OpenAI once claimed AI solved famous unmet math problems — that collapsed under scrutiny. Does its newest math claim hold up any better?

This reads the question as asking how OpenAI's unit-distance counterexample compares with the company's earlier Erdős announcement, which fell apart. The short answer from the corpus is that the shape of the story repeats but what's inside it has changed. Both times there was a big public claim, then outside mathematicians examined it, then the headline shrank to something narrower. The difference is how much was left after the examination. The first time, almost nothing was. This time, a real result was.

Start with the earlier episode. OpenAI researchers said GPT-5 had solved several open Erdős problems. Thomas Bloom, who maintains the Erdős problems database, pointed out that 'open' on his site only meant he didn't know of a solution, not that mathematics had none. The problems already had published solutions, and GPT-5 had found those papers. What GPT-5 actually did was a strong literature search, not new proofs Did GPT-5 really solve previously unsolved math problems?. That's worth knowing because the mistake wasn't about whether the model reasoned well. It was about how the claim was labeled, and that kind of mistake is easy to make again.

The unit-distance result holds up better. The counterexample is checkable, and it rests on classical number theory: Golod–Shafarevich towers and number-field methods. The new step is to let the degree of the number field grow without limit. That lets a single fixed prime keep two key quantities (the class number and the discriminant) small enough to build sets of points in the plane with more unit distances than the conjecture allowed What made OpenAI's unit distance counterexample succeed?. Notice the structure: well-known tools, combined in a way nobody had tried. That's close to the earlier 'retrieval' story, but this time the combination produced something new. Read the two episodes together and the line between finding existing work and discovering something is blurrier than either announcement suggested.

What repeats across both episodes, and across the wider wave of AI-on-Erdős claims, is a gap between 'the proof checks out' and 'someone understands it.' Erdős problems became a popular AI test because they cover many areas of math at very different difficulty levels. But formal verification by software and human understanding are tracked as separate outcomes, and understanding usually comes later Why did Erdős problems become a popular AI testing ground?. The Erdős Problem 728 case shows the same split. The Lean proof (a proof checked line by line by the Lean software) is beyond dispute. Whether the AI really worked 'autonomously,' and whether readers can follow the argument, are both still open Did an AI system truly solve Erdős Problem 728 autonomously?. Formal verification also hides more than it seems to. A proof of one theorem leans on a large prebuilt library of definitions and lemmas (Mathlib), so 'verified' can hide how much existing structure the result depends on Can autoformalization work on individual statements alone?.

Here's the part you might not expect: the field's response is starting to look like a pattern too. Terence Tao argues that a model's opacity matters less if its output goes through a reliable checker Can opaque machine learning models help prove new mathematics?. That's what separates the unit-distance result from the GPT-5 episode, where the checking happened in public and after the announcement. Nature uses the unit-distance proof, verified but opaque about how it was found, as its main example of why mathematics' Leiden Declaration on AI disclosure should become a model for other sciences Can AI governance models from mathematics work across scientific fields?. So the pattern runs from claim, to dissolution, to a verified but opaque result, to new rules about disclosure. One limit: the corpus doesn't document how OpenAI itself presented the unit-distance announcement. Whether the company changed its own framing between the two claims isn't something this collection can answer.