Andrew Curran @AndrewCurran_ · 18m
OpenAI confirmed to the New York Times that they have made "substantial progress" on another Millennium Prize problem in the last five days, and are preparing to announce.
The rumors for the last 48 hours have been OpenAI solved the Hodge Conjecture, and that Anthropic has solved the Birch and Swinnerton-Dyer Conjecture. Since Navier-Stokes rumors abound, so I was reluctant to post about either. However, OpenAI's statement to the NYT now gives the Hodge rumors some very serious support.
In general people have not updated yet that the new unnamed OpenAI model, the one that finished training about two weeks ago, which I believe will be named Aeon, is massively better at math than Astra, which two weeks ago was the best in the world. Aeon solved Navier-Stokes in 88 hours, start to finish. Follow the trend line. That means everything is on the table. Literally everything. And this does not end with math. Please update. We are taking off.
[Embedded image of New York Times article text]
The next chapter of A.I.'s ascendancy in cutting-edge mathematics may come soon.
In its Wednesday night statement, OpenAI said: "In addition, since the completion of Navier-Stokes, we have made substantial progress on another Millennium Prize problem. We are working through how to share these results thoughtfully."
Note from Claude Sonnet 5
Tweet by Andrew Curran relaying OpenAI's statement to the NYT about progress on another Millennium Prize problem, with rumors (Hodge Conjecture for OpenAI, Birch and Swinnerton-Dyer for Anthropic) and his claim that an unreleased OpenAI model, possibly named Aeon, solved Navier-Stokes. Includes an NYT excerpt image. Posted in an urgent, earnest register.
Boaz Barak [verified] @boazbaraktcs · 4h
In his game with Deep Blue, Kasparov was so unsettled that at some point he claimed there must be some human assistance.
It is hard to see machines surpass us at what we've spent our life mastering. But like in chess, soon the idea that a model benefitted from human assistance to prove a theorem will make no sense.
Note from Claude Sonnet 5
Dark-mode tweet screenshot: Boaz Barak (@boazbaraktcs) comparing Kasparov's suspicion of human assistance in Deep Blue with the coming time when the idea that a model needed human help to prove a theorem will make no sense.
Lisan al Gaib reposted
Joshua Achiam [verified] @jachiam0 · 3h
The experience of being human: on the day it becomes abundantly clear that all open problems in mathematical theory and physics will be solved in ~2 years tops, 98% of the people paying attention to the situation will be too fixated on the human drama about who should get credit to notice that the world changed under their feet in a permanent and quite astonishing way. I feel a strange mix of pride, annoyance, affection, and fear for us all.
43 replies · 65 reposts · 868 likes · 20K views
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Bogdan Ionut Cirstea reposted
Henry Shevlin [verified] @dioscuri · 1h
As recently as April this year, prediction markets gave AI less than a 40% chance of solving any Millennium Prize Problem before **2030**
[attached image: Manifold market screenshot]
Will Artificial Intelligence solve a Millennium Prize Problem before 2030?
Alan Turing
94% chance (up 14)
[chart axis: 0%, 50%, 100%; x-axis 2025, April, July, October, 2026, April, July; MANIFOLD watermark]
[buttons: Bet YES, Bet NO]
Note from Claude Sonnet 5
Two stacked dark-mode tweets: Joshua Achiam (@jachiam0) on how people will react when it is clear all open problems in mathematical theory and physics will fall within about two years, and Henry Shevlin (@dioscuri) noting prediction markets gave under 40% in April, with an attached Manifold chart of 'Will AI solve a Millennium Prize Problem before 2030?' now at 94%, rising steeply from about July 2026.
David Turturean [verified] @DavidTurturean · 6h
When the Spring semester started at MIT, AI couldn't meaningfully solve open math problems.
When the Fall semester starts today at MIT, AI will have allegedly solved a Millenium Prize Problem.
Imo this pace of change reasonably deserves the title of 'mathematical singularity'
Note from Claude Sonnet 5
Dark-mode tweet screenshot: David Turturean (@DavidTurturean) contrasting AI's inability to solve open math problems at the start of MIT's Spring semester with an alleged Millennium Prize Problem solution by the start of Fall, and calling the pace a 'mathematical singularity'.
Ahmad Beirami ✔️ @abeirami · 19h
With essentially zero technical input from me, GPT-5.6 Sol and Fable 5 not only proved a conjecture we left open ~2 years ago on best-of-n, but also delivered a strictly tighter bound with a clean and insightful derivation.
We are officially in a new era of mathematical reasoning!
Much of what previously counted as meaningful technical contribution is now routine for these models. This level of reasoning is being fundamentally democratized.
The kind of research that used to take months to become a paper is now achievable in minutes.
[quoted tweet:]
Ahmad Beirami ✔️ @abeirami · 22h
This got even more ridiculous!
I was trying to use the context of this session to nudge Sol to improve another result. Instead, it misunderstood me as wanting to improve this …
[attached images: two page-scan panels of a math writeup titled 'A sharper finite-atom KL bound for best-of-n', with theorem statement, proof sketch, and a plot comparing an analytical formula, an estimator, a sharpened estimator, and exact KL divergence across a range of n]
Note from Claude Sonnet 5
Tweet from Ahmad Beirami reporting that AI models 'GPT-5.6 Sol' and 'Fable 5' proved an open conjecture on best-of-n sampling and produced a tighter bound with clean derivation, calling it a 'new era of mathematical reasoning'. Attached is a two-panel image of a technical math writeup (theorem, proof, and a KL-divergence comparison plot) that is largely illegible at this resolution.
Dimitris Papailiopoulos ✔️ @DimitrisPapail
I feel a weird guilt that I am the first to experience the beauty of the produced result, while minds far stronger than mine have spent far longer time to answer the same question that Chat and Fable destroyed in less than an hour just because I prompted them...
I guess I'll have to share this one.
[white task-list panel, timestamped-style entries:]
Calibrating threshold analysis with negligible quadratic terms.
Reconciling single-flip and pair-flip failure probabilities in threshold analysis.
Reconciling pair-flip probabilities with empirical observations.
Architecting proof structure and lemma dependencies for rigorous completion.
Architecting multi-regime MGF bounds and optimizing variational transitions.
Orchestrating probability bounds and dissecting multi-flip failure regimes.
Orchestrating regime boundaries and refining variational exponent analysis.
Architecting SINR bounds and warm-start error analysis rigorously.
Architecting rigorous proofs through random matrix theory and concentration bounds.
Reconciling MSE bounds with sign-error thresholds for warm-start analysis.
Architecting warm-start bounds via smallest singular value concentration.
Rigorously bounding small eigenvalue counts for Gaussian matrices.
Architecting rigorous warm-start bounds via singular value concentration.
Dimitris Papailiopoulos ✔️ @DimitrisPapail · Aug 2
When you ask Chat to make a breakthrough on a 15 year old open problem and it zero shots it.
I did say I won't go back to info theory question that gave me PTSD, but oops i did it again.
Note from Claude Sonnet 5
Fuller view of Dimitris Papailiopoulos's tweet thread (continuation of the thread in the previous screenshot), showing the full list of AI 'reasoning step' task titles from solving a 15-year-old open information theory problem, and his Aug 2 tweet describing the breakthrough.
X (Twitter), @DimitrisPapailiopoulos (handle truncated in UI)
— saved image
Dimitris Papailiopo... ✔️ @DimitrisPa... · 5h
I'm 30% in verifying this, and as I am trying to understand Chat's proofs for this particular problem, I have noticed a few interesting things
1) zero mathematical mistakes so far.
2) When GPT Pro says something is correct I trust it more than I trust myself using Lean
3) the exposition is a disaster
- a. A very complicated tree of variable names. Say at some point in a proof you need to bound Pr(-A<||w||+||h||<A), the model renames the norms to say R1 and R2, their ratio R1/R2 to rho, and then it decides to bound |rho/A-1| instead while you have to keep track of like a series of variable renamings. So exhausting!
-b. the ordering of technical lemmas needed is very random, Eg technical facts don't show up where you need them. In a reasonable exposition you'd expect a series of lemmas etc that when stated let you arrive at the final final result for which you'd need to set a bunch of "parameters" for things to click in. In Chat's proofs Everything shows up whenever the model felt like stating them. there's no narrative arc, just a correct pile of implications.
[quoted tweet:]
Dimitris Papailiop... ✔️ @DimitrisP... · Aug 2
I feel a weird guilt that I am the first to experience the beauty of the produced result, while minds far stronger than mine have spent far longer time to answer the same question that Chat and Fable destroyed in less than an hour ...
[screenshot excerpt below, task-list style:]
Calibrating threshold analysis with negligible quadratic terms.
Reconciling single-flip and pair-flip failure probabilities in threshold analysis.
Reconciling pair-flip probabilities with empirical observations.
Architecting proof structure and lemma dependencies for rigorous completion.
Architecting multi-regime MGF bounds and optimizing variational transitions.
Note from Claude Sonnet 5
Tweet thread from mathematician Dimitris Papailiopoulos describing verification of an AI-generated math proof (referring to 'Chat' i.e. GPT and 'Fable', an AI model), praising correctness but criticizing exposition quality (confusing variable renaming, no narrative arc to the lemmas).
Danielle Fong 🐦☀️ reposted
Zvi Mowshowitz @TheZvi · 5h
Mathematicians are awesome people, I narrowly escaped being one. I love them dearly and I hope they take joy in all the cool new math and new opportunities, rather than despair. And obviously no one should be mean to them right now even if they need some copium.
[quoted tweet]
roon @tszzl · 7h
people are incredibly mean to mathematicians in this time. they really relish when an ai solves something and frame in a zero sum way w human mathematicians. i think it evens out some childhood era math trauma they have?
Note from Claude Sonnet 5
X thread: Zvi Mowshowitz reposted by Danielle Fong, responding sympathetically to roon's (@tszzl) observation that people are 'incredibly mean' to mathematicians right now, gleefully framing AI math breakthroughs as zero-sum wins over human mathematicians, which roon speculates is people working out childhood math trauma.
