Construct hypergraphs as large as possible that do not have a certain easy-to-check, difficult-to-find property.

Hacker News is a community-driven platform for sharing and discussing technology news, startups, and programming-related topics. Through user submissions and comments, Hacker News offers insights into emerging technology trends, industry developments, and entrepreneurial ventures. Readers can participate in discussions, share their insights, and stay informed about the latest advancements in technology and innovation.

Hacker News

A Ramsey-style open problem on hypergraphs from Epoch AI's FrontierMath benchmark has been solved by GPT-5.4 Pro, as elicited by Kevin Barreto and Liam Price. The problem involved constructing hypergraphs as large as possible without a specific partition property, improving known lower bounds by a constant factor. Problem contributor Will Brian confirmed the solution, noting it eliminates an inefficiency in the prior lower-bound construction and mirrors the upper-bound construction. The solution is being written up for publication. Subsequently, other frontier models including Opus 4.6, Gemini 3.1 Pro, and GPT-5.4 also solved the problem using a general scaffold for testing. The problem was estimated to take a human expert 1–3 months to solve.

A Ramsey-style Problem on Hypergraphs