OpenAI posted on X that its latest reasoning model has generated a proof that disproves a geometry conjecture first introduced by Paul Erdős in 1946. The firm frames the result as the first time artificial intelligence has autonomously solved a prominent open problem central to a mathematical field.

The model, which OpenAI describes as a general‑purpose reasoning system rather than a tool built specifically for mathematics, produced a new family of constructions that outperform the "square‑grid" solutions mathematicians have relied on for nearly eight decades. According to the company, the proof emerged without human direction, showcasing the system’s capacity to maintain long, difficult chains of reasoning and to connect ideas across disparate domains.

OpenAI’s announcement includes endorsements from several researchers, including Noga Alon, Melanie Wood and Thomas Bloom, the latter of whom runs the Erdős Problems website. Bloom said AI is helping the community explore the "cathedral of mathematics" built over centuries and hinted that more hidden discoveries may lie ahead.

The claim arrives after a previous episode that raised eyebrows in the research community. Seven months ago, former OpenAI vice president Kevin Weil posted on X that GPT‑5 had solved ten previously unsolved Erdős problems and advanced work on eleven others. That statement proved premature; the solutions cited already existed in the literature. Critics such as Yann LeCun and DeepMind CEO Demis Hassabis called out the misrepresentation, and Weil later removed the post.

OpenAI insists the current proof differs from the earlier misstep. It emphasizes that the model was not specially engineered for the Erdős conjecture, suggesting a broader leap in AI reasoning ability. The company argues that such capability could have ripple effects beyond pure mathematics, potentially influencing biology, physics, engineering and medicine.

While the announcement has sparked excitement, the mathematics community remains cautious. Independent verification of the proof will be essential before the claim can be accepted as a genuine breakthrough. Nonetheless, the involvement of respected mathematicians in supporting the result adds weight to OpenAI’s narrative.

OpenAI’s statement also highlighted the collaborative nature of the effort, noting that the proof was accompanied by remarks from the endorsing mathematicians. The firm’s messaging underscores a vision of AI as a partner in scientific discovery rather than a replacement for human insight.

As the proof undergoes peer review, the episode illustrates both the promise and the pitfalls of publicizing AI achievements. OpenAI’s latest claim marks a notable moment in the ongoing dialogue about how artificial intelligence can contribute to solving long‑standing scientific challenges.

This article was written with the assistance of AI.
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