Sometimes AI commentary feels like whiplash. It’s hard to stake out any long-term positions because everything moves so quickly. Just a few weeks ago, I thought it was hard to see a visible path forward for OpenAI. After Mythos was released by Anthropic, it seemed to leave everything else in the dust. Then came the Chinese models and then came the Astra math-optimized models and all of a sudden it’s a brand new day again. Anthropic still owns the business space. But OpenAI seems to have found a path through with a lock on advanced brute force reasoning that may be able to solve our solvable knowable (aka verifiable) unsolved problems through its long-horizon research/reasoning capabilities, first deployed on mathematical problems. Is this intelligence? It may not be that simple, but what happened today gave us a glimpse of what the future of solving finite problems could hold.

Sam Altman is not finished, generative AI has not reached its ceiling, and none of what happened this week is AGI. Those three statements hold together because the thing OpenAI demonstrated on August 1 is not general intelligence. It is a machine that generates enormous volumes of candidate mathematical arguments and discards the ones that fail a checker, running at a scale and cost no human career can match. That method closed ten problems that had resisted mathematicians for a decade or more, and it will keep working anywhere a checker exists.

Ten problems, two thousand dollars

OpenAI published ten results in mathematics and theoretical computer science, produced by an internal version of a model family it is calling Astra. Each problem had seen no progress on its main result for at least ten years, and most for considerably longer. The results span group theory, high-dimensional geometry, coding theory, arithmetic circuit complexity, operator algebras, quantum complexity, lattice cryptography and extremal combinatorics. One establishes the existence of non-sofic groups. Another disproves Connes’s rigidity conjecture. Three close Erdős problems.

The tokens spent generating all ten would have cost roughly $2,000 at the Sol API rate. That works out to about $200 per decade-old conjecture. Every argument ships with a Lean 4 certificate in a public repository, alongside a 249-page manuscript and a walkthrough of the model’s reasoning for each result.

The checker is the story

May’s Erdős unit-distance disproof rested on expert sign-off. Someone qualified read the argument and said it held. This set rests on a program that recompiles the proof and confirms it line by line without trusting whoever wrote it. A skeptic who is not a specialist in operator algebras can now interrogate a claim about operator algebras.

That property, and not the number ten, is what makes these results a different category of announcement. It also identifies exactly which problems this method can reach. These conjectures had no known solutions. What they had was a way to test a candidate answer cheaply and decisively. The limit is not that the search space is small. The space of high-dimensional sphere packings is infinite. The limit is that checking one candidate costs almost nothing, so a system can afford to be wrong ten thousand times on the way to being right once.

Human mathematicians cannot work that way. Generating a candidate proof costs a person weeks, so the entire discipline is organized around generating few candidates and choosing them well. Taste, intuition and elegance are adaptations to an expensive generation step. Astra removed the expense.

Volume beats insight where rejection is free

Noam Brown, one of the researchers behind the test-time reasoning technology Astra draws on, noted that OpenAI failed on other major problems and that the runs were not expensive. His framing is that test-time compute could be pushed much further. The ceiling described here is a budget, not a capability limit.

The arithmetic is still the argument. OpenAI reports that the solution-finding tokens for all ten results would have cost roughly $2,000 at Sol API rates—an average of $200 each, excluding training, human preparation and subsequent formalization. Astra drew on patterns learned from a vast mathematical corpus to search at enormous scale. The successful arguments were then formalized and checked in Lean. The dataset supplies the priors, test-time compute supplies the volume, and Lean supplies the certificate. This is learned search at brute-force scale, not blind enumeration.

Mathematics is taking this badly, and reasonably

Przemek Chojecki described the field as organized into silos where everyone knows who else is working on which problem, and where the slowness of the work is what makes that social arrangement function. A problem you have thought about for months can now be closed out of the blue by an amateur with API credits. He called it demotivating and frightening.

Fortune quoted mathematicians describing a very rapid and very unsettling change, with the sharpest edge falling on junior researchers. Sixteen researchers from fifteen universities published the Leiden Declaration in June, asking the profession to settle questions of attribution, transparency and peer review before AI-generated results are absorbed into the literature. Abhishek Saha of Queen Mary described frontier models in his area as at least the equal of a solid and tireless PhD student.

Thomas Bloom, who runs erdosproblems.com, called the results big news and rejected the replacement framing on the grounds that the system draws on a century of accumulated theory, was built by mathematicians, and trained on everything mathematicians have written. He is right, and it does not help the postdoc whose thesis problem evaporated overnight.

The same capability arrived at bitcoin from a different direction

Anthropic disclosed that an unreleased Mythos Preview model found a practical key-recovery attack on HAWK-256, a lattice-based post-quantum signature candidate that NIST advanced to a third round in May. The model found a mathematical shortcut in the lattice structure that cut the work required against the smallest parameter set from roughly 2^64 operations to 2^38. The flaw had survived two years of expert review. The run took about 60 hours and $100,000. HAWK’s authors withdrew it the next day.

That result does not touch bitcoin’s signing model, which uses ECDSA on secp256k1 and has nothing to do with HAWK. What it touches is the assumption underneath every migration plan, which is that human review time is a meaningful filter on cryptographic soundness. The model worked for three days. Two human experts spent nearly a month verifying what it produced.

The Coldcard sweep the following night made the same point in cash. A firmware routing error that silently bypassed the random number generator for five years was exploited in a 25-minute window, moving roughly 594 BTC initially and, by later estimates, over 1,128 BTC worth around $71 million. Coinkite has acknowledged that its own review using a leading AI model failed to find the flaw beforehand. Whether the original attacker used AI remains unestablished, though independent researchers reproduced the discovery with models once the weakness was known.

What has not fallen

No Millennium Prize problem has been solved. Epoch AI’s open-problems benchmark records zero solutions in its two hardest categories, Major Advance and Breakthrough. Graph theory yields readily to these methods while other fields resist. Astra is internal and unreleased, external specialists have not had time to work through arguments of this weight, and the published account does not specify how much human problem-shaping preceded each run.

The claim is a rising floor in domains where verification is cheap, demonstrated at a cost low enough that the constraint is now budget rather than possibility.

Cancer, aging, and the boundary that matters

The method transfers to any domain with a verifier, which covers a great deal of what we mean by science. Protein structures have validators. Materials have simulations and then assays. Drug candidates have wet-lab confirmation. Each of those checkers is real, and each is slower and more expensive than Lean by many orders of magnitude. The generation step becoming free is a genuine acceleration of discovery, bounded now by how fast the world can say no.

Governance, procurement, policy and judgment have no verifier at all. Correctness there is a matter of expert consensus, contested interest, and time. The systems that just cleared decade-old conjectures for $200 apiece remain, in that territory, a source you check by hand.

Brute force will take us further than human intelligence has in every domain where checking is cheap. That is most of mathematics, a large and growing share of science, and almost none of politics. the gap between human intelligence and artificial intelligence of the generative kind does not seem to be closing. It seemed to be diverging along two parallel tracks, two very different kinds of intelligence that should support each other. The question remains: what innovation will carry us forward next, what will drive it, and who will see it coming?