OpenAI Says Internal AI Model Cracked 80-Year-Old Erdős Conjecture

OpenAI says one of its internal reasoning models has produced an original proof that disproves a famous geometry conjecture first posed by Paul Erdős in 1946, a result that, if it holds, marks the first time an AI has autonomously cracked an open problem central to a field of mathematics.

What the model actually did

The problem in question is the “unit distance problem,” a foundational question in combinatorial geometry that asks how many pairs of points can be placed exactly one unit apart under certain constraints. For decades, mathematicians believed the most efficient constructions resembled square-grid arrangements. According to OpenAI, its model identified an entirely different family of constructions that outperformed those classical assumptions, effectively disproving the conjecture.

“What the model did is totally different from the ‘square grid’ construction,” Sellke says. It instead constructed a more elaborate grid, one living in a kind of higher dimension. This higher-dimensional lattice of points had special mathematical symmetries that facilitate the separation of even more pairs by the same distance.

Why this one is different

The proof came from a new general-purpose reasoning model, rather than from a system trained specifically for mathematics, scaffolded to search through proof strategies, or targeted at the unit distance problem in particular. That distinction matters: this was not a math-specialist tool.

The proof has been checked by a group of external mathematicians. They have also written a companion paper explaining the argument and providing further background and context for the significance of the result.

Not OpenAI's first claim

If this sounds familiar to you, it’s because this isn’t the first time OpenAI has made such a bold claim. Seven months ago, the AI giant’s former VP Kevin Weil posted on X: “GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others.” It turns out, GPT-5 didn’t actually solve those problems; it just found solutions that already existed in the literature.

Taunts from rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis followed, and Weil promptly took down his premature post. This time, OpenAI lined up external review before the announcement.

Do you want to see how to make more plays? Do you want to find gains yourself?

Unusual Whales helps you find market opportunities through our market tide, historical options flow, GEX, and much, much more.

Create a free account here to start conquering the market with Unusual Whales.

How mathematicians are reacting

Unlike all those previous feats, this result would merit publication in a top math journal, as well as major media attention, even if it were performed by humans alone. “No previous AI-generated proof has come close” to meeting those high standards, wrote Timothy Gowers, a mathematician at the University of Cambridge, in commentary solicited by OpenAI.

OpenAI mathematicians Mehtaab Sawhney and Mark Sellke, who have made headlines recently for using AI to solve a number of less prestigious “Erdős problems,” fed the conjecture to an internal large language model trained for general reasoning. They asked it whether Erdős was right. After churning out hundreds of pages of careful logic and calculations, it beat his long-standing record.

The trade angle

OpenAI says this is significant because it means AI systems are now more capable of holding together long, difficult chains of reasoning and connecting ideas. For markets, that is the part that matters. The pitch behind the AI capex cycle has been that frontier reasoning models will eventually do real research-grade work, and this is the closest data point yet.

Expect this to feed back into the narrative around AI compute spend, enterprise adoption, and the premium investors are willing to pay for the model-layer winners.

Options market and stocks to watch

Watch for reaction across the AI complex on the back of this milestone:

• MSFT: OpenAI's largest backer and infrastructure partner; any narrative win for OpenAI tends to flow through here first.
• NVDA: Watch for renewed bid on the idea that frontier reasoning models will demand more, not less, compute.
• GOOGL: DeepMind is the most direct rival on AI-for-science; watch for any response from the Google camp.
• META: Yann LeCun's prior skepticism of OpenAI math claims makes Meta's AI lab a natural counter-voice to watch.
• AMZN: Anthropic's primary backer; the reasoning-model race is the relevant competitive axis here.

Keep an eye on other news and flow into the names above for confirmation.

Want more market intelligence? Create your free Unusual Whales account for options flow, market tide, GEX, and the full toolkit.