GPT-5 Aids Researchers in Solving 10 Open Erdős Problems, Reshaping Mathematical Research

Cambridge, MA – In a groundbreaking development for mathematics and artificial intelligence, researchers Mark Sellke and Mehtaab Sawhney have utilized thousands of queries to OpenAI's GPT-5 to find solutions for 10 previously open Erdős problems. The collaboration also yielded significant partial progress on 11 additional problems, marking a potential paradigm shift in scientific research methodologies.

"Update: Mehtaab and I pushed further on this. Using thousands of GPT5 queries, we found solutions to 10 Erdős problems that were listed as open: 223, 339, 494, 515, 621, 822, 883 (part 2/2), 903, 1043, 1079," Mark Sellke announced on social media. He added that for 11 other problems, GPT-5 found "significant partial progress that we added to the official website."

One notable instance involved Erdős Problem #339, which GPT-5 Pro "solved" by uncovering a 2003 paper by Gábor Hegedűs, François Hennecart, and Alain Plagne that had already provided the solution, yet the problem remained listed as open. This highlights the AI's "superhuman literature search" capabilities, efficiently navigating vast academic archives to connect overlooked proofs with open problems.

The researchers' work also shed light on Erdős Problem #827, where the AI's analysis indicated an error in Erdős's original paper. Subsequent work by Martínez and Roldán-Pensado had already explained and corrected this argument, a detail brought to the forefront by the AI-assisted investigation.

Mathematician Terence Tao, a Fields Medalist, commented on the development, suggesting that AI's most impactful applications in mathematics will likely stem from its ability to handle "trivial, time-consuming, but indispensable research stages" such as literature review and verification. This allows human researchers to focus on higher-level conceptual thinking.

Mark Sellke is an Assistant Professor at Harvard University, and Mehtaab Sawhney is a Clay Research Fellow and Ph.D. candidate at MIT, both recognized for their contributions to mathematics. Their pioneering use of GPT-5 demonstrates a new frontier where advanced AI systems act as powerful research assistants, accelerating the pace of discovery and re-evaluating the status of long-standing mathematical conjectures.