| ▲ | prometheus1992 3 hours ago |
| Can someone with more knowledge help me with this silly question in my head? >>Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems Did a human check the 13 million lines of code? How does QA'ing this type of work works? |
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| ▲ | stabbles 2 hours ago | parent | next [-] |
| There is a simple piece of code that can check simple steps, and many people agree this checker is correct. Then there is a formalization of the theorem which many people agree defines the theorem accurately. Then there is 13 million lines of proof that nobody has read, but the proof checker validated each step. That's enough. So, all you have to verify is the formalization of the theorem, and believe that the proof checker is free of bugs. You don't have to read the actual proof. |
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| ▲ | Jblx2 2 hours ago | parent [-] | | You still have to trust that the AI didn't exploit a bug in the Lean kernel. There was just such an instance of a bug a little over a month ago: https://leodemoura.github.io/blog/2026-8-1-postmortem-for-ke... | | |
| ▲ | vessenes an hour ago | parent [-] | | True, .. and. In this case, the original proof is considered rigorously checked, so finding a bug in the kernel would be nice to know about, but in my opinion would not take away from the accomplishment (FLT in lean using agents) nor the many benefits of getting these mathematical objects formalized and usable in Lean in the future. |
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| ▲ | lordnacho 2 hours ago | parent | prev | next [-] |
| This was my question as well. The way I understand it, it's like a compiler, it implements rules, in this case logic/math rules that tell you whether something follows from assumptions you've given it. But how do you know you told it what you intended to tell it? |
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| ▲ | babelfish 2 hours ago | parent | prev | next [-] |
| A human definitely didn't, but one of the benefits of formal verification is that even if the work done to achieve something is slop-y or excessively verbose, solvers like Lean guarantee that the initial proposition (assuming it was written correctly and in this case was definitely reviewed by humans) is definitively True. This is true across other domains of formal verification outside of math as well |
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| ▲ | hyperhello 2 hours ago | parent | prev | next [-] |
| The point of writing Lean code is that Lean checks it accordingly. Lean is a domain specific language to encode mathematical reasoning in a way that can’t be fooled. Note to other users: don’t downvote this kind of comment, answer it. |
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| ▲ | stratos123 2 hours ago | parent | next [-] | | encode mathematical reasoning in a way that can’t be fooled.
I would be a bit careful asserting that in full generality, given https://github.com/James-Hanson/junk-theorems-in-lean | | |
| ▲ | mswphd 25 minutes ago | parent | next [-] | | junk theorems aren't the concern, soundness issues in the lean kernel are the concern. Notably, junk theorems are true. Nobody would debate that the junk theorem is true. The main thing people would say is that junk theorems, while being true, are sensitive to precisely how you encoded mathematics, so despite being true, they are perhaps not conceptually meaningful. As an example of a junk theorem, sasy you use the definition of the natural numbers using von neumann ordinals https://en.wikipedia.org/wiki/Set-theoretic_definition_of_na... Then for any natural numbers n, m, they're implicitly sets. So n \intersect m = min(n,m). This is the wrong way to think about natural numbers. You should not use this ever in proofs. But this isn't because your proofs would be false, but instead because it is a fundamentally confusing way to think about the natural numbers. It is in this sense it is a "junk theorem". | |
| ▲ | hyperhello 2 hours ago | parent | prev [-] | | Isn’t there some theorem that any sufficiently complex mathematical languages will have statements that can’t be proven? :) | | |
| ▲ | fn-mote an hour ago | parent [-] | | This would be funny if it were relevant. Seems like a statement about false negatives instead of false positives. False negative = could not find a proof of a true theorem. False positive = erroneous proof of a theorem. |
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| ▲ | epgui 2 hours ago | parent | prev [-] | | Is Lean a DSL? I’d argue it’s a general purpose programming language that excels at proofs. | | |
| ▲ | mswphd 21 minutes ago | parent | next [-] | | it is a general-purpose programming language. for example, it's standard library allows you to do file io, networking, etc. | |
| ▲ | hyperhello 2 hours ago | parent | prev [-] | | Well, there’s actually a very small set of operations that allow all computation, so it doesn’t take much to be a DSL and a GP too; I’d be surprised if a proof language couldn’t swing it. |
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| ▲ | fwip 2 hours ago | parent | prev | next [-] |
| The nice thing about theorem provers is that you don't need to read the intermediate lines. You need to make sure that the goal/result actually matches what you think it says - but everything in the middle is validated by the prover. |
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| ▲ | tossandthrow 2 hours ago | parent | prev [-] |
| No. No human checked it. But a type checker did. And that is much better. |
