OpenAI model solves 80-year Erdős planar unit distance problem

On May 20, 2026, OpenAI announced that an internal general-purpose reasoning model autonomously solved the planar unit distance problem, a longstanding question in discrete geometry first posed by Paul Erdős in 1946. External mathematicians reviewed the work and confirmed the proof.

The planar unit distance problem concerns how points can be arranged on a plane so that many pairs are exactly one unit apart. For decades researchers used constructions that resembled square grids; OpenAI reported the model produced a counterexample to that assumption and provided a formal argument accepted by reviewers.

OpenAI described the model as general-purpose and said the result was produced without step-by-step human guidance. The company added the proof drew on methods from algebraic number theory rather than the more common geometric techniques for this problem.

OpenAI framed the result as part of efforts to automate parts of the research process and suggested similar systems could assist work in biology, physics, materials science and medicine where problems are large or technically complex. Company representatives emphasized that human researchers continue to choose problems, set priorities and validate results.

The lab did not disclose the model’s full architecture, its training data or the chain of internal checks used to reach the result. The company added that human judgment remains central to deciding which problems to pursue and how to interpret outcomes.

The announcement comes as OpenAI prepares an initial public offering filing and after a U.S. jury cleared the company in litigation brought by Elon Musk. Rival firm Anthropic is projecting revenue of $10.9 billion for the period and Andrej Karpathy has joined Anthropic to work on frontier model research.

Investors and industry leaders have discussed how more autonomous systems could affect high-skilled work. Citadel chief executive Ken Griffin recently warned that agentic AI is beginning to perform PhD-level finance tasks faster than humans.

Experts outside OpenAI said they will examine the proof and the model’s methods in the coming weeks to determine whether the techniques can be generalized to other mathematical problems or applied research areas.

OpenAI wrote: “Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946.”