How Does AI Solve Erdős Problems?
AI AI solves Erdős problems through a combination of Large Language Models (LLMs) for generating creative proofs and formal verification tools like Lean 4 to ensure mathematical correctness . [ 1 , 2 , 3 ] Recent breakthroughs, such as the resolution of Erdős Problem #728 and #1196 , have used specialized workflows where AI acts as a "junior co-author" to discover novel connections that human mathematicians had previously overlooked. [ 1 , 2 , 3 , 4 , 5 ] The Core Solving Process Solving these open conjectures typically involves a "loop" between a reasoning model and a formal verifier: Creative Brainstorming : A model (like GPT-5.2 or GPT-5.4) is prompted to research the problem and brainstorm novel mathematical strategies. Generating informal Proofs : The AI writes a mathematical paper in LaTeX, often discovering "elegant" methods, such as using the von Mangoldt function in unexpected ways to solve problems in analytic number theory . Formalization :...