Bengaluru: If you are a mathematician, then you may want to take a seat before reading further—this is how Fields Medalist Timothy Gowers told the world about an OpenAI model having solved a problem that had stumped mathematicians for 80 years.
The problem in question is the planar unit distance problem. Dubbed, Erdős problem 90, it was first posed by Hungarian mathematician Paul Erdős in 1946.
It’s been described as “possibly the best known (and simplest to explain) problem in combinatorial geometry.”
It’s not the first maths problem solved by AI; it’s not even the first Erdős problem solved by AI. But researchers are taken aback by the way the large language model solved problem 90.
As mathematician Thomas Bloom explained in the companion paper to the mathematical proof, Erdős had proposed a certain foundational assumption from which the problem has been thought about. All human effort has been based on this. The OpenAI model did the opposite. It started from the presumption that Erdős was wrong and started hunting for a counterexample.
This shows how AI is moving beyond the role of helper to having original ideas. OpenAI’s article on the milestone explains why this is significant beyond mathematics.
The field of mathematics is a “clear testbed for reasoning”. The better it gets at math, the better it gets at research.
“If a model can keep a complicated argument coherent, connect ideas across distant areas of knowledge, and produce work that survives expert scrutiny, [then] those are also useful abilities in biology, physics, materials science, engineering, and medicine…they are part of our longer-term path toward more automated research,” the article read.
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Exploring the cathedrals of math
In a video released by OpenAI celebrating the achievement, Gowers calls it the most important moment in the history of mathematics.
An earlier solution—to Erdős problem 1196—showed the first glimmers that original thought is possible in an AI output.
Erdős posed problem #1196 in 1968, it was solved last month using GPT-5.4 Pro by 23-year-old Liam Price, who has no formal training in the field.
“This one is a bit different because people did look at it, and the humans that looked at it just collectively made a slight wrong turn at move one,” said Terence Tao, a mathematician at the University of California, Los Angeles, to Scientific American.
Overcoming this mental block is a significant advantage AI has.
Bloom noted that AI produces “the most surprising results by persevering down paths that a human may have dismissed as not worth their time to explore, combining superhuman levels of patience with familiarity with a vast array of technical machinery.”
Mathematician Daniel Litt, who called AI’s solution to problem 1196 “reasonably interesting”, was won over by its solution to problem 90.
He called it the first time he found an AI-produced proof “exciting in itself”.
Experts in the field are opening themselves up to partnering with AI. Bloom said it can help fully explore the “cathedral of mathematics” that humans have built over centuries.
He also notes that AI alone isn’t enough and humans are a vital part of the research process. The proof produced by AI, he said, was improved by the work of human researchers.
OpenAI too noted that human judgement remains the most valuable tool.
Thang Luong, who heads the Superhuman Reasoning team at Google DeepMind, has a vision for AI and math.
“I hope that perhaps by 2030, AI and mathematicians can jointly win a Fields Medal,” he said to Nature.