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.
This is great feedback (thank you for taking the time), & you especially bring up a fair point on the writeups needing to be more human readable. I'll work on that
This reminds me of certain simple but addictive video games: "What are these virtual coins good for?" "You can buy better equipment" "Why do you need this equipment?" "To get more virtual coins of course!"
I also had this sort of thoughts when finishing my master's degree. I guess what breaks the cycle is that proofs (like other artefacts in other human activities) deliver aesthetic bliss.
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.
Thank you for the kind words! I agree, it's exciting that we can now build advanced AI systems for solving novel math (but i still love pen & paper too)
I own a dedicated 48vCPU with even 160GB RAM.. its not that expensive, check ebay, maybe now with mem prices it will be a bit more steep but as a hobby it's not crazy to think one owns such a piece of hardware.
My dual GPU setup was more expensive I think.
When I looked into this a year ago, it was like €60/mo through Hetzner auction. Might be more now but even if it's double or triple it's not that crazy for a hobby.
If you built yourself out of used parts you could do it for under a grand back then too.
No, the people growing their food built modern civilization.
(Or millions of disconnected stakeholders with different incentives collectively built modern civilization, but who wants to put that on a bumper sticker)
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/
Poor wording on my end, thanks for flagging. I pull the OAuth refresh token from each Codex account into a custom broker, which mints short-lived access tokens per request and load-balances across the pool.
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?
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?
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?
The thing about math is we don't usually know what is pure fancy and what is civilization altering until far after the discovery. Once in a while it's a real targeted crack at something practical but most often it's collecting things which seem trial until you use them together and suddenly you have computers running LLMs.
If it were really just about funding people who like math to have fun then it's easy to do forever: just don't have them look at the results and keep paying.
Mathematicians will be the ones who can tell us if the computer theorems are decent or not.
Otherwise they’ll be the ones like Erdős who pose the questions in the first place.
Either way it will always be humans who decide what matters. AI is speaking our languages, not the other way around. We’re in charge. It’s impossible for us not to be, unless we can train an AI from dolphin data or other natural phenomenon.
The AIs intelligence is tuned to us and in 300 years we’ll need new training runs for the update from human zeitgeist language and the 2200 century famous mathematicians.
> Either way it will always be humans who decide what matters. AI is speaking our languages, not the other way around. We’re in charge. It’s impossible for us not to be, unless we can train an AI from dolphin data or other natural phenomenon.
AI companies are accruing power by virtue of its knowledge and ability to do work. If endowed with agency, which seems likely at this rate, it is the AI itself that will be powerful. And we'll be in charge because AI is trained on human language? I can't fathom the logic behind this.
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 also had this sort of thoughts when finishing my master's degree. I guess what breaks the cycle is that proofs (like other artefacts in other human activities) deliver aesthetic bliss.
I still like doing maths by pen and paper, but this is fun too.
"He is currently CTO at Xinobi AI, a Japan-based startup developing personal AI agents."
How many of these are you paying for out of pocket??
If you built yourself out of used parts you could do it for under a grand back then too.
(Or millions of disconnected stakeholders with different incentives collectively built modern civilization, but who wants to put that on a bumper sticker)
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/
GPT-5.6 is a closed source model and this seems to be a personal project and not something done by OpenAI.
Unfortunately P vs NP, on the other hand, is going to have to wait for GPT 7
If it were really just about funding people who like math to have fun then it's easy to do forever: just don't have them look at the results and keep paying.
Otherwise they’ll be the ones like Erdős who pose the questions in the first place.
Either way it will always be humans who decide what matters. AI is speaking our languages, not the other way around. We’re in charge. It’s impossible for us not to be, unless we can train an AI from dolphin data or other natural phenomenon.
The AIs intelligence is tuned to us and in 300 years we’ll need new training runs for the update from human zeitgeist language and the 2200 century famous mathematicians.
AI companies are accruing power by virtue of its knowledge and ability to do work. If endowed with agency, which seems likely at this rate, it is the AI itself that will be powerful. And we'll be in charge because AI is trained on human language? I can't fathom the logic behind this.
An automatic proof solver doesn't make mathematicians obsolete any more than the excel sheet made accountants obsolete.