Two of the nine Erdős problems that Google DeepMind's AlphaProof Nexus solved had been sitting unsolved for 56 years. That is the number that will get quoted. The number that matters more is the one attached to it: nine out of 353 open problems on the list, in a single study, published in Science this week with the solutions peer-reviewed before the paper went out. DeepMind's team also posted the proofs online ahead of publication, the way you do when you want the field to check your work on its own schedule rather than on the journal's. The Erdős list is not just a list of open questions. It is a priced one, maintained with the same dollar-valued bounties Paul Erdős started attaching to his own problems in the 1960s, so that a hard problem carries a number in the hundreds of dollars and a very hard one carries one in the thousands, and the estate and the community keep the prices current. A machine that clears nine at a time, at a compute cost that the study puts in the same order of magnitude as the bounties themselves, is not just solving problems. It is making the price tag obsolete, which is a different and more interesting thing for a field that has run its economy on that tag for sixty years.
The system itself is a pipeline more than a model. It runs on Gemini 3.1 Pro, which drafts proofs in Lean, the formal language that acts as a referee: every draft gets machine-checked after each edit, and the error messages from the check drive the next attempt. When the sub-problems get hard enough, the system can escalate to AlphaProof, a specialized proof tool, and it is worth noting that the nine Erdős results held up even without that escalation. Beyond Erdős, the same machinery proved 44 conjectures out of the OEIS integer sequence database, closed an open question in algebraic geometry, and improved a known bound in min-max optimization.
That last item is the one I would underline if I were the editor, because min-max optimization is a technique used to train some AI models. The machine that improved the bound on the class of method its own kind of system depends on is doing something that reads less like a benchmark win and more like a gear shift. The model is no longer just applying math. It is moving the ground the training loop stands on.
The split that is actually the story
There is a second half to this week, and it is not about capability. Capability was table stakes by Tuesday. The second half is about what happens after the machine produces the proof: who gets to say the proof is real, and what the community does when the two answers collide.
OpenAI, over the past few weeks, dumped roughly 372 AI-generated mathematical proofs onto GitHub rather than submitting them through journals. The framing on the OpenAI side, in the coverage of it, was essentially "the academic world can keep up." The response came from the Association for Human Mathematics, an organization Terence Tao leads, and it was not a response. It was a call to boycott.
DeepMind did the opposite of the dump. It put the work through peer review before publishing, and it gave the results a paper, a journal, and a record that the field can stand behind with its names on it. Both labs have machines that can produce proofs the field cannot read quickly enough. What separates them now is not the machine. It is the channel, and the channel is where the trust lives, and the trust is the thing a mathematical result actually is when it is more than a string of symbols. A proof no one has verified is a claim. A proof a referee has checked is a result. One lab is manufacturing claims at scale. The other is manufacturing results, slowly, and the slow one just got the prestige.
Why the boycott is the right read of the room
It is easy to dismiss the Association for Human Mathematics as gatekeepers protecting turf. The better read is that they are protecting the verification layer, and the verification layer is the only part of the enterprise that was ever doing the work the machines now do better. Mathematicians have been the check on mathematics for as long as mathematics has existed, and the check is the product. When 372 proofs land in a repository with no referee, no sign-off, and no one accountable for the errors inside them, the check has been removed and the product is just text. The boycott is not a trade restriction. It is a quality control measure, and it is aimed at the one lab that decided speed was more valuable than standing behind the work.
DeepMind, by going through Science, just bought the opposite asset: the field's credit, on the field's terms. The cost of the buy is time and a willingness to let a referee find the mistake in the draft. That is a small price for a lab that has everything else, and it is the price OpenAI chose not to pay, and the choice is going to show up in every citation, every hiring decision, and every future collaboration, for longer than the 372 proofs will take to rot in a repository. There is also a quieter cost to the dump that the OpenAI side has not priced in: a repository of unrefereed proofs is not a body of work. It is a liability, in the exact proportion it is wrong. When the first error in one of the 372 turns up, and it will, the cost of finding it falls on the reader, not the author, and the reader in this field is the person whose career is built on the habit of assuming the text in front of them has been checked. The dump does not just skip the referee. It transfers the referee's job to everyone who ever opened the file, and it does it without telling them.
What the 44 OEIS conjectures actually signal
The Erdős results are the headline, but the OEIS work is the one with the labor economics in it. Integer sequence conjectures are the grunt work of mathematics: a long, open list of small questions that a whole generation of early-career researchers works through to learn the craft. A system that can clear 44 of them at a time is not replacing the top of the field. It is removing the training ground. The people who used to learn mathematics by working the sequence list now have no list, and the field is going to feel that in the pipeline before it feels it in the frontier. That is a slower, quieter, and more consequential consequence than any benchmark number, and it is the one worth watching over the next two years of graduate admissions.
Hot takes
The peer review was cheap marketing. DeepMind did not need to go through Science to prove the result. It needed to go through Science to make the result belong to the field, and that is a different and more valuable thing than the result itself. The journal is the receipt that says someone looked, and the receipt is the asset. OpenAI's 372 proofs are the same math without the receipt, and they are going to be read, in a few years, the way we read the work of a fast, careful, and ultimately unverifiable source: with a discount.
Terence Tao is the firewall, and the firewall just got a name. Before this week, the resistance to AI-first mathematics was a mood, a set of conference remarks, a scattered set of letters. Now it is an association with a leader and a boycott call, and that changes the cost of the next dump. The lab that runs the next 372-proofs-onto-a-repository is going to run it against an organized field that has already said, in so many words, that it will not engage. The firewall is load-bearing now, and it is named, and named things are easier to plan around, on both sides.
The min-max bound is the line the researchers will re-read. Not the Erdős headline, not the OEIS count, the improved bound on the optimization class that trains a chunk of the models doing the optimizing. That is the loop closing, one turn, and it is the only result in the paper that changes the next paper's assumptions. The others change what the field knows. That one changes what the field can build, and it is the one that will still be cited in five years when the rest of the list has been superseded by a faster model with the same journal, and a longer name.
The bottom line
The machine was never the interesting part of this week. Two labs now have machines that produce proofs the field cannot read fast enough, and the interesting part is what each lab did with the receipts. One put the work through a referee and got the field's credit with its names on it. The other skipped the referee and got a boycott from the one organization the field now has for saying no. The mathematics is the same. The standing is not. And in a discipline where a result is only as good as the check behind it, the check is the only thing left that is worth more than the speed.