It's kinda funny to realize that Lean is apparently so slow that for Fermat's Last Theorem proof verification runs only 1 order of magnitude faster than agents could generate the Lean code (15h verification with 230GB of RAM vs 11 days to generate it).
To what extent can you optimize Lean? It has to be simple enough to be auditable, does that mean you cannot use opaque optimizations to make it run faster?
It's because anthropic vibemathed it. I forgot the name but some other guy is working on a handwritten version of it and I bet it'll be more than just 1 magnitude faster.
What would be the point of that though? I think the reason Kevin wants to optimize it is for the understanding that will result from the process, not because anyone cares about having a Lean proof that compiles quickly...
Weren't the agents massively parallel, whereas the lean verifier presumably is not? Also, I presume said agents were themselves running the verifier on their own parts many times.
Sure, but to clarify the article is describing formalization (writing a correct program), not verification (compiling said program). The author is not making the same comparison.
Verification is also open ended (not sure about lean specifically) - you could in theory give just the Navier-Stokes problem definition to an ATP and let it run.
But what hardware was the verification vs agents on? Because you are likely comparing verification on a single beefy machine (say XX TFLOPS total) to agents running on a substantial inference cluster (say XXXX TFLOPS). So you're 1 order of magnitude might actually be 2-4 orders of magnitude.
Yeah, in essence. This is actually a pretty cool part of working in Lean. It's a somewhat normal convention to write something in a human readable way and then write a second optimized implementation with some kindness of correctness theorem connecting them. There was a whole open "competition" for writing a faster Lean kernel/proof checker that didn't sacrifice on soundness called Lean Kernel Arena. Fun reference point: https://kim-em.github.io/blog/2026-7-24-why-lean-is-faster-t...
There's a project called lean4lean that implements lean in lean. I guess ideally, if you had a kernel optimisation idea you could do a copy of the Lean model lean4lean has created, add the optimisation, then prove your new lean is equivalent in terms of what it can prove to the old lean
To what extent can you optimize Lean? It has to be simple enough to be auditable, does that mean you cannot use opaque optimizations to make it run faster?