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Hacker News front page32 min readintermediate

I vibed a proof of Conway's conjecture

Read on overreacted.ioHN 269·294 comments

Summary

The author used Claude to generate a Lean formalisation and proof of Conway’s refinement conjecture for omnific (surreal) integers. The proof passes mechanical checks and informal review but lacks independent verification. The post narrates the workflow, token cost, and reflections on AI‑assisted theorem proving.

  • AI can produce a complete Lean proof of a non‑trivial open problem in surreal number theory, but the result still needs expert validation.
  • Mechanical verification (Lean kernel, Palomar registry) catches low‑level errors, yet higher‑level mathematical correctness remains a human responsibility.
  • The experiment highlights practical concerns: token usage, prompt engineering, and the difficulty of interpreting AI‑generated formal code.

If AI can reliably generate correct formal proofs, it could dramatically accelerate research in areas with heavy formalisation overhead, such as number theory, cryptography, and verified software. However, the need for independent peer review underscores that AI‑generated proofs are not a substitut…

4/10
aileanformal verificationsurreal numbers

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