The floodgates are open. Right on the heels of OpenAIās new large language model producing the biggest math breakthrough in two decades, the company just released no less than 372 results from the same model. Each resolves or makes substantial progress on a major open question in mathematics or theoretical computer science, the company says.
OpenAI revealed the results in a GitHub repository at 6 P.M. EDT. The deluge will take mathematicians months to parse through and understandāincluding to determine whether the proofs contain novel and important ideas or are mostly mash-ups of existing techniques. But many of the results have already been verified in Leanāa programming language that validates a proofās logicāand are therefore all but certain to be correct.
Among the results claimed are a solution to the four-dimensional Kakeya conjecture, improvements on some of the worldās most important computer algorithms and actual progress toward mathās scariest problem, the Riemann hypothesis.
A spokesperson for OpenAI told Scientific American that the new modelāwhich the company has not released to the publicāproduced almost every one of the results in response to a single prompt handed to a single AI agent. This would be a striking difference from OpenAIās earlier blockbuster solution to the Navier-Stokes problem, which was produced through the collective efforts of a 10,000-strong agentic swarm that cost millions of dollars in computing power. If true, it would mean that unprecedented mathematical power could soon be accessible to anyone. But OpenAIās reputation, among mathematicians, for bold claims and little transparency is causing considerable skepticism.
āUntil and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified,ā says Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology. āWe should ask for receipts.ā (The OpenAI spokesperson also told Scientific American that some results might have taken multiple attempts.)
OpenAIās handling of the Navier-Stokes solutionās release has proved so controversial that, on September 21, the company announced it was assembling an independent advisory group of mathematicians to provide recommendations on responsibly publishing AI-generated results. The recommendations that the group developed call for a company that releases such results to make public the model, exact prompt and compute time behind each one. In spite of the groupās recommendations, though, OpenAI is choosing only to reveal the average compute time for a problem, with some additional statisticsāand no prompts
The OpenAI spokesperson told Scientific American that the team is taking the advisory groupās guidelines seriously and doing its best to comply but added that the company is not bound by these recommendations.
The recommendations are particularly critical of AI companies using āproprietary internal modelsā that arenāt broadly accessible to mathematicians. OpenAI told Scientific American that the company is working to release the model as quickly and responsibly as possible.
As the Navier-Stokes dispute unfolded, comments from OpenAI personnel led some mathematicians to believe the companyās model had produced additional results but that it was hesitating to publicize them. This raises a vital question: Is it more harmful to unload heaps of unexplained proofs on the community or withhold them entirely?
āIf we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us,ā says Daniel Litt, a mathematician at the University of Toronto. āTo me, itās going to be a good thing for mathematics.ā
On the other hand, the famed mathematician Terence Tao has vocally criticized OpenAI and other āfrontierā AI labs for the āinsaneā pace of their AI-generated results.
Such results may even be coming too fast for the labs themselvesāthe OpenAI spokesperson told Scientific American that many of the companyās newly released results are not yet understood by its own mathematicians. Still, they donāt plan on slowing down. The company wants to put as powerful a tool as possible in mathematiciansā hands.
Moreover, OpenAI maintains that it canāt slow down because these math problems are an indispensable test to show that their AI really is getting smarter.
But for the practitioners who see mathematical truth as an end rather than a means, the consequences of this race are becoming harder and harder to predict.
So thatās over 1,000 unverified proofs published now?
At that volume, it becomes noise; someone still has to read, understand, validate and be able to apply those proofs before they become useful.
I am not from the math field, but heard a couple of days ago a talk in which Lean was part of it. As far as I understand Lean is used to proof assist these theorems (please correction my wording, if necessary) which is also mentioned in the text. As an AI skeptic I still am with you, we need to proofread it. Therefore I would like to know how much of an assistance Lean is in these proofs.
Itās been some weeks since I dove into it, but this article claims that OpenAI solved the Navier-Stokes problem earlier, which is simply didnāt as far as I remember? They did some novel development related to the problem based on someone elseās solution if I remember correctly.
They said they hoped their developments were independent, but that the model did have access to data about the other, at this stage unpublished, solution.
I hope theyāre employing a lot of talented mathematicians.
I can imagine a scenario where a machine spouts out information, only for it to be indecipherable to the controllers. Human-analysis is required to prove that it is or is not true and that can only be done at human-speed, whilst the machine creates at hyper-speed. Itās more costly to refute nonsense than it is to create.
It could also be perceived as provoking free-labor from specialized individuals.
I am clueless about mathematics though so Iām just creating more nonsense. I feel a bit morose. Itās as if the whole world is just talking about computers, whilst the natural world dies.



