MC retweeted
I don’t think there is much reason to believe that the health of mathematics, the dissemination of knowledge, or the future of humankind are of any real concern to these companies. What is certain is that they are positioning themselves for an IPO. If any of the individuals at their helm are motivated by something beyond personal wealth, I suspect it’s personal power and influence. Assuming otherwise seems a bit naive.
It’s frankly disheartening to watch journalists interview them as though there were some higher purpose at work.
It’s the magic of our times: relentlessly cynical about everything and everyone, yet somehow willing to take at face value anything said by the rich and powerful.
MC retweeted
My point was that Altman is fully aware of the damage done to the community of mathematicians and that this is not the last community he is willing to destroy for "the benefit of humanity"
MC retweeted
AI数学の発展によって学生やポスドクが何を感じているかの調査結果が発表された。執筆したのはMITの博士課程の学生たち。
全ての数学者は一旦研究を止めてこの結果に向き合うべきだと思う。
「博士・ポスドク終了後に研究を続ける可能性は？」
７割が減ったと回答。
「AIの発展によって研究への意欲は高まったか？」
８割近くが減ったと回答。
付録では様々な質問に対する自由記述の回答が15ページにわたって続く。
そこには、数字だけでは見えない若手の切実な声が並んでいる。
arxiv.org/abs/2610.40584
MC retweeted
First, what exactly do we gain from a committee taking "custody of the proof" and "shephard(ing) the release process"?
Second, this is a math problem. Approaching David Gross looks like an attempt to buy credibility instead of technical scrutiny
Statement of Yang-Mills Working Group, a scientific collaboration to interpret AI result related to the existence of quantum chromodynamics & completions of the Standard Model, including a subproblem proving the existence of the Quantum Yang-Mills theory. buff.ly/BwV89Tk
MC retweeted
"Before AI, you could publish open-source code, write blog posts to share ideas or inspire other people, write expository texts like tutorials, forum posts, textbooks etc. to teach people. After AI, what’s the point?"
borretti.me/article/no-man-i…
MC retweeted
As Anthropic prepares to IPO for over $1 trillion, a reminder of Dario Amodei’s words shortly after founding the company:
“Distributed human labor is being used to train AI models by large, centralized actors, who concentrate the resulting profits while in the long run making the human labor obsolete.”
In other words, this IPO will be built off the backs of the world’s creatives - who will get nothing out of it except obsolescence.
It is a totally unjust transfer of wealth and opportunity from artists, writers, musicians & other creatives to a tiny tech elite.
I hope it is remembered as such.
(this quote is from a document he wrote that was unsealed in Bartz v. Anthropic)
MC retweeted
In case anyone missed this, OpenAI has proved the Kakeya conjecture in all dimensions.
Hong Wang got the Fields medal in 2026 for proving the Kakeya conjecture in dimension 3.
In fact OpenAI appears to have committed, in mathematics terms, what may be fairly termed a massacre, proving a far stronger result. It has proved the local smoothing conjecture, which sits at the very top of the tower of conjectures as described in the Quanta article in the reply.
I am not an expert in this area -- so happy to be corrected -- but the methods appear to be PDE based and basically bypasses a lot of work of the last two decades. This is the equivalent of Arbreans showing up to earth with an everything killer and explaining to us we have been doing warfare all wrong.
Announcing three major scientific discoveries, one each in mathematics (harmonic analysis), computer science (complexity theory), and physics (quantum field theory).
AI starting to help us improve our understanding of the universe! openai.com/index/building-sc…
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There is something odd about this. With all due respect to past achievement, setting up a collaboration where the lead is 85 and one member is 88 doesn't look optimised for science. Why not get the best modern QFT experts here? I could name the people who should be on this.
The physics collaboration will understand and explain a result that gives a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.
As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. These proofs are all formally verified in Lean.
Our models produced a natural language proof for Yang–Mills existence, and then subsequently produced a proof for QCD After the formalization completed, we reached out to David Gross. David will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work, and we will defer to them on the release of materials.
Gross’s work on asymptotic freedom in Yang-Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millenium Prize problem with Witten and also envisioned the idea of Millennium Prize problems and co-founded the Clay Mathematics Institute. Douglas has already been a steward of this problem over the last 20 years; Klebanov helped pioneer the application of gauge–string duality to confinement, an important property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings; and Nekrasov has done groundbreaking work on exact methods for generalizations of Yang–Mills theory.
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An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4
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Wooow – Kakeya conjecture solved in all dimensions by OpenAI in a 50 page paper!
Actually this paper proves a much more general conjecture. Looks from afar like very significant progress on that topic!
github.com/openai/math/blob/…
openai.com/index/building-sc…
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Our letter to the community invites ideas for organizing this effort and, separately, for addressing the broader questions raised by AI-generated results:
docs.google.com/document/d/1…
OpenAI's announcement is here: openai.com/index/building-sc…
MC retweeted
As was well-known, and circulated a number of times even on here, Ethan Sussman has been writing up existence of YM4 publicly via Balaban’s approach, and has posted existence of QED3 and YM3 and an old preliminary outline of YM4 on his repo, working with countless community members in understanding the arguments. I kept telling him to not be too deferential and modest because he would be publicly scooped at any opportunity. Instead of contacting him to work with him, as has been suggested publicly many times, the people at OpenAI chose to do this.
“Our work builds on Balaban’s approach in constructive quantum field theory. As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang Mills Theory Clay Mathematics Institute Millennium Prize problem.”
We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.
openai.com/index/building-sc…
MC retweeted
they should IMMEDIATELY release this
we do no need shepherds
The physics collaboration will understand and explain a result that gives a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.
As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. These proofs are all formally verified in Lean.
Our models produced a natural language proof for Yang–Mills existence, and then subsequently produced a proof for QCD After the formalization completed, we reached out to David Gross. David will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work, and we will defer to them on the release of materials.
Gross’s work on asymptotic freedom in Yang-Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millenium Prize problem with Witten and also envisioned the idea of Millennium Prize problems and co-founded the Clay Mathematics Institute. Douglas has already been a steward of this problem over the last 20 years; Klebanov helped pioneer the application of gauge–string duality to confinement, an important property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings; and Nekrasov has done groundbreaking work on exact methods for generalizations of Yang–Mills theory.
MC retweeted
Two physicists asked AI to choose a problem on its own, solve it and write a paper that could be published in a prestigious journal. In two hours, AI produced a paper with a novel, significant result.
MC retweeted
Since I'm now blocked by bluey from replying to this thread, I answer here by quote tweet
the openAI construction has more to do with convex integration than anything else.
In convex integration, the oscillations are typically built by hand and the iteration procedure creates wild weak solutions. The non-uniqueness construction of Albritton–Brué–Colombo used an unstable vortex to split solutions apart. The Córdoba–Martínez-Zoroa singularities amplify vorticity across scales by strain. In the openAI paper, a fluid instability is clever made so that the flow itself generates the oscillations: they grow by drawing energy from the background shear. The Reynolds stress then becomes the force that creates the collapsing smooth vortex. Using a physical instability to create the stress in this way has no precedent, and it is what produces a smooth force rather than a merely rough one.
Some on these ideas are in the literature (e.g. Leibovich-Stewartson 1983) but the way they are combined is definitely insane and definitely nowhere in the literature previously.
I also don't know of anyone suggesting that convex integration would play a role in the creation of a blow-up solution like this.
On a technical level, the paper is unbelievable, maybe beyond what a human could have come up with but not beyond human understanding: there are several different groups of pde experts working on understanding it who say that they more or less understand now. I expect digestions soon
td;lr: anyone saying that this OAI result is unsurprising is bullshitting
sorry!
Or it’s reasonable. Especially considering what the models were trained on, and that they spent $15M in compute instead and of $15M in consulting fees for specialist mathematicians to just do research (no teaching no service).
I don’t know why mathematicians want to pretend that no relevant progress was made before OAI released their solution.
MC retweeted
OpenAI's proof of the Haldane gap in the S=1 antiferromagnetic Heisenberg chain: Expository notes
haltasaki.github.io/writings…
MC retweeted
My friend and colleague Bill Banks has just uploaded a very nice exposition on the proof of no Siegel zeros:
arxiv.org/abs/2610.15483
