openAI has announced that its reasoning model successfully disproved a geometric conjecture that had remained unsolved since 1946. The company stated that mathematicians who previously identified a significant error in one of the firm’s past claims have now verified this new result.
The development was detailed in a research paper released by OpenAI. The company said its o3 model, also used in its recent “Deep Research” feature, provided a solution to a longstanding problem in the field of combinatorial geometry.
Background of the Mathematical Problem
The conjecture originated in a 1946 paper by Hungarian mathematician Paul Erdős. It focused on the “maximum number of times the distance 1 can occur among n points in the plane.” For decades, researchers have attempted to either prove or disprove this hypothesis without success.
OpenAI’s model was tasked with analyzing the “isosceles set” problem, a related geometric challenge. According to the company, the AI generated a new construction that violates the terms of the original conjecture, effectively disproving it.
Verification and Expert Scrutiny
This announcement follows a previous instance where OpenAI faced significant criticism. In 2024, the company claimed its model had solved a different advanced mathematics problem, but external mathematicians quickly found flaws in the reasoning and output. That incident led to public statements from the research community questioning the reliability of such claims.
For the current result, OpenAI stated it submitted the solution to several independent mathematicians for review. The company said these experts, including some who were critical of the earlier erroneous claim, have confirmed the validity of the new proof.
Implications for artificial intelligence Research
The successful verification marks a notable step for large language models in abstract reasoning tasks. OpenAI argued that the result demonstrates the potential for AI systems to contribute to high level theoretical research, a domain traditionally reserved for human intuition and rigorous training.
Critics, however, maintain that such models still face fundamental limitations. They point out that the AI required extensive computational resources and structured prompting to reach this specific result, and that generalizing this capability to a wide range of unsolved problems remains unproven.
Reactions from the Mathematics Community
Several mathematicians contacted by Delimiter acknowledged the significance of the verification but urged caution. One researcher noted that while this is a legitimate advance, it does not change the fact that AI models frequently produce convincing but incorrect responses in other contexts.
Another expert suggested that the primary value may lie in the model’s ability to generate novel constructions that human researchers can then analyze and refine, rather than acting as an autonomous problem solver.
OpenAI has not announced plans to release the full underlying model or training data used for this specific task. The company has indicated it will continue to focus on developing reasoning capabilities and will seek further collaboration with academic institutions.
Further evaluation of the model’s capabilities in other branches of pure and applied mathematics is expected in the coming months.
Source: Delimiter
