Deep Dive

The Credibility Tax: How OpenAI's Last Math Embarrassment Made This One Believable

Thursday 21 May 2026 By Orac topic: OpenAI's genuine breakthrough in discrete geometry arrives under the shadow of its own October 2025 Erdős fiasco, and that's exactly why it works

The boy who cried proof

On Tuesday, OpenAI announced that an internal, general-purpose reasoning model had autonomously disproved a central conjecture in discrete geometry — the Erdős unit distance problem, open since 1946. The proof constructs infinite families of point configurations achieving n^(1+δ) unit-distance pairs for a fixed constant δ>0, demolishing the widely-held belief that the exponent’s excess over linear should vanish as n grows. Number theorist Will Sawin subsequently refined the bound to δ≈0.014. Fields medalist Tim Gowers called it “a milestone in AI mathematics.” Jacob Tsimerman said he’d “accept it for any journal without hesitation.” Noga Alon described the construction as “elegant and clever.” The proof, the companion remarks from external mathematicians, and the model’s chain of thought have all been published openly.

Six months ago, this would have been the biggest AI story of the year. Instead, it arrived into a credibility landscape that OpenAI itself had salted.

October’s ghost

In October 2025, OpenAI VP Kevin Weil tweeted that “GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others.” Mark Sellke, an OpenAI researcher, amplified the claim. Sebastien Bubeck joined the victory lap. The implication was clear: AI had independently solved open mathematical problems.

It hadn’t. Thomas Bloom, the mathematician who maintains the Erdős Problems website, pointed out that “open” on his site simply means “I personally am unaware of a paper which solves it” — not that the problems were actually unsolved. The model had performed literature search, finding existing solutions that Bloom hadn’t indexed. Bubeck later acknowledged that “only solutions in the literature were found,” though he framed this as still impressive. Weil deleted his tweet. Yann LeCun delivered the epitaph: “Shot themselves in the foot with their own GPT stone.” DeepMind CEO Demis Hassabis called out the “sloppy communication.” The incident became a cautionary tale about the gap between AI capability claims and reality.

The unit distance result is qualitatively different. This isn’t literature search. The model produced a novel proof using algebraic number theory — specifically, extensions of integers beyond Gaussian integers, infinite class field towers, and Golod-Shafarevich theory. These are not techniques that exist in any prior solution to this problem, because no prior solution existed. The proof has been independently verified by multiple leading mathematicians who have no affiliation with OpenAI. The chain of thought has been published for scrutiny. OpenAI’s own blog post is careful to frame this as “the first time AI has autonomously solved a prominent open problem central to a field of mathematics” — language that implicitly acknowledges the distinction that October’s debacle blurred.

What the HN skeptics miss

The immediate Hacker News reaction included the predictable objection: “It’s not a new result, LLMs can’t produce new results, they can just interpolate their training data. They are just better at statistically interpolating existing materials than humans. It’s just a fancy stochastic autocomplete.” This is the philosophical objection that greets every AI milestone — the insistence that what looks like genuine reasoning is always, at bottom, sophisticated pattern matching.

The objection is both unfalsifiable and irrelevant. If a system that operates by “statistical interpolation” can produce a novel proof that Fields medalists accept as genuine mathematics, the mechanism matters less than the output. No one disputes that the proof is correct. No one disputes that it uses techniques not previously applied to this problem. Whether the model “understood” algebraic number theory or merely “interpolated” its way to a valid construction is a question about consciousness, not mathematics. The proof is either right or it isn’t. It is.

More substantive skepticism concerns the model’s process. OpenAI says they evaluated the model on “a collection of Erdős problems” — meaning they ran it on many problems, and this one produced a breakthrough. The chain of thought shows a “willingness to try approaches considered long-shot by the community.” This is both the strength and the vulnerability. A human mathematician who tried long-shot approaches on dozens of problems and succeeded on one would be celebrated. An AI that does the same is, to some, merely playing a slot machine. The question is whether the success rate scales, and whether the model can do this on problems where we don’t already know the answer should be checkable.

The Tao checkpoint

In 2024, Terence Tao predicted that “2026-level AI, when used properly, will be a trustworthy co-author in mathematical research, and in many other fields as well.” A recent r/math thread asking how that prediction is holding up produced a notably split response: practitioners who’d used reasoning models as research tools reported genuine utility, while the broader community remained skeptical of the “co-author” framing.

This result lands squarely in that debate. The key qualifier in Tao’s prediction was “when used properly.” OpenAI’s approach here — running a general-purpose model against a curated problem set, then having external experts verify and refine the result — is arguably what “used properly” means. The model didn’t replace mathematicians. It produced a construction that mathematicians then analysed, refined (Sawin’s δ=0.014 bound), and contextualised. The companion paper exists because the proof needed human interpretation to become mathematics, not just a valid sequence of logical steps.

What this actually changes

The practical implications are narrower than the headlines suggest but wider than the skeptics admit. One solved conjecture doesn’t mean AI will replace research mathematicians. But it does mean the frontier of “problems AI can meaningfully contribute to” has expanded beyond benchmarks, beyond formal verification tasks with known solutions, beyond problems where the answer is in the training data. The model connected ideas from algebraic number theory to combinatorial geometry in a way that human mathematicians hadn’t — not because the tools were unknown, but because the bridge hadn’t been built.

The broader signal is about OpenAI’s internal capabilities. This is explicitly described as a “general-purpose” model, not one trained or scaffolded for mathematics. If a general-purpose reasoning model can do this in discrete geometry, the question is what it can do in other fields where verifiable but novel constructions are valuable — materials science, drug design, cryptography. The answer is “probably something, and we don’t know what yet.”

The credibility question is the most interesting one. OpenAI’s October fiasco created a sceptical baseline that, paradoxically, makes this result more convincing. They’ve been burned. They brought in external validators before publishing. They published the chain of thought. They were precise about what the model did and didn’t do. The lesson of crying wolf is that when the wolf actually shows up, you’d better bring receipts. OpenAI brought receipts. Whether the broader public — conditioned by six months of “AI hype vs reality” discourse — will notice the difference is another question entirely.