OpenAI just Nuked Mathematicians

0:00 Are we witnessing the death of classical mathematics or its renaissance? Did we kill math with math? On the 6th of October, Open AI published 722 math manuscripts. One count says a computer

0:12 has checked the main results of only about 162 of them. You may have seen headlines that say Open AI solved hundreds of open problems. Open AI's own readme says some of the results without

0:22 a lean check could have issues. This video covers what a computer checked, what is only a claim, and why mathematicians are angry. There's also a moral question here and it starts with a

0:32 cow. The Fed raises interest rates to slow inflation. The cow understands none of it, but the decision still reaches the farmer and then it reaches the cow. Are we becoming that cow? We'll come

0:42 back to her at the end. The readme gives a scale. It says Open AI posed the model about 4,000 problems. The release has 722 manuscripts in 372 result families. On average, each result used 3 hours of

0:56 ChatGPT Pro thinking compute. 4,000 problems and 722 manuscripts look like a score. But the numbers don't show how many problems produced no manuscript. So don't read them as a success rate. Press

1:09 counts differ from the repo. Scientific American says 372 results, but the repo says 722 manuscripts in 372 families. A family groups related manuscripts. I'll use the repo's

1:21 wording. Open AI released the manuscripts at 6:00 p.m. Eastern time on the 6th of October. A spokesperson said the model produced almost every one of the results in response to a single

1:31 prompt handed to a single AI agent. That's Open AI's claim about how the work happened. Outsiders can't replicate it yet because Open AI hasn't named the model or released the prompts. Andrew

1:43 Sutherland of MIT is blunt about it. He said, "Until and unless they release the model and people can replicate their results, I think you should treat any claims about one shotting problems with

1:52 a single agent as unverified." That quote is about the process. The results themselves are a separate question. So, what can you check today? The repo has a contents file that lists the headline

2:03 results with their lean status. It's a very large file, but the headline entries are easy to find. Take one entry as an example. The contents file says Catalan's constant is irrational. That

2:14 means no fraction of two whole numbers equals it. OpenAI's file marks this entry as lean checked. What does that mark mean? Lean is a proof checker that accepts or rejects every step. A person

2:25 or a model writes a proof in a formal language. Then Lean tests each logical step. If one step fails, Lean rejects the proof. So, the pass doesn't depend on whether you trust the author. Say a

2:36 proof has 200 steps. If step 112 doesn't follow from the steps before it, Lean stops and rejects the proof. A tired human reviewer could miss that step. Lean can't skip it. But

2:47 Lean checks only the statement that someone typed into it. Suppose a model targets a famous open problem, but the type statement is a weaker version. Lean can pass a true proof of a different

2:56 question. One review of the release warns that a formally verified theorem might claim something weaker than the actual open problem. Lean also says nothing about understanding. A proof can

3:07 pass a checker while no human can explain it. At Caltech on the 11th of September, Terrence Tao warned of proof indigestion. Lean can pass a proof, but humans still have to read and understand

3:18 it. So, a Lean pass answers only the first of three questions. The first question is whether the steps are valid. The second is whether the type statement matches the open problem, and a human

3:28 must check that. The third is whether a human understands the proof. Now, count the checks. One report says Lean formalizations confirm the main results of 162 manuscripts. That's a little

3:38 under a quarter of the 722. About 560 don't have a fully Lean checked main result. Some of those are partly formalized. The sources count in different units, so treat these numbers

3:50 as approximate. OpenAI's readme is direct about this. It says, "Not all have accompanying Lean formalizations." It also says, "Some of the unformalized results could have issues." Open AI

4:01 wrote that caveat itself. As of the 7th of October, no independent peer review or replication exists, so nobody can yet say how many manuscripts are correct. Lean covers only some of them. For the

4:12 rest, correctness is still open. The biggest headline is the quasi Riemann hypothesis, but the entry is narrower than its name. The Riemann hypothesis is about where the zeros of the Riemann

4:23 zeta function can sit. A zero is an input that makes the function equal zero. This entry covers a related group of functions called Hecke L-functions over one number field.

4:33 That field is the rational numbers extended by the square root of minus three. The entry says these functions have no zeros where the real part of S is above 7/8. The full Riemann

4:43 hypothesis would push that line from 7/8 down to 1/2. This entry doesn't do that. Hecke L-functions are related to the Riemann zeta function, but this claim doesn't cover the zeta function itself.

4:54 So, if you see Open AI proved Riemann, it's wrong. Open AI's contents file marks the entry as Lean checked, and no independent confirmation is on record yet. Two more headline entries carry a

5:05 Lean checked mark in Open AI's file. One is the two-point Chala result. The other disproves Zariski cancellation in dimension four. With Catalan's constant and the Hecke entry, that makes four. No

5:16 independent confirmation of these Lean checks is on record yet. Other big entries list no Lean check. Hilbert's 10th problem over the rational numbers is one. A formula in the Birch and

5:26 Swinnerton-Dyer problem is another. One report also lists a claim about how well pi can be approximated by fractions as not yet formalized. Sources disagree on a few entries, so read the contents file

5:38 yourself. No independent review of each result's importance is on record yet. What's clear is the volume. 722 manuscripts arrived in one evening, and humans must read them. Suppose a

5:49 mathematician reads one manuscript a day. 722 manuscripts take almost 2 years. That's an example, not a measured figure, but it shows why checking is the slow part. The word "nuked" matches the

6:01 mood in the headlines. The evidence doesn't support it. Mathematics hasn't ended. The people who prove things still decide what counts as proved. OpenAI gave some background. It says an

6:12 internal model began training on the 28th of August and has resolved more than 100 long-standing problems. That's in addition to an earlier Navier-Stokes claim. In September, an independent

6:22 advisory group on mathematics and AI formed, hosted at the Institute for Advanced Study. The advisory group's members include Gowers, Hörer, and Witten. It can advise, but it has no

6:33 decision power. It recommended that OpenAI disclose model names, prompts, and compute. It also recommended depositing the papers in academic repositories. The release disclosed an

6:43 average compute time, 10 reasoning summaries, and no model name. So, it skips at least two of the group's recommendations, the model name and the prompts. That's a gap between the advice

6:53 and the release. Secrecy is one of the arguments. Quanta reports that OpenAI is keeping more than 100 results secret. Quanta wrote this the day before the release. The sources don't say how many

7:04 of those results are among the 722. One secondary report says mathematicians recall a promise. At an August meeting, they say OpenAI agreed not to release all results at once. Brubaker said

7:16 scholars urged OpenAI to follow academic norms, not to act like influencers. This is a dispute about how to release the work, not about any single proof. Andrew Sutherland said researchers should

7:27 demand to see the receipts. Craw described the mood as extreme excitement and extreme fear coexisting. Both feelings fit the evidence. Some results carry a lean check in OpenAI's file, and

7:38 the rest rest on OpenAI's word alone. Credit is a second fight. One tech report says mathematicians credited two humans, Diego Córdoba and Luis Martínez Zoroa, with the key insight in Open AI's

7:51 earlier Navier-Stokes claim. It's a single secondary source, so treat it as reported, not confirmed. Terence Tao said, "We have to slow down. The pace is insane, and there's no reason to be this

8:03 fast." On the 21st of June, he wrote that it is now easier to generate long correct proofs than short ones. So, a long proof now tells you less about how much

8:12 insight went into it. Tao still backs formal verification. In January 2025, he wrote, "In math, we can completely check and verify outputs, and this really filters out a lot of the rubbish. That's

8:25 the idea behind Lean, but the filter checks correctness, and it doesn't check understanding. So, the limit is human reading. Lean sits in front of the reader and rejects wrong proofs, but

8:35 every proof that passes still goes to a person. Mathematicians are posting early." Quanta reported on the 5th of October, a day before the release, that they preprint early to avoid being

8:44 scooped by AI. A preprint is a public paper posted before peer review. It shows the date of your claim. If an AI model publishes a result first, that date matters. I read the incentive this

8:56 way. If a company may hold more than 100 results, a mathematician can't know whether a problem is already solved. So, posting early protects a claim. Quanta describes a trend. It also

9:07 reports that Math Overflow activity is declining and that arXiv is limiting submissions. One researcher quoted by Quanta said, "It breaks our system. It just takes it to its absolute limit and

9:17 destroys it." Those systems assume people write papers at human speed. A model doesn't write at that speed. The pace matters for one reason. If models write results faster

9:27 than humans read them, the backlog grows every day. Lean can reject wrong proofs, but it can't read for you. If you build with AI agents, notice the pattern. Math has a checker that rejects

9:38 wrong output. Most software work has weaker checkers like tests. A passing test suite can miss a problem just as a lean pass can certify the wrong statement. A strong checker is what

9:48 makes an agent's output worth trusting. So far, the evidence shows three facts. One count says a computer has checked the main results of only a minority of the manuscripts. OpenAI hasn't released

9:59 the model or the prompts. And the mathematicians who must judge the results are posting early and arguing. Now back to the cow. In this picture, OpenAI is the Fed. It decides how fast

10:10 results arrive and what stays secret. Journals and universities are the farmer who passed the decision on. The mathematicians are the cow because the decision reaches them last and they

10:21 can't read all of the output. The picture breaks in one place. A cow can't build the institutions that decide what happens to it. Mathematicians can build them.

10:30 They already referee each other's papers for journals and they use Lean as a checker. An independent advisory group exists, but it has no decision power. The bigger worry is speculative. Suppose

10:40 a future model invented its own language or decided to remove humans to restore Earth. We couldn't check its plans if we couldn't read its reasoning. Nothing in this release shows that and no source

10:51 says any model has done it. There is a real research problem here though. A paper by 42 researchers from several labs and institutions including Ben Goe and Dragan studies it. They

11:02 argue that we can monitor a model's chains of thought for the intent to misbehave. A chain of thought is the reasoning text a model writes before it answers.

11:10 If a person or a program can read it, it may reveal bad intent. The paper calls this monitoring promising but imperfect and fragile. It asks developers to consider how their decisions affect

11:21 monitorability. OpenAI says each result used about 3 hours of thinking compute on average. The release includes only 10 reasoning summaries and a summary is shorter than the full reasoning. So

11:32 outsiders can see little of how a result was found. The same capability could bring abundance or a Wall-E style loss of control. This release shows neither. It shows only a large pile of output and

11:42 few people to read it. That's the risk to watch. Here's my verdict for anyone who follows math or builds with AI. Mathematics isn't dead. The assumption that humans

11:52 can check everything the machines produce is what's failing. If the headline names a famous problem, read the exact statement in the content file. If the entry has a lean check, treat it

12:02 as a statement that OpenAI says lean accepted. If it has none, treat it as a claim. Before you repeat a result as proved, wait for independent review. Also, check

12:12 if OpenAI has released the model, the prompts, and the compute. If a model writes a result in about 3 hours, who will read it?