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Lean Proof Found To Be False
Дата публикации: 13-10-2026 14:49:06



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  • Thread starter Thread starter Hornbein
  • Start date Start date Oct 12, 2026
Hornbein
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From AI. I'm too lazy to check it.
  • Publication: On July 25, 2026, Ramana Kumar published an AI-assisted Lean repository containing a sorry-free formal proof purporting to show that the Collatz conjecture was false by exhibiting an orbit that does not return to 1. [1, 2]
  • The Kernel Bug (Issue #14576): The proof did not contain a valid mathematical refutation. Instead, it exploited an implementation bug in how the Lean 4 kernel handled nested inductive types with phantom parameters. When eliminating a nested occurrence, these parameters disappeared from the generated auxiliary type, allowing an ill-typed term to bypass checks and prove a contradiction (False). [1]
  • Independent Checker Bug: The repository also coincidentally bypassed an independent checker (Nanoda) due to a separate, unrelated bug in Nanoda's projection node verification. [1]
  • The Fix: Kiran Gopinathan reduced the exploit to a small proof of False on July 28, 2026, and Lean's creator Leonardo de Moura pushed a patch to fix the kernel bug within an hour. The Collatz conjecture remains completely unresolved. [1, 2]
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Science Advisor
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sbrothy
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sbrothy
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sbrothy
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If you mean that as critique I’ll take it as such, it just looked pretty valid.

Nothing personal.

Science Advisor
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If you mean that as critique I’ll take it as such, it just looked pretty valid.

Nothing personal.

Nothing personal. I know nothing about this subject, but I am very skeptical, in general, about the current wave of AI LLM efforts. IMO, any AI LLM results require very careful review.
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