OpenAI announced that its new reasoning model achieved an original proof that disproves a famous unsolved geometric conjecture from 1946. The problem was posed by the legendary mathematician Paul Erdős and had resisted all attempts for nearly eight decades.
This time, unlike a previous announcement that ended in controversy, the company published supporting statements from several recognized mathematicians. Among them are Noga Alon, Melanie Wood, and Thomas Bloom, who maintains the Erdős Problems website and had labeled a previous OpenAI post as a “dramatically misleading representation.”
According to the company, for nearly 80 years mathematicians believed that the best possible solutions resembled square grids. OpenAI's model discovered a completely new family of constructions that work better.
A breakthrough with scientific backing
The announcement marks, according to OpenAI, the first time that an artificial intelligence has autonomously solved a significant open problem in a field of mathematics. Most notably, it was not a system specifically designed for mathematics, but a general-purpose reasoning model.
This suggests that current AIs are capable of maintaining long and complex chains of reasoning and connecting ideas from different fields in ways that researchers may not have explored before. The implications could extend to areas such as biology, physics, engineering, and medicine.
Thomas Bloom highlighted the achievement by stating that “AI is helping us to more fully explore the cathedral of mathematics that we have built over centuries.” He wondered: “What other invisible wonders await us?”
The recent precedent had generated skepticism. Seven months ago, then vice president Kevin Weil posted on X that GPT-5 had found solutions to 10 unsolved Erdős problems and made progress on another 11. It was later confirmed that the solutions already existed in the scientific literature, which drew criticism from figures like Yann LeCun and Demis Hassabis. Weil deleted the post.
Implications for the future of AI
This time, OpenAI avoided repeating the same mistake. The announcement publication included supportive comments from specialists, which lends greater credibility to the result. Mathematicians validated that the proof is original and effective.
Such achievements reinforce the idea that artificial intelligence tools are maturing towards deeper reasoning capabilities. They are no longer limited to retrieving existing information but can generate new constructions in highly abstract domains.
Consulted experts agree that the finding opens a new stage in the interaction between humans and machines at the frontier of mathematical knowledge. The Erdős conjecture was considered a central problem in combinatorial geometry.
While the scientific community still needs to review the proof in detail, the initial backing from prominent figures generates expectations about possible practical applications arising from such advances.
The news also revives the debate about the role of AI in basic research. Far from replacing mathematicians, it seems to be becoming a powerful tool for exploring territories that were previously out of reach due to time constraints or computational complexity.
OpenAI emphasizes that this result was not the product of specific training for this problem, but rather of general reasoning capabilities that the model applies autonomously. According to the company, that is what makes the advancement particularly significant.
