Sabine really be doin the Goomba fallacy
Mathematicians: How do you dare releasing such terrible AI-written proofs before humans checked them!
Also mathematicians: Release the proofs immediately!
Alright I’m coming around to this perspective. I still hope for a galaxy brain F_un solution but the possibility of an ANT bash succeeding is high enough that I now guess RH to be second-soonest, after Yang-Mills mass gap.
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I try not to let hype steer my Bayesian priors on these things, but my actual *personal* belief is RH may very likely fall by the end of next year.
Sure, people want to see F_1-geo, noncom algebra, Deninger cohomology, etc, but I think AI will soon be capable of theory building.
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The Yang-Mills proof is apparently 1147 pages!
In any case, they should release it immediately in my opinion. They write that they first want to assess the correctness before releasing. But how long would that take for work of that magnitude?
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@ElliotGlazer Could we do all four? Either for $1k each or $250 each from me, against $20k each or $5k each from you? Each bet would settle at 10 years or at first disproof. Positive proofs wouldn't settle the bet(s) because ZFC is in question.
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@tilmanbayer @Frances01896069 No. Appointing shepherds and then hiding behind their decision does not absolve you of responsibility
oh, i know this one!
7 is quite special there
161 also gives a nice answer
55 works with a cube root
@AcerFur So this was mostly a bet on autoformalization, but a problem-solving point: I’m super bullish on models’ finitary algebra reasoning, so “parallelize the proof and fill in the holes” seems tractable to me.
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1. Congrats for formalizing CFSG! Imo the importance here is that this is a blackbox result for which a mere "truth certificate" is intrinsically valuable and adds confidence to many results atop.
2. The biggest correction was of a wrong proof of UGT, which already had other proofs since then. I think this largely justifies the common wisdom "There are mistakes in the literature, but CFSG has long been proven."
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The largest math proof in human history is now computer-verified.
Today, Axiom announces a complete Lean auto-formalization of the Classification of Finite Simple Groups, the "periodic table of symmetry."
About 15,000 pages, built by over 100 mathematicians across generations.
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The ETH repository has a paper where it appears an Anthropic internal model independently disproved the Exponential Time Hypothesis?
good read for what might come next:
My ranking has not updated whatsoever, btw
This is why God gave us Astra folks. I’m sure one of you already has agents working around the clock to formalize Con(ZFC) in PowerPoint.
@ElliotGlazer @ereliuer_eteer yo. i took K230 and compiled it into an explicit Wang tile set. 975 tiles _ one seed, and the seeded half-plane tiles iff K230 never halts, i.e. iff ZFC is consistent. So it’s an explicit finite tile set whose tileability is independent of ZFC
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I now have a literal Peano Arithmetic proof that K215 halts iff ZFC is inconsistent, formally verified in Metamath Zero.
K215 is a 215-state Turing machine discovered by @ereliuer_eteer, which encodes my single-schema set theory K.
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My take is it's somewhere between the convex hull and the generated subgroup, but the hull is closer. If we literally allowed unbounded application of existent techniques in this metaphor, that would surely contain every ZFC-derivable theorem...
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Based on a hot tip: I had Astra check the OpenAI paper "Algebraicity of Weil classes on split abelian eightfolds", and it seems to be flawed. This is one of the nonformalized results. Concerning.
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My ranking has not updated whatsoever, btw
@JDHamkins So in summary, in the extension of L by \aleph_1 Cohen reals, there is a unique-up-to-isomorphism ℝ-sized countably saturated model of PA, and a unique-up-to-isomorphism ℝ-sized hyperreal field, each without any definable instantiation.
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@JDHamkins So in summary, in the extension of L by \aleph_1 Cohen reals, there is a unique-up-to-isomorphism ℝ-sized countably saturated model of PA, and a unique-up-to-isomorphism ℝ-sized hyperreal field, each without any definable instantiation.
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@JDHamkins There was a clear route to success. I just needed to prove this conjecture: “In L adjoined by \aleph_1 random reals, every definable set of size \aleph_1 consists of definable elements.” Here definability allows ordinal and real parameters.
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@gregeganSF Oh, then you will love the part where a community came together and used AI agents and formal verification to replicate and improve on the secret result:
