Mathematician with wide interests. My job is at Barnard in NYC. Talk to me! Twitter is for fun 🦋
NYC
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I’ve made a visualization of the counterexample to the jacobian conjecture which involves high school math, three lines and two parabolas. In fact this diagram can be easily be turned into a proof that the construction gives a counterexample. Enjoy! jacobiancounterexample.net @__alpoge__
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People on this app don't appreciate how well purely human mathematics is doing. People prove major results literally every few weeks, with proofs that are insightful, beautiful, and solve many problems simultaneously. Currently reading this wonderful thing: arxiv.org/pdf/2608.26392
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At the moment we seem very obviously in the centaur era of math — and it is cool. (And imo Navier Stokes really counts since there is a lot of human infrastructure in the setup.) I like these short arguments that someone should have found long ago!
SITUATION DETECTED: Holomorphic Dynamics. The wandering domain results got destroyed by the machine.
A paper of Ye proves a much stronger result just using hyperbolic metric considerations. The machine found the argument.
arxiv.org/abs/2609.23834
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Semon Rezchikov retweeted
SITUATION DETECTED: Holomorphic Dynamics. The wandering domain results got destroyed by the machine.
A paper of Ye proves a much stronger result just using hyperbolic metric considerations. The machine found the argument.
arxiv.org/abs/2609.23834
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Semon Rezchikov retweeted
Hide the proofs inside plastic eggs and have mathematicians hunt for them in a big outdoor event.
This advisory group created by IAS is advising OpenAI in how to release their math results
Mathematicians can give their opinion in this link
agmai.org
I share publicly my opinion below (more than happy to have debate / disagreements in the responses!)
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A faculty friend of mine once gave me this (amazing) classification of motivations present in professional mathematicians for doing mathematics: 1. Science (understanding of phenomena) 2. Art (beauty, style) 3. Systematization (what is the “right language”) 4: Sport (prizes).
Different mathematicians have different mixes, all are quite present in aggregate. These different motivations explain many of the different reactions to the AI advances!
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Hmm, have you made any public statements in the capacity of a journal editor?
For instance, would a journal where you’re an editor accept a paper “explaining” the proof of S^6? Would it accept the original paper by Fable?
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One of the interesting things about the implicit argument posed by the AI labs is “planning for the future is pointless”. Because we will have AGI in <4 years, ASI soon after. So anything that involves planning for after that (institutions etc) is silly (unless AI related).
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This (time horizon >4 years is dumb) came up when talking to my colleague Prof. Corwin about his AI-math essay. I said that “we need academic institutions for long term human capital” doesn’t engage with the argument that we need no new human capital. He didn’t like that.
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The funniest possible reply
Oh hey, thanks for trying this! Just to give context, the challenge I issued is a special case of a Corollary of a more general theorem in a recent paper series by Sean Cotner and myself (and I would be remiss not to mention that Cotner did most of the math and writing). This manuscript literally uses our work, which handles the general case, to deduce the special case. So it certainly doesn't "count" for the challenge! (There's a reason I said 72 hours.) As Thomas Bloom said, "Think things through for yourself", folks!
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It would be nice to ask the Math-AI world to produce a '"proof" that the Lean kernel is consistent' before requiring that wholly human-non-understood leanslops are considered to be 'proofs', since the current situation is a degradation of the historical standard of proof even by Hilbert's standards. (And pre-Cauchy mathematicians would certainly not be inspired.) Here the idea of a "proof" would be something that fits the standard of proof established over the past 100 years since Hilbert.
I am a dum-dum and don't understand formal proofs. One way that I personally would feel good about Lean being proven 'consistent' is if there was a human-understandable proof that there is a model of Lean 4 in ZFC. Is this plausible? (I mean both the mathematical statement, and separately the idea that someone might actually produce a proof of this.) I've been trying to wrap my head around how different things like lean4lean and con-leche are from this very 'classical' approach and I'm still fairly unclear on how these relate to whatever I learned 'proof' to be.
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proposal for pacing the frontier: each AI lab invests 30% or more of its compute budget to train and deploy agents to hack into, degrade and/or take down the other labs' abilities.
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Real question: given that the lean kernel has bugs, what are *currently* the practical strategies for making sure that these ai generated massive lean “proofs” do not rely on kernel bugs?
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I enjoyed Tao’s comments on the mathematics in Buckmaster-Alpöge-Claude-Codex’s argument, as well as his comments on the mathematical value of the work. Worth a read! mathstodon.xyz/@tao/11723352…
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To be honest I thought this ns blow up result was supposed to happen last summer, what took everyone so long?!!
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