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.

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

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/

Are there practical applications of any these problems being solved? No judgement implied, I'm well aware that "no" only means "not yet".

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