OpenAI's new reasoning model has produced an original mathematical proof disproving a geometry conjecture first posed by Paul Erdős in 1946. The disproof—verified by mathematicians Noga Alon, Melanie Wood, and Thomas Bloom—represents the first time AI has autonomously solved a prominent open problem central to a field of mathematics, according to OpenAI. For nearly 80 years, mathematicians believed the best possible solutions to the problem looked roughly like square grids.
The proof comes seven months after OpenAI prematurely claimed GPT-5 had solved 10 previously unsolved Erdős problems and made progress on 11 others. That claim, posted by then-VP Kevin Weil, collapsed when researchers discovered the solutions already existed in published literature. Yann LeCun and Google DeepMind CEO Demis Hassabis mocked the error publicly before Weil deleted the post. Thomas Bloom, who maintains the Erdos Problems website, called that earlier claim a dramatic misrepresentation.
The new proof came from a general-purpose reasoning model, not a system designed specifically to solve math problems or this conjecture in particular. OpenAI says the model discovered an entirely new family of constructions that perform better than the grid-like solutions mathematicians had assumed were optimal since 1946. The company argues this capability demonstrates AI systems can now hold together long, difficult chains of reasoning and connect ideas across fields in ways researchers may not have previously explored.
Key facts
- 01OpenAI's reasoning model disproved Paul Erdős's 1946 geometry conjecture about optimal grid-like solutions.
- 02The proof marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.
- 03Mathematicians Noga Alon, Melanie Wood, and Thomas Bloom verified the disproof.
- 04Seven months ago, OpenAI falsely claimed GPT-5 solved 10 Erdős problems—the solutions already existed in literature.
- 05The proof came from a general-purpose reasoning model, not a specialized math system.
The stakes extend beyond pure mathematics. OpenAI claims the same reasoning architecture could apply to biology, physics, engineering, and medicine—domains where long chains of interdisciplinary inference are similarly required. The company did not disclose the model's name, parameter count, or training details.
Bloom, who seven months ago criticized OpenAI's false claim, endorsed the new result in a statement. The mathematician said AI is helping researchers more fully explore the cathedral of mathematics built over centuries. He asked what other unseen wonders are waiting in the wings.
The verification by named mathematicians marks the key difference between today's announcement and the November 2025 debacle. Alon, Wood, and Bloom are recognized experts in the field—Bloom's Erdos Problems website is the authoritative catalog of open conjectures tied to the Hungarian mathematician's legacy. Their public support provides the credibility Weil's solo post lacked.
OpenAI's insistence that the proof came from a general-purpose model also distinguishes this result from specialized theorem-proving systems. AlphaProof, developed by Google DeepMind, uses reinforcement learning specifically trained on formal mathematics. If OpenAI's claim holds, the model solved an open problem without domain-specific fine-tuning—a step toward more general reasoning.
The risk remains that OpenAI oversold the novelty again. The company did not publish the full proof or specify whether human mathematicians guided the model's search. Without the formal proof in hand, peer review remains incomplete. Bloom's endorsement carries weight, but the mathematical community will demand the construction be published and checked line-by-line before accepting the result as settled.
The repeat claim also invites scrutiny of OpenAI's internal vetting process. The company evidently failed to verify Weil's November post before he published it, prompting public mockery from rivals. If the same team approved today's announcement, the track record suggests caution. The presence of three named mathematicians offering support mitigates but does not eliminate that concern.
OpenAI's IPO target of September 2026 makes the timing notable. A verified mathematical breakthrough would bolster the company's narrative that its reasoning models are approaching or exceeding human expert capabilities in cognitively demanding fields. Investors pricing a late-2026 offering will weigh whether the disproof represents a reproducible capability or an isolated result. The earlier false claim will shadow that assessment until the proof is published and peer-reviewed.
The conjecture disproved was one of thousands posed by Erdős, a prolific mathematician who offered cash prizes for solutions and traveled the world collaborating with researchers. His problems span graph theory, combinatorics, number theory, and geometry. Many remain unsolved decades after his death in 1996. The problem OpenAI claims to have solved concerned optimal constructions in finite geometry—a subfield focused on discrete structures rather than continuous shapes.
If the proof stands, it validates OpenAI's thesis that scaling reasoning models will unlock scientific breakthroughs across disciplines. If it collapses under scrutiny, the company will have twice claimed a milestone it did not achieve, undermining credibility ahead of a public offering. The mathematical community's full verdict is not yet in.
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