APREX · EST. 2026
A breakthrough that has remained unsolved since World War II has now apparently been cracked — not by a human mathematician, but by an AI model from OpenAI. And this time, recognized experts have vouched for the result.
The Problem That Waited Since 1946
In 1946, the Hungarian-American mathematician Paul Erdős formulated what has since become known as the «planar unit distance problem» — a problem in discrete geometry concerning how points can be placed in a plane with specific distance properties. For eight decades, the problem remained unsolved.
Now, OpenAI claims that the company's internal reasoning model has not only tackled the problem but actually disproven a central conjecture related to it, according to TechCrunch.
The model connected abstract algebraic number theory with a concrete geometric problem — a connection mathematicians had not foreseen beforehand.
Not Specialized — But General
What makes the result particularly remarkable is that it is not a specialized math program. OpenAI's model is a general reasoning model, designed to handle long and complex chains of logic without needing step-by-step guidance from humans.
The model produced a new mathematical proof by drawing connections between concepts from algebraic number theory — including what is described as «class field towers» and «Golod-Shafarevich theory» — and the concrete geometric problem. According to the research material underlying the case, this connection was not foreseen by mathematicians beforehand.
Prominent Names Confirm the Result
What distinguishes this news from previous AI mathematics claims is who stands behind it. Fields Medalist Tim Gowers and number theorist Arul Shankar are both said to have independently verified the proof, according to TechCrunch. They highlight the model's ability to formulate original and clever ideas as particularly impressive.
This is not the first time OpenAI has made big claims in mathematics, and the company has previously been criticized for exaggerating results. The fact that the very mathematicians who have previously exposed weak claims are now backing this one gives the case significant weight.
AI and Geometry: A Rapidly Developing Field
OpenAI's result comes at a time when AI systems are generally making significant progress in mathematical reasoning. Google DeepMind's AlphaGeometry 2, launched in 2025, solved 42 out of 50 geometry problems from the International Mathematical Olympiad (IMO) for the period 2000–2024, achieving what is described as gold medal level. According to the research material, the system is 100 times faster than its predecessor.
Princeton's open theorem prover Goedel-Prover-V2, launched in July 2025, improved its performance on a standard mathematics benchmark from 60 to 90 percent.
What nevertheless distinguishes OpenAI's latest claim from these results is the nature of the problem solved. Olympiad problems are challenging, but they have known solutions. An open research problem is of an entirely different category — there is no answer key to check against, and the solution must be evaluated on its own merits by experts in the field.
What Does This Mean Going Forward?
If the result holds, it represents a qualitative shift in what AI systems are capable of in mathematics. It is no longer just about solving problems faster than humans, but about contributing new knowledge to the field.
It remains to be seen whether the proof will withstand full peer review and eventual publication in a scientific journal. But with two independent verifications from top-tier mathematicians, there is reason to take the claim seriously.