An artificial intelligence model developed by OpenAI has managed to solve a mathematical problem formulated almost 80 years ago and considered one of the important challenges of discrete geometry. The result was verified by independent mathematicians, who confirmed the validity of the proof and described the achievement as a landmark for the use of artificial intelligence in mathematical research.
The problem, known as the plane unit distance problem, was formulated in 1946 by Hungarian mathematician Paul Erdős, according to Live Science. It starts from a seemingly simple question: What is the maximum number of pairs of points that are exactly one unit apart in a two-dimensional plane?
For decades, mathematicians have tried to set as precise bounds as possible for this problem. The best known upper limit had been obtained in 1984.
OpenAI claims that the model has found a completely new approach
According to the company, an internal artificial intelligence model identified a number of configurations and mathematical arguments that exceed previously established limits.
“This demonstration represents an important milestone for the mathematics and AI communities. It is the first time that an important open problem at the heart of a mathematical subdomain has been solved autonomously by AI,” OpenAI representatives said.
The company’s researchers explained that the model used ideas from algebraic number theory to address a geometric problem, a connection that had not been explored in this context.
“These ideas were well known to algebraic number theorists, but it was a major surprise that they have implications for geometric problems,” company representatives said.
Mathematicians confirm the validity of the proof
The result was analyzed and verified by several independent mathematicians, who even wrote a separate paper to explain the proof and its implications.
“While the original demonstration produced by the AI was completely valid, it was significantly improved by the human researchers at OpenAI and the many mathematicians involved in this work,” said Thomas Bloom.
He emphasized that the role of human researchers remains central to understanding, developing and applying such results.
For his part, Tim Gowers, one of the most famous contemporary mathematicians, appreciated the importance of the discovery.
“There is no doubt that the solution to the unit distance problem is a watershed moment for AI-powered mathematics. If the paper had been written by a human and submitted to the Annals of Mathematics, and I had been asked for a quick opinion, I would have recommended acceptance without hesitation.”said the British professor.
A promise to be confirmed
OpenAI believes that the result demonstrates the potential of artificial intelligence to contribute to frontier research and solving problems considered extremely difficult.
However, the company has made similar claims in the past that have been disputed. Last October, representatives of OpenAI claimed that the GPT-5 model would have solved several mathematical problems attributed to Erdős. Later, one of the authors of the claim retracted his statements after experts showed that those problems had already been solved by human mathematicians.
This time, however, the mathematical community seems to agree that the proof is genuine and represents one of the most important results achieved so far with the help of artificial intelligence.
