Claude Fable solves a 150-year-old math conjecture

Threads this week covered Claude Fable producing a counterexample to the Jacobian Conjecture, a major open problem in algebraic geometry that has resisted proof for over a century. A separate digest post tried to walk through the math using GPT-5 prompts as scaffolding for understanding. The HN comments ranged from 'what does this actually overturn, intuitively?' to links to the Lean formal verification tutorial, which generated its own discussion about using proof assistants to verify AI-produced mathematics.

The Lean tutorial thread had an interesting adjacent observation: languages with strong compile-time checking, combined with LLMs, may be a powerful pairing for producing verified correct code and proofs. The argument is that formal verification gives you a ground truth the LLM can target, and the LLM gives you productivity the formal methods community never had alone.

Whether the Jacobian result holds up under scrutiny is still being evaluated, but the signal is clear: AI is now operating in domains where the outputs are genuinely hard for humans to check quickly.