AI reportedly cracks Erdős problem #728 with minimal human guidance

An AI system has reportedly produced a solution to Erdős problem #728 with little human intervention-a notable milestone for automated mathematics. What’s notable here isn’t that AI touched a famous name; it’s the level of autonomy claimed. Prior efforts have seen machines explore search spaces or check human proofs (think SAT-solver certificates or Lean/Isabelle formalizations). This result, if accompanied by verifiable artifacts, suggests a tighter loop: propose, test, refine, and validate with scarce hand-holding.

Under the hood, progress like this typically pairs generative search with rigorous checkers-SAT/SMT solvers, proof assistants, or program-synthesis feedback-so correctness isn’t “AI says so,” it’s machine-verified. The bigger picture: a shift from AI as a tool that assists mathematicians to systems that can independently traverse conjecture space and return certifiable proofs or counterexamples. For industry, the implications extend beyond pure math: stronger auto-formalization, better search over discrete structures, and workflows that turn LLM creativity into verifiable outputs. Worth noting: the bar for “solved” in this community is public proofs, reproducible runs, and independent verification. What’s actually new vs. hype will hinge on released code, proof logs, and peer review. If those boxes are checked, #728 becomes less a one-off headline and more evidence that the generate-and-verify stack is maturing into a reliable engine for discovery.