Did an AI really solve an 80-year-old math problem?

Every researcher I know has the same reflex when an "AI discovers X" headline crosses the feed: not "is this true," but "who verified it, and how would I know?" That reflex has a perfect teaching case now, because the same company made essentially the same kind of announcement twice, seven months apart, and got opposite results. Both stories are documented in public. Put them side by side and you get a usable rule for reading every one of these headlines.

Act one: a literature search wearing a discovery costume

In October 2025, Kevin Weil, then a VP at OpenAI, posted that "GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others." Paul Erdős left behind hundreds of open problems, and a mathematician named Thomas Bloom maintains erdosproblems.com, the database that tracks which ones are still open. Ten of them falling to a language model in one go would have been extraordinary.

Bloom responded directly, and his correction is the single most useful sentence in this whole affair. He called the post "a dramatic misrepresentation," and explained what had actually happened: "GPT-5 found references, which solved these problems, that I personally was unaware of."

Read that carefully, because the mechanism is subtle and it will recur. The problems were marked "open" on the site. But "open" on that site meant Bloom was not personally aware of a published solution, not that no solution existed anywhere in the mathematical literature. GPT-5 went and found the papers. It did a very good literature search across a scattered, century-spanning body of work, and it surfaced solutions that a human curator had missed.

That is genuinely valuable. Finding a forgotten 1974 paper that answers a question people think is open is real scholarly work, and models are unusually good at it. It is simply not the same thing as solving the problem. The reaction was brutal: Demis Hassabis of Google DeepMind said flatly, "This is embarrassing," Yann LeCun of Meta got in a joke at OpenAI's expense, and Weil deleted the post.

Act two: an actual result

On 20 May 2026, OpenAI announced that an internal reasoning model had disproved the Erdős unit distance conjecture. This time it held up.

The problem, posed by Erdős in 1946, is easy to state: take n points in the plane, and ask how many pairs of them can be exactly one unit apart. Erdős conjectured the maximum was very close to linear in n, bounded by n^{1+c/log log n}. The intuition was that the best arrangements look roughly like square grids. Nobody had beaten that guess in eighty years.

The model produced a construction that beats it: point sets with more than n^1+ε unit distances, built not from a grid but from algebraic number theory, using number fields of large degree and small discriminant. The conjecture is false. That is a real mathematical result, and it is the kind of thing no amount of literature searching produces, because the paper did not exist.

What the humans did

Then the mathematicians went to work, and this is the part the coverage compresses into nothing.

Will Sawin published "An explicit lower bound for the unit distance problem" on arXiv the same day. His abstract describes the division of labor precisely: "We show that there are sets of n points in the plane with n arbitrarily large that contain more than n^1.014 pairs of points separated by a distance exactly 1. This improves on very recent work of a team at OpenAI, who proved the same result with an inexplicit exponent greater than 1." The model showed some exponent above 1 exists. A human worked out what it actually is.

Alongside it came a companion note, "Remarks on the disproof of the unit distance conjecture," signed by nine mathematicians: Noga Alon, Thomas Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, and Melanie Matchett Wood. Bloom, note, is the same person who took apart the October claim. Its abstract is three sentences long and every clause earns its place:

We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdős unit distance conjecture, and a sequence of reflections on it. The argument relies crucially on ideas that may, at least in retrospect, be attributed to Ellenberg-Venkatesh, Golod-Shafarevich, and Hajir-Maire-Ramakrishna.

Three words in there carry the whole story. Human-verified: the output became a result when nine people checked it, and that step was not ceremonial, since the October claim died at exactly this stage. Digested: what the model produced needed to be reworked into something a mathematician could read and confirm. And relies crucially on ideas attributable to three prior bodies of work: the model combined existing machinery from separate subfields in a way nobody had. That is a fair description of most human breakthroughs too, so it is not a knock. It is just not invention from nothing, which is what "AI solves 80-year-old problem" implies.

The problem is still open

Here is the precision point that almost every headline dropped, and it is not pedantry.

A conjecture was disproved. The problem was not solved. Erdős guessed the answer was near-linear, and the model showed that guess was wrong. But the unit distance problem asks for the actual maximum, and that is still unknown. The best proven upper bound remains O(n^4/3), from Spencer, Szemerédi and Trotter. The lower bound is now around n^1.014 after Sawin, sharpened further in the weeks that followed. The truth sits somewhere in that gap, and closing it is the open problem, same as it was in 1946, just with the map redrawn.

"AI disproves an eighty-year-old conjecture and shows the expected answer was wrong" is a fantastic headline that happens to be accurate. Somebody decided it was not quite good enough.

The signal

I read this as a lab person, and from that angle it is completely familiar. An instrument gives you a reading. The reading is not a result. It becomes a result when someone checks it against a standard, reproduces it, and writes down what it means and what it does not. A spectrometer that reports a peak nobody confirmed has not discovered a compound. Nothing about that changes because the instrument is a language model instead of a magnetron.

What actually changed between October and May was not the model's intelligence. It was the apparatus around it. In October, a claim went out on social media with no external check and died in public in about forty-eight hours. In May, the claim arrived with an explicit lower bound worked out by a named mathematician and a human-verified companion note signed by nine of them, including the person most motivated to knock it down. Gowers, a Fields Medalist, said he would recommend the result for the Annals of Mathematics without hesitation. Same company, same general technology, opposite outcome, and the variable was verification.

So the question to ask any "AI discovered X" story is never whether the model is impressive. It is: what did the machine produce, who independently checked it, and is the thing being claimed the thing that was actually shown? In October the answers were a literature search, nobody, and no. In May they were a novel construction, nine mathematicians by name, and mostly, if you ignore the word "solved."

That is the same test that applies when an AI predicts millions of materials nobody has made, or when a model nails a protein's shape and misses the pocket that matters. And it is why who is doing the checking is quietly becoming the most important question in AI-assisted science. The models are going to keep producing things worth checking. The bottleneck, and the safeguard, is the checking.