Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel

Very interesting, on many levels: first, the raw additional compute / search harness is worth reading about; huge numbers of Lean 4 theorems, thousands of vCPUs available for spreading out search, embedding databases of proofs, all very interesting.

Second, the proofs -- I understand the Lean 4 proofs to be refereed by Fable, and generated by Chat 5.6 Sol. Unlike the leaked proof of the Cycle Double Cover Conjecture last week which had a very nicely readable nearly humanlike writeup, the proof summaries (from Fable) read like Claude tends to read to me these days - real difficulty with the theory of mind of the reader, they are filled with technical phrases, acknowledgment of hard bits and oblique reference to solutions. In short, they suck. I didn't see the word load-bearing, but I bet it's there.

That said, a Lean 4 proof is a pretty compelling output artifact. I find it interesting that it's an additional type of effort to turn these into human readable / appreciable / beautiful / non-shitty proofs.

To those who say who cares -- indeed. But. One of the major reasons things like the Erdos problems are valuable is that they can at times spur new techniques and concepts. The best of these concepts are applied elsewhere, advancing the frontier. While we gain a lot from solving these problems, we'll gain even more from that next step of distillation / explanation into something humans and computers can grok together. I'd hope that with so many tentatively marked 'solved' we will see some new techniques / ontology / concepts. If not, still pretty amazing.

My mouth is agape at the fact that this project is basically what I have been working on non-stop for the last three weeks and just yesterday gotten to the point of evaluating; hats off... I only have one novel proof (non-Erdos) and 13 first-time formalizations thus far.

I still like doing maths by pen and paper, but this is fun too.

Very cool! It seems you've got a great setup. An addition that would be very convincing is going the extra mile and making a comparator setup for your Lean proofs. (https://github.com/leanprover/comparator) This ensures that the AI is not, in any way, modifiying the Lean context in ways that could lead to unsoundness.

I was studying Erdos problems by only taking ChatGPT 5.5 outputs and just asking it to keep on attempting to solve it by asking it to go further. I haven't started doing this with chatgpt 5.6 I have some partial results here https://chatgpt.com/g/g-p-69f03400f420819192418b18ca90ffee-d...

What was really interesting is that during the process it was able to find lemmas or theorems that might be related or relevant to be published.

While I was doing that I was also trying to use Aristotle to do the Lean formalization and I have a WIP system to do that at https://github.com/aconsapart/thesisus/

Who is funding this? Sounds like a fun experiment but that’s a huge amount of compute if I understand correctly.

GPT 5.6 is an incredible model. It's comfortably more intelligent than Fable, which is also an incredible model, and it's much much cheaper in practice. It's hard to deny we're past a reasonable definition of AGI.

We ran it through our multi-agent coding evaluations at https://gertlabs.com/rankings

What kind of harness does the exploration? Where did the corpus of Lean proofs come from? Is the code backing Ton 618 open source?

I'm not sure how to interpret this part: "each running its own GPT-5.6 instance".

GPT-5.6 is a closed source model and this seems to be a personal project and not something done by OpenAI.

I've been wanting to experiment with using AI to prove math theorems, but compute is obviously a massive limiting factor here. Are there any plans to open source this?

Have people tried these on Millenium problems.. letting it run all night? You never know.

I didn't know people could just have GPT running on their own hardware. How does one...do that? Do you have a special relationship with OpenAI and they lock down your servers or something?

surely it's not copy pasting answers from some obscure polish forum right bros

Isn't this sucking the fun out of math? It's not like we're going to get any tangible benefit out of them, so why not let mathematicians keep their jobs?