A tweet from user "Leeham" has announced that OpenAI's GPT-5.4 Pro has successfully solved Erdős Problem #1196, a significant mathematical conjecture that has eluded human mathematicians for an extended period. The achievement, reportedly accomplished in approximately 80 minutes, underscores the rapidly advancing capabilities of artificial intelligence in complex problem-solving. Liam Price prompted the model, which subsequently prepared its solution as a LaTeX paper.
Erdős Problem #1196, a conjecture by mathematicians Erdős, Sárközy, and Szemerédi, concerns primitive sets of integers and a specific summation inequality. Mathematician Jared Lichtman, who has dedicated seven years to the problem, expressed his satisfaction, stating in a related comment, "This problem has been thought about for some time which makes this reasonably impressive and meaningful." The problem's status was officially updated to "PROVED" on the erdosproblems.com website, crediting GPT-5.4 Pro (prompted by Price).
The solution reportedly utilized a novel Markov chain technique, a creative step that human mathematicians had previously overlooked despite years of dedicated work. Esteemed mathematician Terence Tao commented on the development, noting that the AI-generated paper "inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit." This suggests the AI's contribution extends beyond merely solving the problem to revealing new mathematical insights.
OpenAI released GPT-5.4 Pro on March 5, 2026, positioning it as their most advanced model. It is designed for complex, high-stakes tasks, featuring enhanced reasoning capabilities, a 1M+ token context window, and support for text and image inputs. The model is optimized for step-by-step reasoning, instruction following, and improved factual accuracy, making it particularly adept at multi-step problem-solving and agentic coding.
This breakthrough reignites discussions about AI's potential to discover new knowledge in mathematics and other scientific disciplines. While some debate whether LLMs can truly "discover" or merely synthesize existing data, the solution to Erdős Problem #1196, with its novel technique and newly identified mathematical connections, indicates a growing capacity for AI to contribute meaningfully to fundamental research. Formalization of the proof is currently underway within the mathematical community.
