstodon.xyz 2026-08-20 00:23
Here is my AI assisted research, lots of stuff and very fancy animated app. @tao@mathstodon.xyz https://zeta.pukapasoft.xyz/
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@tomkalei@machteburch.social 2026-08-20 07:28
@tao@mathstodon.xyz To stay in your analogy, we could face a future in which suddenly almost no child is conceived in the 'traditional way', though. To push it even further, the non-traditional children/proofs will also be much stronger and punch the traditional children to steal their breakfast all the time. I think the analogy has reached its limit.
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@srinivas@mathstodon.xyz 2026-08-20 08:47
@tao@mathstodon.xyz I had thought incentives strongly favoured your present position after reading your initial "proof-parenting" post. I take your metaphor to mean "division of labour for proof-work". I'll use it as such to avoid fraying a nice metaphor. If mathematicians are selflessly proof-minded, it seems to make sense to formally divide labour for proof-work so each division may be undertaken by the agent (human/AI) best suited for it. However, if we assume personal mathematical motivation, "proof-adoption" may seem bleak since it forebodes less natural "proof-conception", "proof-gestation" etc. as AI learns to be best suited for every necessary task. The motivation for AI to prove something seems to have at least one natural source, @kangmeister@mathstodon.xyz - the utility of the proof to the larger sci./engg. agenda: a proof guarantees a claim, minimising the risk in making decisions with it and saving costs downstream. Currently a proof requires human insight and understanding. If, instead, these are mere niceties afforded by AI, then they will likely disappear over time when their utility - getting enough mathematicians to feel safe adopting & training AI - is fulfilled. However, I still think there is a strong argument for engaging in part of this dynamic.
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@sk123@mastodon.social 2026-08-20 14:22
@tao@mathstodon.xyz So is the point of this to actually formalize the math development process? Do you want people to exactly state whether their article is a generation, verification etc.. to make it easier to do peer review and assign credit? To me it would be better to look seriously into decentralized remunerated peer review since that's really the main issue with academia long before AI is now pressure testing it.
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@gotanegra@mathstodon.xyz 2026-08-20 18:38
@tao@mathstodon.xyz AI will discover, verify, explain and canonize mathematics better than we can. If not in one year, then in five. Moving “mathematical value” to whichever stage remains human is not a principle; it is a retreat. The scarce resource will be the question.
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@TaliaRinger@mathstodon.xyz 2026-08-28 02:49
@tao@mathstodon.xyz I think in open source software (if the proofs are formal, for example) this just happens naturally with reasonable licensing. The clash with academic research is that the credit systems are not aligned with that, so there is little incentive within academia to be the one who adopts or disseminates. Though in computer science research, there is some prestige involved in doing this, even if it is orthogonal to other prestige markers like publications