To clear up a few misconceptions:

- Aristotle uses modern AI techniques heavily, including language modeling.

- Aristotle can be guided by an informal (English) proof. If the proof is correct, Aristotle has a good chance at translating it into Lean (which is a strong vote of confidence that your English proof is solid). I believe that's what happened here.

- Once a proof is formalized into Lean (assuming you have formalized the statement correctly), there is no doubt that the proof is correct. This is the core of our approach: you can do a lot of (AI-driven) search, and once you find the answer you are certain it's correct no matter how complex the solution is.

Happy to answer any questions!

I don’t think it can really be said to have occurred autonomously then?

Looks more like a 50/50 partnership with a super expert human one the one side which makes this way more vague in my opinion - and in line with my own AI tests, ie. they are pretty stupid even OPUS 4.5 or whatever unless you're already an expert and is doing boilerplate.

EDIT: I can see the title has been fixed now from solved to "more or less solved" which is still think is a big stretch.

Or someone like Terence Tao might figure out how to wield AI better than anyone else, even the labs, and use the tools to take a bunch down at once. I'm excited to see what's coming this year.

Are you getting the same value in your work, in your field?

EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle (https://arxiv.org/abs/2510.01346) is key here folks.

EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM (vision transformers, anyone) and if you aren't training on language (e.g. AlphaFold, or Aristotle on LEAN stuff), it isn't a "language" model.

> ... to me, the more interesting capability revealed by these events is the ability to rapidly write and rewrite new versions of a text as needed, even if one was not the original author of the argument.

> This is sharp contrast to existing practice where the effort required to produce even one readable manuscript is quite time-consuming, and subsequent revisions (in response to referee reports, for instance) are largely confined to local changes (e.g., modifying the proof of a single lemma), with large-scale reworking of the paper often avoided due both to the work required and the large possibility of introducing new errors. However, the combination of reasonably competent AI text generation and modification capabilities, paired with the ability of formal proof assistants to verify the informal arguments thus generated, allows for a much more dynamic and high-multiplicity conception of what a writeup of an argument is, with the ability for individual participants to rapidly create tailored expositions of the argument at whatever level of rigor and precision is desired.

Of course this implies that the math works which is the Aristotle part, and that's great ... but this rebuts the "but this isn't AI by itself, this is AI and a bunch of experts working hard, nothing to see here": right, well even "experts working hard" fail to iterate on the paper which significantly hinders research progress.

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!!

Though I suppose if the problem statement in Lean is human-generated and there are no ways to "cheat" in a Lean proof, the proof could be trusted without understanding it

People are still going to be moving the goalposts on this and claiming it's not all that impressive or that the solution must have been in the training data or something, but at this point that's kind of dubiously close to arguing that Terence Tao doesn't know what he's talking about, which to say the least is a rather perilous position.

At this point, I think I'm making a belated New Years resolution to stop arguing with people who are still staying that LLMs are stochastic parrots that just remix their training data and can never come up with anything novel. I think that discussion is now dead. There are lots of fascinating issues to work out with how we can best apply LLMs to interesting problems (or get them to write good code), but to even start solving those issues you have to at least accept that they are at least somewhat capable of doing novel things.

In 2023 I would have bet hard against us getting to this point ("there's no way chatbots can actually reason their way through novel math!"), but here we are are three years later. I wonder what comes next?

Edit: Found it here https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/Er...

The METR institute predicts that the length of tasks AI agents can complete doubles every 7 months.

We should expect it to take until 2033 before AI solves Clay Institute-level problems with 50% reliability.

https://github.com/teorth/erdosproblems/wiki/AI-contribution...

It classifies the advancements based on the level of AI input. In particular, the entry in Table 1 related to the original post has both a green and yellow light, reflecting the skepticism from others.

Meanwhile I can’t get Claude code to fix its own shit to save my life.