Liam Price and ChatGPT-5.4 Pro solve Erdős's primitive set problem
Updated
Updated · NewsBytes · Apr 30
Liam Price and ChatGPT-5.4 Pro solve Erdős's primitive set problem
4 articles · Updated · NewsBytes · Apr 30
Price, a 23-year-old maths enthusiast, said the pair reached a solution to the 1960s problem in about one hour and 20 minutes.
The AI reportedly reused an overlooked formula in a new way rather than creating a wholly new method, overcoming a point where experts had repeatedly stalled.
UCLA mathematician Terence Tao said leading researchers had missed the route, highlighting AI's potential to help humans revisit longstanding mathematical problems rather than replace them.
Could AI-human collaborations like Price and ChatGPT-5.4 Pro soon become the standard for solving unsolved mathematical problems?
What risks arise as AI systems take a larger role in mathematical discovery, and how can we ensure their solutions remain trustworthy?
How might the rise of AI-generated mathematical proofs challenge traditional concepts of authorship and creativity in mathematics?
How AI’s Bias-Free Reasoning Cracked Erdős Problem #1196 After Six Decades
Overview
In early 2026, amateur mathematician Liam Price used ChatGPT-5.4 Pro with a unique "vibe matching" approach to generate a novel proof solving the 60-year-old Erdős Problem #1196. The AI's bias-free reasoning led to a breakthrough by applying the von Mangoldt function in an unexpected way. After Price shared the rough AI-generated proof, Fields Medalist Terence Tao and Jared Lichtman rigorously verified and refined it, confirming its validity and elegance, which Lichtman called a "Book Proof." This success sparked excitement and skepticism in the mathematical community and highlighted AI's potential to democratize research, tackle complex problems, and transform education, while emphasizing the need for ethical oversight.