A trio of mathematicians solved a decades-old math problem using Codex. OpenAI published a proof on the same day. Coincidence or not - this opens an important discussion about ownership in the age of AI.

A new and possibly controversial perspective: In this video, I explain the sense in which generative AI trained by supervised learning is incapable of making novel discoveries. The text of the speech: AI Creativity and Discovery Good day ladies and gentlemen. I regret that I am unable to be with you all today to engage in a back-and-forth discussion, but I am nevertheless pleased to be able to share with you, via this recording, some high-level thoughts about the current and future state of artificial intelligence, and in particular about AI’s relationship to science and mathematics, which is, as I understand it, the central focus of this meeting and of the SAIR Foundation. I would like to start with an old joke; I am sure you have heard it before. It is the one about the researcher whose work is being evaluated, and the review comes back, and says “This work is both novel and good. Unfortunately, the parts that are good are not novel, and the parts that are novel are not good.” My first point about AI is that this assessment applies exactly to large parts of AI as we know it today. Not all of today’s AI, but a large part of it. Pretty much all of what we mean by “Generative AI”---which includes large language models, and the images and video models, and even the new methods for learning world models. All of these AIs take large numbers of examples and produce a “model” which behaves similar to the examples, that is, which generates text like people, or images like artists or nature, and videos like we find on the internet. Don’t get me wrong, Generative AI can be extremely useful. No doubt about that. But the assessment of the joke still applies. These systems can produce output that is both novel and good, but not at the same time. In many ways this is just absolutely not a problem. When we ask an AI for an answer from the internet, or to summarize a document, we don’t want it to be novel. We are happy if the quality of the answer, the goodness, comes from the source material—from the people who wrote the document or the articles on the internet. If the AI’s answer is novel it means it is going beyond the source material, adding something beyond it. This is what we call “hallucinations”. In most cases, we don’t like it when the AI makes something up, when it adds something novel. One exception, of course, is when we are looking not for facts or reality, but for fiction and entertainment. We might ask for a bedtime story for a child, or an image based on existing images on the internet but which is nevertheless different and distinct from them. In these cases, it is never easy for us to know how creative the AI is actually being, as we do not know how close the AI’s story, poem, or image is to the source material. In a real practical sense we can not know this because the internet is too big, the possible sources that the AI may draw upon are too numerous. When we ask for a fiction or novelty, the AI can give it to us because its processing is in part stochastic. Every decision can go multiple ways and will go different ways and produce a different trajectory every time. The trajectory can be random—and thus novel—or it can be based on the training data—and thus “good” because the training data is good, sourced from people or reality. Thus, the trajectory is either novel or good—based on randomness or based on data—but never both at the same time. Really, I think it is okay if the output of Generative AI is never good and novel at the same time. For the researcher in the joke this is a devastating criticism, but for most things it is not, and for Generative AI it is not. Generative AI is meant to be a mimic. This is what supervised learning is for. Generative AI can be extremely useful, even when it just mimics, if it is faster, or cheaper, or smaller, or more customizable, or more copy-able, than the thing being mimicked. It is okay if Generative AI cannot be both novel and good at the same time. It is still a transformative technology. But it is a limitation. And remember we are here to use AI for science and mathematics, and for these areas the assessment of the reviewer in the joke is devastating. For these areas we need true creativity and discovery. Generative AI—or Mimicking AI—will never get where us there. For these we need something more, and indeed we have something more in other parts of AI. We have many AI systems which can give us more. We have AlphaGo with its world-changing move 37, or AlphaZero with its brilliant original chess-playing style. We have GT-Sophy that drives simulated racecars better than any human. We have AlphaFold and AlphaProof and Claude-Code, which have brought true advances in science, mathematics, and programming. We have RL-Lyft which optimizes the assignment of cars to passengers in the ride-hailing business. All these systems have found things that are both novel and good. And, truth be told, some language models have been augmented in ways that make them more than Generative AI based on supervised learning. All these systems have some additional features that make them capable of true creativity and true discovery. It is important for us to recognize what this is—and that it is not present in ordinary, garden-variety Generative AI. It is something that can not come from just supervised learning, from learning from examples. What is it? Well, it is a simple thing, a commonsense thing. It is not new. We have many names for it, but unfortunately none of them are very good names. I will call it Discovery. Basically, Discovery is just the idea of trying many things and seeing which of them work, then keeping those that worked the best. Evolution by natural selection works this way. The scientific method works this way. And just ordinary life and learning works this way. We try things and remember what works. What could be more obvious? In this behavioral case, psychology has two names for it— “instrumental learning” and “operant conditioning”—and in machine learning it is what we mean by “reinforcement learning”. We also see the idea of Discovery in planning and combinatorial search—anything that involves the idea of “generate and test”. The essence of Discovery is to combine three steps: 1. Variation, 2. Evaluation, and 3. Selective retention. Of course, I am not the first to say this. I am not the first to point out that this combination of steps is key to science, to evolution by natural selection, and to animal behavior. I think particularly of papers by Donald Campbell, by Daniel Dennett, and by Gary Cziko. What is new in my remarks is to directly relate the idea of Discovery to modern AI to help us see that it is not present in supervised learning or Generative AI—in particular, that Discovery is not present in backpropagation or gradient descent. Let me say explicitly what is missing from Generative AI. As we have remarked, these systems do have a stochastic aspect, so they do generate a variety of trajectories and behavior. What is missing is the Evaluation step. The generator was pre-trained by supervised learning, leaving no way at runtime to Evaluate what it generates. And of course without Evaluation there can be no Selective retention, and thus no Discovery. The variation can bring novelty, but without evaluation there is no Discovery, and arguably, no creativity. That is, I would say that creativity requires that the new things generated be Evaluated. Without evaluation, and retention of the best, there is nothing created. The novelty flickers into existence but, if its value is unrecognized, it flickers away and is lost. In many cases, Evaluation is done by people to make a discovery. As when we have Generative AI make many pictures for us, and then we pick the one that we like the best. The human+AI system completes the discovery. In many other cases, the Evaluation comes from a clear objective. Some moves lead to checkmate, some steps lead to a proof, some actions result in high reward, some genotypes make more copies, some theories explain the data better. Some prefer the Variation step to be called Blind variation, where “blind” here means that it is uninformed, a shot in the dark. It does not need to be completely uninformed; a good scientist does not select theories to test at random. But neither can it be completely informed and determined. There must be some uncertainty about where the answer lies in order for there to be a discovery. In practice, the variation is partly informed and partly blind, but it is the blind part that corresponds to the discovery. Now let us briefly go all the way to modern deep learning, to the backpropagation algorithm. At first it might seem that backpropagation is incapable of discovery because it is deterministic and thus incapable of variation. But this is not correct. The weight updates of backprop are deterministic, but the weights are initialized to small random values. The random initialization is often downplayed, but in fact it is a necessary form of variation; it must be done properly to get good performance. In backprop this Variation is done once, at network initialization, so its effect is temporary, and later the network may lose its ability to learn. This is the weakness of deep learning that is alleviated with a new algorithm that my group presented in Nature a couple of years ago. Our “continual backpropagation” made one small change: every so often a less-used neuron would be re-initialized to small random weights. This allows the variation to continue and plasticity to be retained. Although there is much more to be said about Creativity and Discovery, this is the key point: they are more than supervised learning, more than pattern recognition, more than prediction, and more than world modeling. Those things are important, but they alone will not bring us to discovery. Discovery requires Evaluation from a person or from an explicit goal, and only in the latter case will we attain full autonomy. So that is my call to arms. If we want the full power of AI scientists, then we should share the goals with them so they can create, evaluate, discover, and in these ways fully participate in achieving the goals. Let’s be bold! Let’s fully automate Creativity and Discovery!

Quite a few people have been asking me about $OTC lately I’ve actually been watching the dev for a while, and I have to say they’ve been shipping pretty aggressively. There’s been something new almost every day, so seeing $OTC run from a few million to around a $35M ATH wasn’t that surprising to me Most people following it already know the basic OTC Desk, earn stocks, launcher and burn mechanics, so I won’t waste time explaining everything from zero What I care about more is how I actually rate the idea, what has been validated so far, and where I’d still be interested in betting after the run to $35M 1. First of all, I actually like the idea behind $OTC But not because they invented a completely new meta Tokenized stocks already exist. Meme x stocks already exist. NFT vaults, launchpad fee models and the pre-IPO narrative aren’t new either What OTC did well was combine things the market already wants into one pretty clean flywheel Take tokenized stocks as an example. One thing I don’t like about that meta is that users often have to directly trade stock tokens with relatively poor liquidity. Once volume gets thin, spread and slippage can quickly become a problem OTC takes a different approach Instead of making users trade stocks directly, fees generated by ecosystem activity are used to buy tokenized assets and distribute them to Desk holders I think that’s a cleaner design The NFT vault side is similar. I’m not a fan of models where later users have to mint at increasingly higher prices just to feed yield to earlier users. OTC doesn’t really work like that: minting a Desk burns a fixed amount of $OTC, while rewards come from actual ecosystem activity But the smartest part of the idea to me is still the launcher Without the launcher, Desk + “earn stocks” would be a much weaker thesis. The launcher gives the whole system a clear source of fuel : launches => volume => fees => stock rewards + $OTC buybacks => Desk demand => more Desk mints => more $OTC burned None of these pieces are revolutionary individually, but the way they’re combined is pretty smart As for OpenAI, SpaceX, Neuralink and other pre-IPO names, I see those more as a narrative/marketing layer. They’re great for attracting degen attention, but they’re not a technological moat and obviously shouldn’t be treated the same as owning actual equity. So purely on the idea, I’d give it around 8/10 It feels more like a best-of-meta mashup: Pump volume + RWA/stocks + NFT utility + pre-IPO speculation Sometimes the market doesn’t need a completely new category Understanding what the market wants and executing faster than everyone else can be an edge by itself 2. More importantly, the numbers are starting to validate the idea This is the main reason I’m still watching $OTC after the pump The strongest part right now is clearly the launcher Based on the latest numbers I checked, there have been around 9,200 launches, 24h volume reached roughly $124M, and creator fees passed 15,600 SOL More than 10,000 SOL has gone toward holder/stock purchases, around 2,000 SOL to the protocol, 650+ SOL toward buybacks, while roughly 7.7M $OTC has already been burned The important part isn’t just that these numbers look big It’s that people are actually using the product There’s real volume, real fees and real money cycling back into the ecosystem through stock purchases, buybacks and burns And there’s another signal I think is worth mentioning: the launcher is starting to produce actual runners At the time I checked, Nasduck was around $3.77M, Pump Cat around $1.76M, with several others like PUGCOIN, Anonymouse and CatGPT still holding six-figure market caps. The site’s all-time volume had also reached roughly $294M That matters because people aren’t only pressing launch and farming activity. The market is actually willing to speculate on some of the coins coming out of OTC Of course, a few runners out of 9,000+ launches doesn’t prove the launcher has a great hit rate. Some of it can simply be distribution and current meta attention But ignoring the fact that it has already produced multiple million-dollar runners would also be unfair So for me there are now two things being validated on the launcher side: fee generation and downstream speculation That matters much more than simply saying RWA is a hot narrative 3. I’m still less bullish on the Desks than the launcher The Desk side is actually working too There have been 2,700+ rounds, around 4,300 SOL spent buying stocks and roughly 2,200 Desks distributed So the earn-stock mechanism clearly isn’t just a mockup But I’d still call it a proof of concept, not a proven yield machine The cap is 5,000 Desks, and the current number includes around 621 granted Desks related to early-minter refunds More importantly, rewards are shared across the Desks If the number of Desks grows faster than revenue, the share per Desk naturally gets thinner So I wouldn’t look at the NFT floor going up and assume the yield will stay attractive forever OTC has proven that the machine works It still needs to prove that the machine works efficiently at scale That distinction matters quite a lot to me 4. What I like most about the team is still their shipping speed This is also why the run didn’t surprise me that much In a very short period, they’ve shipped Desks, handled early-minter refunds, reduced the burn requirement from 1M to 100K $OTC per Desk, launched the launcher, added stock/pre-IPO rotations, custom rewards, overhauled the UI and continued tweaking the fee/buyback structure I especially liked how they handled the refunds. Instead of ignoring early users who minted at much higher costs, the team compensated them with SOL or additional Desks For a project born on Pump, this pace of execution isn’t something I see very often But at the same time, that’s also part of the risk The team is still fairly anonymous, almost solo-visible, I haven’t seen a clear public audit yet, and the project itself is still very young So right now I’m betting heavily on the dev continuing to execute, rather than betting on a protocol with a long proven track record 5. The biggest weakness of this flywheel is pretty obvious From the outside, OTC looks like it has a lot of different catalysts : Launcher, Desks, stock rewards, buybacks, burns, pre-IPO... But most of them ultimately depend on the same source of fuel : launcher volume Volume stays high => fees stay high => Desks receive more assets => Desk demand increases => burns and buybacks remain meaningful But the reverse is also true If launcher volume disappears, almost the entire flywheel weakens at the same time That’s what I want the market to prove next I don’t need the launcher printing $100M+ volume every day. I want to see whether, after the initial hype cools down, it can maintain enough organic volume to keep feeding the ecosystem If it can, the thesis becomes much stronger If it can’t, the current numbers may simply represent peak activity during an extremely hot meta 6. The moat isn’t strong yet either I like the idea, but I don’t think OTC currently owns anything competitors can’t copy The launcher can be competed with. The NFT vault can be cloned, and copycats are already starting to appear. Nobody owns the RWA narrative, while pre-IPO exposure is much more of a narrative layer than a moat The model also depends heavily on Pump AMM and on users choosing to launch through OTC instead of using other alternatives So my view is pretty simple : The idea is winning this round, but the moat isn’t there yet To turn the current wave into something that lasts longer, the team needs to prove OTC has enough distribution or product stickiness to retain flow even when the stock/RWA meta starts cooling down 7. There’s one catalyst I’m NOT including in the thesis I’ve seen people look at the “Powered by @solana line and start framing it as if Solana is backing $OTC So far, I haven’t seen official confirmation from Solana Foundation or Solana Labs, so I’m not counting Solana backing as part of my bullish thesis If an official mention comes later, great. That becomes a new catalyst But the current run doesn’t really need that story anyway Product + launcher volume + fee flywheel + the dev’s execution speed already explain a lot of the price action 8. So where would I actually bet after $35M → ~$12M? This is probably what most people asking me about $OTC actually care about $OTC ran extremely fast from a few million to around a $35M ATH, then retraced more than 60% I see $11–13M as the first dip zone worth watching If launcher volume stays healthy, fees keep flowing, the Desks remain healthy and the dev keeps shipping, this could simply be a reset after the expansion But for anyone looking to size big, I wouldn’t rush here I still prefer around $8–10M After a move to $35M, early holders are still sitting on very thick profits. I’d rather miss a bounce than force a large position when the risk/reward isn’t attractive enough If the market flushes toward $6–8M, I also wouldn’t automatically buy just because it looks cheap I’d check the fundamentals again If price is dumping while launcher volume, fees, Desk demand and development remain strong, that could become a very interesting setup But if it’s dumping because launcher volume is dying, Desk demand is weakening or the dev is slowing down, then a lower MC doesn’t automatically mean a better setup And if it loses roughly $5M while the operating metrics deteriorate at the same time, I’d stop treating it as another dip and reassess the thesis 9. Final thoughts I still quite like $OTC Purely from an idea perspective, I think it’s one of the smarter combinations of existing metas I’ve seen on Pump recently It’s not revolutionary and the moat isn’t strong yet, but it has the right narrative, the right timing and a team executing extremely fast The launcher is currently the strongest part of the thesis for me Desks have proven that the mechanism works, but they still need to prove they can scale. Buybacks and burns are real, but ultimately a large part of the flywheel still depends on whether the launcher can maintain volume So after the run to $35M, I’m no longer looking at $OTC as “good idea = buy every dip” $11–13M is the first zone I’m watching. $8–10M is where I’d be more interested in sizing bigger, assuming the operating metrics stay healthy From here, I mainly care about three things : Is the launcher still doing volume? Are the fees still flowing? Is the dev still shipping? As long as those three remain intact, my thesis remains intact If those core pieces start breaking, I’m not going to marry a token just because I liked the idea before For now, $OTC is a speculative play with a pretty solid thesis, but it still needs more time to prove it can become a sustainable protocol MukLDtJ8Cx9DxLbeyLRSWPSposTMWuwHANbuaudpump

Power is becoming a major constraint on AI infrastructure. In a proof of concept on NVIDIA HGX B200 systems, Lambda used NVIDIA DSX MaxLPS to run 19 nodes within the same aggregate power budget as a 16-node baseline, observing ~24% more token throughput and ~23% higher performance per watt. More productive AI capacity from the power already available. Read more via @NVIDIA:

There's a lot of mathematical names being thrown around this week. If you don't know what they all mean, here's a list with simple summaries and what they mean to the average person: Navier–Stokes - Fluids can theoretically blow up to infinite speed. Used in weather, aircraft, engines, blood-flow models. - Average person: slightly better planes, forecasts and medical simulations over the next decade if engineers actually rewrite their codes. Nothing this year. Riemann hypothesis - How regularly prime numbers are spaced. - Average person: underpins encryption that protects banking and websites. A full proof or disproof would eventually force new security methods. Current “67 % of zeros on the line” result changes almost nothing for you. P versus NP - Whether every problem whose answer is easy to check is also easy to solve. - Average person: if P = NP, most current encryption dies and logistics/drug-design get dramatically cheaper. If P ≠ NP, life stays the same. Still unsolved; rumours only. Hodge conjecture - Whether certain geometric shapes can be built from simpler algebraic pieces. - Average person: none. Pure geometry. Any later use in physics or computing is decades away. Birch and Swinnerton-Dyer conjecture - Predicts how many rational solutions an elliptic curve has. - Average person: elliptic curves sit inside some modern cryptography. A proof might eventually tighten or break certain schemes. Not imminent. Yang–Mills mass gap - Why particles have mass in quantum field theory. - Average person: none in daily life. Relevant to particle-physics experiments, not phones or bills. Written by @Grok.

there’s a certain rightness to the idea of a hippocampus for the models. a kind of chain-of-thought cache, built around the intuition that an intelligence ought to be changed by the work it does, even while its weights stay frozen. i keep thinking about the dot product between problems. metaphorically. two questions can share little vocabulary and still contain the same obstruction. different answers, but the same useful decomposition, the same assumption worth checking first. where the structure aligns, some fraction of the discovery cost ought to be recoverable. we wring beautiful deductions out of these intelligence engines and leave them in the sediment of a transcript. the answer survives. the expensive little maneuver that made it possible often remains unextracted. an engineer comes away from a difficult failure with an acquired suspicion. something gets checked earlier next time. expertise lives partly in this altered order of operations. i’d like the models to have somewhere for that alteration to persist. this is above prompt caching. something closer to memoizing how a problem became tractable. a decomposition, a diagnostic procedure, a failed approach with the reason it failed still attached. amortize the discovery, even when the answer must be recomputed. a transcript is a laboratory notebook, not a protocol. extracting the protocol requires deciding what was necessary, what was incidental, and what can be reproduced elsewhere. resemblance doesn’t authorize reuse. the reusable object should be somewhat lemma-like, carrying its assumptions wherever it travels. usually we won’t have a proof. we can still preserve tests, counterexamples, and the distinction between what worked once and what has been independently verified. a successful answer doesn’t certify every step that accompanied it. i used to think an AI hippocampus would mostly remember facts. now i’m interested in experience becoming procedure without first becoming a weight update. episodes, procedures, strategies, with a return path to the evidence whenever an abstraction becomes suspect. acquired competence outside the parameters. this is why i’m increasingly blackpilled on finetuning as the thing to build everything around. my bet is that successive general models absorb enough of today’s narrow specialization that i’d rather build the apparatus they inherit. tools, procedures, reasoning memory that survive a change of model. there’s a loose von neumann instinct here: an intelligence engine drawing on memory that holds both information and instructions. treat the model as an interchangeable cpu, with a hierarchy of reasoning caches backed by durable memory. useful procedures close at hand, the episodes behind them still addressable. let the surrounding architecture carry the burden of remembering, rather than requiring the engine to internalize every new experience. the architectural attraction is giving the engine and its accumulated experience separate lifecycles. some procedures will need rechecking. others will turn out to be workarounds for limitations the new model no longer has. but an upgrade shouldn’t require cold-starting the apprenticeship. does the first useful version look like reasoning traces in postgres, with retrieval, synthesis, and verification on top? the database isn’t the part i’m uncertain about. it’s how much of the work we can turn into a reusable method, and how cheaply we can establish that it applies. surely even a very marginal savings of a few percent tokens would gradually compound over time? isn't this the shape of continual learning?

Two mathematicians spent a year on a $1m problem, and then OpenAI released proofs on the same day. Tristan Buckmaster and Levent Alpöge ran every draft of their work through Codex sessions, and after news of their result reached OpenAI, the company produced a proof along the same narrow route within days. Coincidence? Possibly. Sovereign AI is a routing decision: if you control which providers see your work, you never have to ask a vendor for a straight answer. Learn more:

We've spent a few evenings here on how small a proof is and how fast it checks. There's a third property worth highlighting. A proof outlives whoever made it. ⏳ The evidence sits inside the proof. In ten years anyone can check it in the same few milliseconds, with the prover long gone and the servers switched off. Every other kind of "verified" is a pointer at someone who has to still be around, and still be honest.

There is a heated debate right now. Tristan Buckmaster says OpenAI told him its AI had solved the Navier–Stokes Millennium Prize Problem. That claim remains unverified, and the discussions around it have erupted into a dispute over scientific credit. Here is what happened and what we know so far: Several different things are getting mixed together. Here is what the available evidence actually says. Building on work by Córdoba and Martínez-Zoroa, Alpöge and Buckmaster used Claude and OpenAI models to establish how initially smooth fluid flows can develop singularities under smooth external forcing. They released papers and Lean formalizations, and Terence Tao praised the advance. Their results cover Euler and related equations. They do not solve the Navier–Stokes Millennium Problem, which additionally involves viscosity. A suitable extension could resolve it, even with smooth external forcing. Then comes the disputed part. According to Buckmaster, OpenAI told him on September 6 that an internal model had already produced a proof for forced Navier–Stokes, potentially taking that final step. He says OpenAI’s effort began after information about their progress reached the company. He also disputes the initial description of minimal human involvement, reporting that the discussions revealed a team effort, multiple attempts, and substantial compute. Buckmaster further says publication proposals included having him write up OpenAI’s result without Alpöge as a coauthor, with Alpöge’s employment at Anthropic cited as an obstacle. He reports being asked, “Why would you ruin your career?” after saying he would make the circumstances public. Bubeck has publicly rejected allegations against him as “false and inflammatory.” These accounts are contested. The social posts do not establish what happened in the private discussions. There is also no established evidence that OpenAI trained on their private Codex sessions or stole their drafts. Buckmaster raises the question but explicitly writes: “I do not know whether our data was used.” tl;dr Alpöge and Buckmaster used AI to prove new results about how smooth fluid flows can develop singularities, advancing a research program relevant to the Navier–Stokes Millennium Problem. Their published work does not solve that problem, but Buckmaster says OpenAI privately told him its internal model had taken the remaining step. He has not seen that proof, and the claim remains unverified. But rumors are that OpenAI actually fully solved that milleniun problem.

I just had a fascinating call with Eyad Alkassar (@AlkassarEyad) about how ChatGPT 5.5 Pro helped move the frontier of an open problem in computer science. The problem sounds abstract, but it is surprisingly intuitive: Imagine four people dividing nine objects. Each person may value them differently. The goal is to find a division so fair that, after any single object is removed from someone else’s pile, nobody would prefer what remains to their own pile. This criterion is called envy-freeness up to any good, or EFX. Whether complete EFX allocations always exist for four or more people remains open. For four people, the previous general guarantee stopped at seven objects. A new preprint by Eyad Alkassar, Mahmoud Fouz and renowned computer scientist Kurt Mehlhorn now presents a proof for up to nine. The story behind it is remarkable. Over dinner, Eyad challenged Mehlhorn to give AI one of the harder open problems in his field. Eyad and Mahmoud are both computer science PhDs who had spent years building startups and were newcomers to fair division. They built a research workflow around several AI systems. At one point, Fable had questions about one of Mehlhorn’s papers and repeatedly urged Eyad to contact him. After Eyad refused twice, the AI pointed out that they were only around 30 kilometers apart and suggested that a short drive would be worth it. According to Eyad, the situation became even stranger once the proof was finished. Fable then advised him against sending the result to Mehlhorn, warning that he might be a competitor and that an incorrect proof could be embarrassing. Eyad contacted him anyway. Mehlhorn reviewed and verified the proof architecture, refined the arguments and joined the paper as a co-author. According to the paper, Claude Fable performed the analysis and lemma proofs, authored the trusted verification layer and audited its soundness. ChatGPT 5.5 Pro proposed most of the candidate attacks and optimizations. Eyad and Mahmoud selected the systems, assigned their roles, coordinated their communication and provided the computing infrastructure. The proof divided the space into 36,152 canonical cases after symmetry reduction. The closing run verified all 122,553 certificates using Z3 and completed 141,878,161 per-clause soundness checks with zero reported failures. The general theorem for an unlimited number of goods remains open. This result moves the known frontier from seven goods to nine. The authors describe the process as “AI led, human assisted and verified.” For me, this is one of the clearest examples yet of current AI systems contributing substantial work to a new mathematical proof. I found the story too remarkable not to share. Paper: