alt Hacker NewsSo I don't know Lean or Mathematics to any degree to really be able to say this with any level of confidence, but speaking from a pure software engineering backgrouand, how do we know that 13 MILLION lines of Lean code are bug-free? It seems to me that for a mathematical proof, bug-free would be an absolute requirement. Maybe the structure of Lean imposes that, I don't know, but that seems highly unlikely to me. That just feels like a LOT of code to be comletely error-free... What am I missing here?
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In lean, a theorem is specified by a type (in their highly complex "dependent type system") and proof is specified by a code that produces a term of that type.
If the compiler certifies that the code indeed produces a term of that type, then the proof is correct.
So, only need to trust: (1) That theorem statement is correctly encoded (FLT has a very short 1 liner description really)
(2) Lean compiler is correct
Lean is like a statically typed programming language and validity is guaranteed if it compiles. The only room for errors is in translating a non-Lean theorem into Lean, so that you are not proving what you think you are proving.
The answer is we don't really know [0]:
> In 2026, AIs designed to spot bugs in software were directed at Lean, and found several loopholes which were then fixed. Perhaps related to this effort, a purported disproof of the Collatz conjecture was announced as verified in Lean. However, this proof was soon determined to rely on a bug in Lean, and once the bug was fixed the proof was found invalid
However it's a bit different than the usual 'bugs' we encounter in normal software development. Lean is more like a type checker. If you can write a false proof in Lean then the bug is in Lean itself, not your code.
In other words, Lean can have bugs, but the amount of code we need to check scales with Lean itself, not with the length of proof. Just like the chance that C compiler has bugs doesn't increase as we write more C code. So the 13M lines of code doesn't really matter here.
[0]: https://en.wikipedia.org/wiki/Lean_(proof_assistant)