OpenAI AI solves 80-year-old math problem with new proof

An OpenAI reasoning model has produced an original proof disproving the Erdős Unit Distance Problem, a famous geometry conjecture that has remained unsolved since 1946, signaling a new era of AI-driven scientific discovery.

"This is a milestone in AI mathematics," Fields Medal winner and Cambridge professor Timothy Gowers said in a companion paper, adding that mathematicians might "need to ensure they are sitting down" before reading the details.

For decades, mathematicians believed the best solutions to the problem resembled square grids. The OpenAI model discovered a new family of constructions using tools from algebraic number theory, such as infinite class field towers and Golod-Shafarevich theory, to generate more unit-distance pairs than previously thought possible.

The breakthrough suggests general-purpose AI can now connect ideas across distant fields to solve complex problems, a capability with significant implications for research and development in biology, physics, and engineering, potentially accelerating discovery and affecting companies like Google's DeepMind.

This marks a significant turnaround for OpenAI, which faced criticism seven months ago after a former executive prematurely claimed that GPT-5 had solved several Erdős problems. Those claims were quickly debunked by mathematicians, including Thomas Bloom, who noted the AI had merely found existing solutions in literature. This time, Bloom is a co-author on the companion paper validating the new proof. "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries," Bloom said in a statement.

The core of the problem, first posed by legendary mathematician Paul Erdős, asks for the maximum number of pairs of points that can be exactly one unit apart on a flat plane. The AI's solution was surprising not just for its result, but for its method. Instead of using traditional geometric approaches, the model linked the problem to deep algebraic number theory, a field most researchers had not considered relevant. Princeton mathematician Will Sawin later refined the AI's result, providing a specific exponent for the improvement.

The use of a general-purpose reasoning model, rather than one specifically designed for mathematical problems, is what makes this achievement particularly noteworthy. It indicates that AI systems are developing the ability to sustain long, difficult chains of reasoning and uncover non-obvious connections between different domains. This capability could be a precursor to AI-assisted breakthroughs in other scientific fields that rely on complex, cross-disciplinary thinking.

Prominent mathematicians, including Noga Alon and Arul Shankar, have lent their support to the discovery, with Shankar stating that the work shows AI can "generate genuinely original, creative ideas." The event moves the needle in the long-running debate about AI's potential for true scientific contribution, a conversation often dominated by rivals like Google's DeepMind and Meta's AI lead, Yann LeCun. For investors, this signals that the massive capital being poured into AI research is yielding foundational results beyond consumer-facing chatbots, strengthening the long-term investment case for companies at the forefront of AI development.

This article is for informational purposes only and does not constitute investment advice.