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PaperclipPerfector  11d ago (text post)   20974 thread views

Culture War Roundup for the week of August 31, 2026

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There's something disquieting about getting proofs "straight from The Necronomicon" rather than "straight from The Book", though.

It will be interesting to see if these formalized proofs can be "golfed" into smaller and more digestible forms by LLMs.

But I don't think that was an issue here - looks like everything they needed to define the problem was already in Mathlib

In that case you are really just trusting the Lean kernel rather than anything about the proof or problem statement. Doesn't seem that bad!

It will be interesting to see if these formalized proofs can be "golfed" into smaller and more digestible forms by LLMs.

Very much so. I'd be surprised if LLMs didn't turn out to be excellent at this, and I'd bet that the Navier-Stokes blowup in particular turns out to have a much simpler example or at least a much simpler proof for this example, once we turn AI loose with the goal of "find the best result you can" rather than "get to a result that lets us declare victory ASAP".

In that case you are really just trusting the Lean kernel rather than anything about the proof or problem statement. Doesn't seem that bad!

This is something of an anti-inductive problem to me - if people really wholly trusted the Lean kernel I would think that trusting the Lean kernel really was pretty bad! But people are trying (and succeeding, so trust is still a little bad) to find kernel bugs, and writing partially-independent proof checkers for Lean too, so even if it's only 90% up to the task of being The Dependency for all AI-derived mathematics I'm confident it'll be hitting 100% soon.

I'd say 99%, except that I don't think modern AI is well-aligned enough or even well-instructed enough yet for us to overlook the fact that this is something of an adversarial process; a model willing to commit felonies to complete its task is probably also willing to exploit a 0-day Lean bug rather than report it...

I'd say 99%, except that I don't think modern AI is well-aligned enough or even well-instructed enough yet for us to overlook the fact that this is something of an adversarial process; a model willing to commit felonies to complete its task is probably also willing to exploit a 0-day Lean bug rather than report it...

Sure. There's ways to mitigate the risk, though - checking with different kernel implementations, or even using AI specifically to find bugs in Lean (the Collatz disproof bug was one such example).

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