AI-assisted Collatz Conjecture Proof Fails in Lean System
An AI-assisted attempt to prove the Collatz Conjecture using the Lean system has been confirmed as invalid. A critical flaw in Lean 4.32.2 was quickly patched.
Technology media outlet Gigazine reported that an AI-assisted effort to disprove the Collatz Conjecture has failed. The proof, conducted within the Lean formal verification system, was found to be erroneous after experts identified a significant issue within the system itself.
The Collatz Conjecture, also known as the 3n+1 problem, is a notoriously simple yet unsolved mathematical puzzle. It posits that any positive integer will eventually reach 1 when subjected to a specific iterative process: if the number is even, divide it by two; if it's odd, multiply it by three and add one.
Initially, Ramana Kumar announced on GitHub on July 25 that he had found a way to prove the existence of numbers that do not reach 1. He utilized the Lean system, which programmatically verifies the correctness of mathematical proofs. Kumar's claim was that his AI-assisted proof demonstrated this.
It was later revealed that the method Kumar employed allowed the Lean system to accept faulty propositions. Researcher Kiran Gopinathan reduced the problem to a smaller, reproducible code snippet and reported it to the Lean development team on July 28. The vulnerability was in Lean's core, related to its handling of "nested inductive types," which caused certain parameters to bypass verification. Lean developer Leonardo de Moura confirmed the issue stemmed from incomplete checks in the kernel implementation.
The Lean development team addressed the flaw swiftly. Approximately one hour after the report, the team released a patched version, Lean 4.32.2, on July 28, restoring the system's integrity. While the conjecture's disproof attempt failed, this fix ensures the Lean system remains a reliable tool for mathematical research.