7/15/2026 at 1:46:35 AM
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.
by vessenes
7/15/2026 at 3:51:20 AM
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 thatby colin7snyder
7/15/2026 at 11:32:28 AM
Keep it up! This is amazing work.by vessenes
7/15/2026 at 12:23:59 PM
I’ve been working on one problem for three weeks with fable if you want the repoby glitch-hunter
7/15/2026 at 7:18:33 AM
Can you explain what you're using the local compute for vs. the API-based frontier models? That was entirely unclear to me.Are you running tool calls that include inference with local fine tunes? And fast math packages? Controlled by the frontier model agents?
Is there a way folks can contribute to this?
by echelon
7/15/2026 at 10:08:21 AM
Thank you for the questions echelon.1) As far as the AI models go, we used GPT 5.6 Sol, Fable 5, and Gemini-2-embeddings across the system
2) Yes, the agents are given bash tools that allows them to interact with the preinstalled mathematics packages/dependencies that are on the VMs
3) This was a setup as a relatively quick project without much thought for future contributions, I will spend some time thinking about how i could make it more open.
by colin7snyder
7/15/2026 at 2:17:07 PM
This is so great!I hate to bother with more questions, but I'm just so curious about this.
If you could roughly sketch out your agentic harness loop in a sentence or two, what does it look like? Which model(s) do the driving? How is progress measured?
What's your daily/monthly budget for this look like, if you don't mind my asking?
by echelon
7/15/2026 at 5:55:26 AM
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!"by cubefox
7/15/2026 at 6:44:10 AM
Which is a metaphor for life.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.
by bananaflag
7/15/2026 at 8:48:08 AM
There still seems to be a difference between useless pure math research and useless science or useless philosophy. Science, even useless science, still has a subject matter that is relevant to us independently of science, the real world. And philosophy studies concepts (like "knowledge") that occur in natural language and thought, and those concepts are relevant to us independently of philosophy. But pure math is entirely self-referential. Pure math abstractions are used only in pure math. Pure mathematics is relevant exactly to pure mathematics and those who study it.by cubefox
7/15/2026 at 9:43:03 AM
But the thing with "pure" math, is that it can unexpectedly get adulterated by debased concerns such as enabling cryptography for the world economy.by falcor84
7/15/2026 at 3:03:28 PM
I doubt that pure mathematics can claim the success of cryptography. For example, no result from advanced mathematics is required to know that factoring the product of two large prime numbers is slow.by cubefox
7/15/2026 at 6:50:28 PM
The fact that mathematicians cannot devise a method to factor that large product, despite large amounts of money and research time, is what’s valuable!But even then your argument breaks down when you consider more complicated cryptographic structures.
by JambalayaJimbo
7/15/2026 at 10:26:24 AM
"useless" pure math often turns out to have scientific applications.And surely you don't mean all pure math, so your argument ends up being circular --- useless math is useless. You happen to think that this math is useless, but you might be, or turn out to be, wrong.
Also, you're misusing the term "self-referential". You seem to mean that it's a closed system ... but it's not, since mathematicians interact with it.
Finally: so what? We do all sorts of enjoyable activities with no benefit other than the enjoyment. Solving Erdős problems seems at least as justifiable as finding the trillionth digit of pi or writing an Apple ][ emulator in Brainfuck or playing those video games that you demonize by calling them addictive. (Compare to, say, compulsively reading Britannica's The Great Books of the Western World ... it's snooty judgments all the way down.)
Postscript to finally: This framework has wider application ... it's not limited to Erdős problems or anything else that someone happens to consider to be useless.
by jibal
7/16/2026 at 12:00:33 AM
So, bad arguments followed by even worse arguments.> I'll just point out that "so what" is not a counterargument.
It really is.
> Speed runners or chess champions or pi digit calculators don't confuse themselves with noble researchers advancing the frontier of human knowledge.
Yow.
by jibal
7/15/2026 at 1:24:46 PM
> "useless" pure math often turns out to have scientific applications.I don't think that's true for a reasonable interpretation of "often". I'm pretty sure the vast majority of pure math research is and remains useless.
> Also, you're misusing the term "self-referential". You seem to mean that it's a closed system ... but it's not, since mathematicians interact with it.
Then which better term do you propose? The point was that its subject matter lies within itself, which is very different from science and philosophy.
> so your argument ends up being circular --- useless math is useless.
It's not circular: You can replace "pure" with "useless" and the argument stays the same. I contrasted useless math with useless science and useless philosophy for a reason.
> Finally: so what?
I'll just point out that "so what" is not a counterargument. If you agree with my point but find it unimportant: that's fine with me.
> Solving Erdős problems seems at least as justifiable as finding the trillionth digit of pi or writing an Apple ][ emulator in Brainfuck or playing those video games that you demonize by calling them addictive.
The difference between achieving a new record for a video game, and pure math research, is that nobody is confused about what the former is: It's a game, or a sport. Speed runners or chess champions or pi digit calculators don't confuse themselves with noble researchers advancing the frontier of human knowledge.
by cubefox