infruset

> "Georges Gonthier, a computer scientist at Inria in Paris"

somehow the article forgets to mention he was the guy who came up with the first Coq (now Rocq) formal proof of the Four Color Theorem..

So as for math of that level, (the best) humans are still kings by far. But things are moving quickly and there is very exciting human-machine collaboration, one need only look at recent interviews of Terence Tao!

I can't disclose that, but what I can say is no one at my company writes Lean yet. I'm basically experimenting with formalizing in Lean stuff I normally do in other languages, and getting results exciting enough I hope to trigger adoption internally. But this is bigger than any single company!

I was waiting for a post like this to hit the front page of Hacker News any day. Ever since Opus 4.5 and GPT 5.2 came out (mere weeks ago), I've been writing tens of thousands of lines of Lean 4 in a software engineering job and I feel like we are on the eve of a revolution. What used to take me 6 months of work when I was doing my PhD in Coq (now Rocq), now takes from a few hours to a few days. Whole programming languages can get formalized executable semantics in little time. Lean 4 already has a gigantic amount of libraries for math but also for computer science; I expect open source projects to sprout with formalizations of every language, protocol, standard, algorithm you can think of.

Even if you have never written formal proofs but are intrigued by them, try asking a coding agent to do some basic verification. You will not regret it.

Formal proof is not just about proving stuff, it's also about disproving stuff, by finding counterexamples. Once you have stated your property, you can let quickcheck/plausible attack it, possibly helped by a suitable generator which does not have to be random: it can be steered by an LLM as well.

Even further, I'm toying with the idea of including LLMs inside the formalization itself. There is an old and rich idea in the domain of formal proof, that of certificates: rather than proving that the algorithm that produces a result is correct, just compute a checkable certificate with untrusted code and verify it is correct. Checkable certificates can be produced by unverified programs, humans, and now LLMs. Properties, invariants, can all be "guessed" without harm by an LLM and would still have to pass a checker. We have truly entered an age of oracles. It's not halting-problem-oracle territory of course, but it sometimes feels pretty close for practical purposes. LLMs are already better at math than most of us and certainly than me, and so any problem I could plausibly solve on my own, they will do faster without my having to wonder if there is a subtle bug in the proof. I still need to look at the definitions and statements, of course, but my role has changed from finding to checking. Exploring the space of possible solutions is now mostly done better and faster by LLMs. And you can run as many in parallel as you can keep up with, in attention and in time (and money).

If anyone else is as excited about all this as I am, feel free to reach out in comments, I'd love to hear about people's projects !

Does anyone have a clue how far we are from having "LLMs for animals"? Even if we don't understand what the LLM is saying to a dolphin or a monkey, does it change much from feeding millions of texts to a model without ever explaining language to it as a prerequisite?

Very nice ! How might one go about adapting this to other languages ? Does a version of the model downloaded exist somewhere ?

I think they are the conference and journal versions of the same paper. Hadn't seen it was mentioned in the article, I should have read it more thoroughly!

Can it be pointed to a remote ollama server ?