Cristiano De Nobili @denocris

Many amazing [if correct] results close to my heart / work: 1) Polyakov's conjecture on the O(n) model [Polyakov's was the first qft paper I read] 2) Quantum annealing for SK model. 3) Reconstruction on trees [Related to conjectures made with Marc Mezard 20 years ago]. 4) k-SAT threshold [Beautiful work by Gaia Carenini has priority here] 5) Free energy for spin glasses on random graphs. 6) Mixing for the SK model. 7) Factor-of-IID threshold for Ising model on trees 8) Free energy of the spherical perceptron github.com/openai/math

The idea of an intelligence explosion caused by recursive self improvement has been around for a long time but until very recently it did not seem imminent. Now many leading researchers think it may happen quite soon. You can read our paper about it here: casp.ac/reports/intell…

friends are regularly surprised when i say i don’t think math is (yet) “solved,” so in the wake of the ns result i figured i’d explain this take a bit more widely. first, this is massively impressive and clearly an example of AI being, in some respects, far more powerful than the human mind. the team deserves huge praise for attempting and succeeding at this. i’d love to read a technical report on the project (one can always hope :) but second, here again we ended up with a counterexample rather than a full proof: option C won the NS problem by proving the conjecture false (which was one valid way to solve the problem for sure) notice a pattern in many of the recent frontier results in ai for math? a striking number involve counterexamples or finding a needle in a haystack. now don’t get me wrong: this is extraordinarily hard and commendable. but it is only one aspect of mathematicians’ work. Math is also about: - finding deep, general mathematical understanding and explanations within proofs - revisiting proven results to find more « elegant » proofs - proposing new conjectures and hypotheses that might open « fruitful » directions - taking the leap of faith of proposing entirely new, « exciting » research programs that may take decades to bear fruit you may say these are simply further increments on the same intelligence scale, and perhaps point 2 above is already within the reach of current models. possibly but you could also see this string of results as an extraordinarily powerful, massively parallel extension of search: explore the haystack, find the needle i.e. the counterexample that breaks the conjecture. that would already be remarkable. but it would still leave open whether models understand the words I emphasized above: « elegant », « fruitful », « exciting ». as tristan put it in his brief report: “the first llm generated proof levent sent me was the most horrendous i have ever read.” despite their formidable technical abilities, models still seem to lack something mathematicians rely on constantly: a type of mathematical taste. the ability to distinguish a beautiful argument from a merely valid one, a fertile idea from a sterile one. i’d be very curious to ask gpt or claude what they think of the result they just proved. do they find it elegant? if they ignore all the human noise about it on the web and history of math, do they appreciate the result and the path to it more than other proofs? my suspicion is that, outside of the human knowledge that this is an important millennium prize problem, it may not 100% register it as fundamentally different from thousands of other proofs. or, more intriguingly, perhaps the beauty they find in mathematics is actually alien to our own sense of mathematical beauty, some « horrendous » proof to us might be deeply satisfying to them… all this to say that we might have significant progress to make in ai for math before declaring the field “solved,” (as too many are posting). in the meantime, ai will be an extraordinary collaborator for mathematicians. i just hope access to these tools be as widely shared as possible (so that you don’t need a Leven or Sebastien working in a big lab to help you), and that companies stop using mathematics primarily as a demonstration of prowess in their private race.

OpenAI @OpenAI

a month ago

We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics. The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra. The problem

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As a mathematician, the OpenAI/Navier-Stokes story feels genuinely historic and unusually dramatic. Navier-Stokes is one of the seven Millennium Prize Problems, each carrying a $1M prize. These are not just hard benchmark questions. They are among the most important open problems in mathematics, and entire research programs can grow around finding even one plausible route toward them. Buckmaster and Levent Alpöge had spent most of the past year pushing a program started by Diego Córdoba and Luis Martínez-Zoroza. Their goal was to take known blowup constructions with rough forcing and push them to smooth forcing, ultimately toward incompressible Euler and Navier-Stokes. By August 15, they had obtained smooth-forcing blowup results for Boussinesq and Euler. They were using Claude and Codex heavily throughout the project, and Buckmaster says they had been putting their drafts into Codex. Then rumors started circulating that “Anthropic” had solved a major open problem. OpenAI says those rumors triggered a large-scale effort on the Millennium Prize problems. Thousands of agents were launched, first attacking nearby Euler problems before the effort moved toward Navier-Stokes. What made Buckmaster immediately suspicious was the direction: forced Navier-Stokes with smooth forcing. In his statement, he says this was precisely the route Córdoba and Martínez-Zoroza had opened and that he and Alpöge had “quietly chosen to attack.” Almost nobody else he knew was working on it. His reaction: “When I heard ‘forced,’ it was a bright red flag.” He then asked whether OpenAI’s model had been trained on, or otherwise had access to, their Codex sessions. According to Buckmaster, he was told the model did not look up user data, but when he asked specifically about training, he did not get a clear answer. OpenAI denies directly accessing their private work, but its own post says: “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” And then the story becomes genuinely dramatic. Buckmaster says he was offered publication arrangements, including one where he alone would present OpenAI’s Navier-Stokes result without Levent Alpöge as an author. He says Bubeck emphasized that Alpöge working at Anthropic was the complication. Buckmaster declined. He then says that when he told OpenAI he would make the episode public if the result was released that way, the response was: “Why would you ruin your career?” Bubeck disputes Buckmaster’s characterization of the interaction. Buckmaster is also careful about what he is claiming. He explicitly writes: “I do not know whether our data was used. I am not accusing anyone of anything.” That distinction matters. But I think Tristan’s most important observation is broader than the dispute itself. He calls this a “Deep Blue-Kasparov moment” for mathematics. For a Millennium Prize problem, the scarce intellectual resource is not merely the final proof. It is often years of taste, failed attempts, literature, intuition, and judgment that tell you where the promising path is. If a small group discovers that path, and simply revealing that it is promising can trigger 10,000 AI agents to attack it, then mathematics may be entering a world where identifying the right question becomes more valuable than solving it. And that could fundamentally change the culture of open mathematics. Tristan Buckmaster’s statement: cims.nyu.edu/~tristanb/stat…

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OpenAI @OpenAI

a month ago

We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics. The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra. The problem

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📣 New preprint out! 🔹 Context: multi-agent systems of LLMs are increasingly deployed in decentralized settings, from autonomous agent swarms to federated systems with no central coordinator. Whether such populations can spontaneously agree on a shared convention, and how fast, is becoming a real engineering, safety, and alignment question. 🔹 Research question: does consensus among a population of LLM agents negotiating a shared convention emerge earlier, later, or never, depending on a single LLM feature such as its decoding temperature, the same way thermal temperature controls order in a magnet? 🔹 Main result: we built a minimal LLM Naming Game, where the classical rule-based listener is replaced by an LLM that can now agree by mistake or refuse to agree when it should. Testing three open-weight models, we find three completely different personalities: one gets noisier and slower as temperature rises, one is entirely unaffected by temperature, and one shows a genuinely counterintuitive effect where lower temperature makes consensus slower, not faster. We back this up with an exact analytical theory explaining why! This gives a concrete, statistical physics-inspired, model-agnostic way to benchmark how a population of any given LLM will reach (or not!) consensus on a shared convention, before you ever deploy it. 📄 Paper: arxiv.org/abs/2608.02178 ✍️ Blog post: cristianodenobili.com/blog/blogs/how… Happy to hear thoughts and feedback!

Very articulate mathematicians pondering the future of math. quantamagazine.org/live-from-icm-…

Anthropic Research Lead: "99% of our engineers run swarms of 300+ self-improving agents. Now everyone is building agentic graphs". In a 20-minute session an Anthropic team member walks through how graph engineering turns isolated agents into systems that improve themselves. Agents -> Loops -> Graphs -> Self-Improving Systems What it actually looks like: Claude moving through graph workflows, plan mode and dynamic orchestration. Everyone else is still running one agent and hoping it holds. This beats most $500 graph engineering courses and costs nothing. Bookmark it, watch the talk, then read the article below ↓

slash1s @slash1sol

2 months ago

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Impressive new paper from Google DeepMind. (bookmark it) It takes Co-Scientist out of simulation and into real-world experiments. A summary of the results: In computer science, it found an inference-time scaling architecture that beat six frontier models on HealthBench Hard and Professional under blinded physician review. The system designed a safe precursor route for MXenes and drove a semi-automated chemical vapor deposition reactor, producing a lamellar 2D material with structural similarities to the Ti3C2Tx lattice. It also tailored growth recipes to laboratory constraints in minutes, enabling single-attempt growth of monolayer MoS2, MoSe2, and WS2. In biology, it predicted E. coli swarming phenotypes across inducer gradients from sparse imaging data, matching unpublished real-world measurements. 30 domain experts wrote 450 reviews on end-to-end generated papers, and the reliability modules reduced hallucination and plagiarism. Paper: arxiv.org/abs/2608.26701 Chat with Paper: academy.dair.ai/papers/co-scie…

Today, we're kicking off the first phase of the research preview for Model Hardware Standard (MHS): a new standard for AI agents to safely operate physical equipment in scientific research and advanced manufacturing. Read more: anthropic.com/news/model-har…

hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)

@s_scardapane @alfcnz Ok thanks! Yes, I am using Web Clipper to connect external stuff but so far I am basically creating a vault for each project. Maybe it's better to have just one vault for everything but I am feeling like it eats a lot of tokens reading unrelated sources. Maybe I am wrong

@tulalanAndLbuta @OpenAI Same to me, crazy. Hope I can access again my project!

Deep Tech opportunities in Europe 🇪🇺 👇 CMBlu Energy, a German cleantech scale-up building Organic-SolidFlow batteries for long-duration energy storage, is hiring a Software Engineer for their battery systems. The Exploration Company, developing Nyx (a modular and reusable space capsule for cargo), is hiring an FPGA Engineer. Don't miss the ESA Kick-starts call, offering up to €75,000 for space-enabled feasibility studies, and many more. Feel free to share this link with your network and help this community grow! ➡️open.substack.com/pub/joinphaset…

New exciting deep tech opportunities in Europe 🇪🇺 👇 open.substack.com/pub/joinphaset…

Sergey Brin said compute is dessert. The companies winning the AI race right now are not the ones with the most chips. They are the ones with the best algorithms. Every headline you read about AI is about data centers, Megawatts, and Nvidia orders. Billions in infrastructure and more. The entire investment thesis of the last three years has been built on compute scaling as the primary moat. Sergey thinks that framing is wrong. He pulled out an example from physics. The N-body problem. Scientists have been running those simulations since the fifties. Over the decades, raw compute improved on Moore's law. But the algorithms to solve the problem improved faster. Not slightly faster. Far faster. The algorithmic gains made the compute gains look small. He says the same thing has happened in AI over the last decade. Compute is not the meal. It is the dessert. You still want it. Nobody is turning down frontier compute. But the companies that figured out the algorithms first are the ones actually ahead. The market is pricing AI winners by who has the most chips. Sergey Brin just said that is the wrong scorecard. The ones who win this are not building the biggest data center. They are solving the harder math problem.

A new post from Phase Transition! Many exciting deep tech opportunities in Europe 🇪🇺 for PhDs and Postdocs: open.substack.com/pub/joinphaset…

Stop killing children in Gaza, civilians in Lebanon. Stop influencing US and EU policies with your lobbies. Stop with your money and investment funds to buy territories by evading the law, as is happening in Albania. Stop blackmailing with your secret services. When you have stopped with this, you will see that anti-semitism and anti-zionism will slowly disappear!

The European 🇪🇺 deep tech ecosystem is growing rapidly. Flower, a Swedish energy tech scale-up using AI to optimise battery energy storage, is hiring a Data Engineer to build the real-time data backbone behind algorithmic energy trading. Quantum Dice in UK is hiring an Applied Research Associate in Probabilistic Computing to develop algorithms leveraging the entropy-driven capabilities of their Probabilistic Processing Unit. You can find more opportunities, summer schools, and workshops in the latest post. ▶️open.substack.com/pub/joinphaset…

Building autonomous agents for scientific discovery? 🧬🤖 @GoogleDeepMind Science Skills is now available on GitHub. We've open-sourced this specialized toolkit to accelerate your agentic workflows with scientific grounding and higher token efficiency. Download now ↓ github.com/google-deepmin…