OpenAI Claims to Solve Decades-Old Math Problem with New Reasoning Model
A new general-purpose model has reportedly disproved a 1946 conjecture by Paul Erdős, marking a significant milestone in AI-led mathematical discovery.
Primary source: TechCrunch AI. Full source links and update notes are below.
Fast summary
Start here
- OpenAI's reasoning model produced an original proof disproving a famous geometry conjecture posed by Paul Erdős in 1946.
- Unlike previous claims that were later retracted, this discovery is supported by external mathematicians including Thomas Bloom and Melanie Wood.
- The proof demonstrates the model's ability to maintain long chains of reasoning and connect abstract concepts across fields autonomously.
What happened
OpenAI announced on May 20, 2026, that its latest reasoning model successfully disproved a long-standing conjecture in geometry originally posed by Paul Erdős in 1946. The company asserts this is the first time an AI has autonomously solved a prominent open problem central to mathematics, moving beyond simply finding existing solutions in literature.
What's new in this update
To validate the claim, OpenAI released companion remarks from high-profile mathematicians, including Noga Alon and Thomas Bloom. This transparency follows a controversy seven months ago when a previous claim involving GPT-5 and several Erdős problems was retracted after it was revealed the model had only identified existing solutions already present in mathematical literature.
Key details
The model discovered an entirely new family of mathematical constructions that outperform the "square grids" previously thought by mathematicians to be the best possible solutions. OpenAI emphasized that the breakthrough came from a general-purpose reasoning model rather than a system specialized for mathematics, suggesting the technology can handle the long, difficult chains of logic required for broader scientific breakthroughs.
Background and context
Paul Erdős was one of the most prolific mathematicians of the 20th century, known for posing difficult problems that often remained unsolved for decades. Previous attempts by AI to claim solutions to his work were met with skepticism, most notably when a former OpenAI executive retracted a public post about GPT-5's purported math capabilities following criticism from Google DeepMind and Meta's AI leads.
What to watch next
Researchers are now evaluating how these reasoning capabilities might be applied to other complex fields such as biology, engineering, and medicine. The successful disproof of a known conjecture suggests that AI may soon play a larger role in uncovering previously unseen theoretical foundations in the physical and mathematical sciences.
Why it matters
The achievement suggests that AI is evolving from a retrieval tool into a system capable of autonomous, original reasoning in complex fields like mathematics and physics.
Read next
Follow this story through the topic hub, more ai coverage, and the latest updates.
Weekly briefing
Get the week's key developments in one concise email.
Get a fast catch-up on the biggest stories, the context behind them, and the links worth your time.
Cadence
Weekly, for a quick catch-up
Coverage
AI, business, world, security, sports
Format
Clear takeaways and useful context
Request the briefing
Leave your email to open a prepared request and get on the list for the weekly briefing.
Author
See who assembled this story and follow more of their work.
Sources and methodology