markusde

"Complex topics" in this case means reading 22 AI-generated paragraphs that supposedly cover the entire chip manufacturing process. If the author seriously thinks this level of detail is complex then they have psychosis.

Thanks! Typeclasses are also something I really like about Lean.

I'm curious what you like about Agda functional programming? Many of the praises I hear about it have to do with it's dependent pattern matching, and I think Lean suffers a lot more in that regard. I'm curious though if you still find Agda friendlier for "normal" fp (and if so, how?)

You should check out the recent PR's to the Agda repo... the community is currently very divided about AI. For better or worse, the people driving the Lean project have been interested in AI for quite some time.

Also a very good question btw, people do both. For some projects Lean is expressive and performant enough to use on its own (or call into using the reverse FFI), other projects use a model of a real programming language like Rust. The disadvantage of the latter is that the Lean model of Rust has to be trusted.

It's almost like context matters

Yeah, but the problem is that programming languages and compilers change all the time, making it hard to maintain a formal model of them. Exceptions exist (CompCert C and WebAssembly are two good examples) but for example, the semantics of raw pointers in Rust are intentionally under-defined because the compiler writers want to keep changing it.

As is "even if it was in my area of specialty". I would not be able to do this proof, I can tell you that much.

> it's really not clear to me that humans would be a valuable component in knowledge work for much longer.

To me, this sounds like when we first went to the moon, and people were sure we'd be on Mars be the end of the 80's.

> Even ARC-AGI-2 is now at over 50%.

Any measure of "are we close to AGI" is as scientifically meaningful as "are we close to a warp drive" because all anyone has to go on at this point is pure speculation. In my opinion, we should all strive to be better scientists and think more carefully about what an observation is supposed to mean before we tout it as evidence. Despite the name, there is no evidence that ARC-AGI tests for AGI.

Yes, the contributions of the people promoting the AI should be considered, as well as the people who designed the Lean libraries used in-the-loop while the AI was writing the solution. Any talk of "AGI" is, as always, ridiculous.

But speaking as a specialist in theorem proving, this result is pretty impressive! It would have likely taken me a lot longer to formalize this result even if it was in my area of specialty.

Very cool to see how far things have come with this technology!

Please remember that this is a theorem about integers that is subject to a fairly elementary proof that is well-supported by the existing Mathlib infrastructure. It seems that the AI relies on the symbolic proof checker, and the proofs that it is checking don't use very complex definitions in this result. In my experience, proofs like this which are one step removed from existing infra are much much more likely to work.

Again though, this is really insanely cool!!

Exactly right. You can pick and use real numbers, as long as they are only queried to finite precision. There are lots of super cool algorithms for doing this!