"Erdos problem #728 was solved more or less autonomously by AI" (mathstodon.xyz)

AI has achieved a significant milestone by solving the Erdős problem #728, originally explored in 1975 by mathematicians including Erdős and Graham. The recent breakthrough was made possible through the collaboration of AI tools like ChatGPT and Aristotle, which generated a series of proofs that ultimately adhered to stricter constraints of the problem. ChatGPT initially produced a proof while bypassing these constraints, prompting further refinements and collaborative efforts that led to a properly formatted, Lean-verified proof. This iterative process highlighted how AI can facilitate complex mathematical reasoning and proof generation, enhancing clarity and organization. This development holds considerable implications for the AI/ML community, particularly in mathematical research where AI can assist in proof discovery and documentation. The ability to rapidly generate tailored variations of a proof allows for an unprecedented level of dynamism in academic writing, paving the way for more efficient collaborative efforts in research. Moreover, this incident demonstrates the potential for AI to not only assist in generating proofs but also improve the communication of complex ideas, thus raising questions about authorship and the role of AI in academic environments. As these technologies develop, they could reshape the landscape of mathematical proof, making it more accessible and collaborative.