GPT-5.4 Pro solves Erdős Problem #1196

OpenAI's latest flagship model, GPT-5.4 Pro, has achieved a landmark breakthrough in automated reasoning by solving Erdős Problem #1196. The problem, posed by the legendary mathematician Paul Erdős in 1993, concerns the existence of certain sequences in combinatorial number theory and had resisted solution for three decades. According to OpenAI's technical report, the model generated a complete, novel proof using a hybrid approach combining Ramsey theory arguments with advanced probabilistic methods. The entire process, from problem statement to verified proof, was completed autonomously in under 72 hours on a cluster of 512 H100 GPUs.

This achievement was validated through formal verification by the Lean theorem prover and has been accepted for publication in the Journal of Combinatorial Theory, Series A. The proof itself introduces a new 'iterative density increment' strategy that experts believe could be applicable to a class of related problems in additive combinatorics. Unlike previous AI-assisted proofs that required significant human guidance, GPT-5.4 Pro formulated the proof strategy and executed the symbolic reasoning steps with minimal human intervention, marking a shift from AI as a research assistant to an independent agent in theoretical domains.

The success stems from architectural improvements in GPT-5.4 Pro's 'reasoning modules,' which allow for deep, chain-of-thought exploration over millions of reasoning steps while maintaining mathematical rigor. OpenAI has indicated that the model's training now incorporates a significantly larger corpus of formal mathematics, including the entire arXiv math repository and interactive theorem-proving environments. This result directly challenges the notion that creative, abstract reasoning is a uniquely human capability and sets a new benchmark for AI performance in STEM fields.