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cloud.google.com·6h ago
Security
Trail of Bits Blog·Sep 9·5 min read
A “proof” of Fermat’s Last Theorem that fits the margin
TL;DR
A bug in Lean, a formal proof assistant, allowed for a nonsensical 'proof' of Fermat's Last Theorem, highlighting a critical issue in string handling. The Lean team quickly addressed the bug, demonstrating efficient problem resolution.
✦ Why It Matters
Review your code for similar string handling issues to avoid logical contradictions.
Key Takeaways
- Investigate string handling in your code to prevent logical errors.
- Stay updated on Lean's releases for critical bug fixes.
- Utilize Lean's validation guidelines for external proofs.
- Consider the implications of machine-checked proofs in your projects.
How It Works
The bug in Lean arises from a discrepancy between its logical definition and compiled native code for string extraction. When attempting to extract a slice from an extremely large position, the logical definition returns an empty string, while the compiled code returns the entire string.
This inconsistency creates a contradiction, allowing Lean to 'prove' that an empty string equals a non-empty string, thus enabling nonsensical proofs.