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)
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 reminds me of certain simple but addictive video games: "What are these virtual coins good for?" "You can get better equipment" "But 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.
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.
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.
> "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.
So whuch 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 you 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 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.
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?
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.
Is this question just for mathematicians in isolation or does it imply the same for most other jobs too? I think the answer for the former is we don't, mathematics would become a hobby the same as we don't hire people to be human calculators anymore because we have machines better st it. For the latter, it depends - some say UBI while the machines do the work, others say dystopia ruled by the machines or their few owners, yet others say anything in between.
Put differently: There is no natural law of the universe of why we pay people to do work. It just works well for us currently. If it stops making sense we do something else that works well for that new currently.
It is for all jobs. We have to be open to new arrangements. I like the recent proposal (https://news.ycombinator.com/item?id=47748123) to tax AI companies that destroy human demand. My point is we have to sort this out now because AI companies are quickly usurping power from labor, and if we wait there will be even more unrest, and worse.
I worked with two philosophy Ph.Ds in corporate strategy years ago. An a chemical engineer, and a nuclear engineer. We were all managing excel documents at the time.
Good example! I think philosophy's purpose is to clarify and systematize unexplored intellectual areas. I imagine philosophers today are already using AI as intellectual sparring partners. I suppose if energy were cheap, we could run AIs all day long to pontificate like humans and write philosophical tracts on the issues of the day. When that happens, we will see if they say anything of merit.
Mathematicians will soon be left only to conjecture, with proofs being automated. The issue I see is that AI will devise proofs that are beyond our comprehension, since humans are already taxing each other (cf. Wiles, Mochizuki, Perelman, etc.) Once humans lose grasp of the proof, how will they propose new conjectures?
In undergraduate math it doesn't matter if someone else did prove a result a hundred years before you.
You still need to write your own proof and deeply understand it.
Maybe in the most advanced PhD math it can have some impact, but these proofs are becoming intractable by humans alone.
I don't envy the talented young research mathematicians. While there's still space to distinguish yourself (inventing completely new mathematics), the path to status is narrower.
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)
When you say "working on" what is your actual contribution? Like, what should I imagine you do? For most people who tell AIs what to do and are proud of it, it's sadly mostly sitting around and staring at "thinking" output, and steering a bit, so I'm curious what the work looks like.
Valid question. If I were further along and had the time to succinctly write up all my contributions, I would just point you at my blog post. I’m generally a poor communicator, so here goes nothing.
I designed and stood up a sovereign inference/compute on my intranet. It uses a trust model that allows for a controller (me) to spin up untrusted inference/forge machines for Lean, Sage, or other runtimes. Untrusted sandbox workers integrate directly into my custom harness as first class “attachments.” This is the “orchestration” layer. It’s mostly on open weights, by design.
I haven’t yet started SFTing since my examples corpus isn’t quite where I’d like it.
I have solved and formalized a one non-Erdos conjecture. I have formalized several pieces of another subfield that does not exist in Mathlib yet.
As for what I am currently working on, I have an idea I want to build out about how we might think about sieving algebraic structures to generating new, insightful conjectures.
Using LLMs and distributed compute here and just a consequence of tools I needed to build to help visualize or materialize things that I am otherwise bad at so I could keep doing the interesting things myself.
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/
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?
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.
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.
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.
As the tools for AI assisted proof become better and mathematicians make it mainstream (could take a while), we're going to be seing some pretty crazy shit. I can't think of a discipline that has more impact on our current toolchains
Thank you for bringing this up pfdietz. No, not defective. The Lean proofs behind both are machine-checked and unchanged. I withdrew them over framing, not correctness.
1) For #129 a couple people pointed out that the report was very confusing. And I agree. So I'm currently attempting to improve it.
2) For #130, a person pointed it out as being a partial solution. This seems correct, so I'm currently working on making it fully end to end.
These are put out as "proposed solutions" for the mathematics community to scrutinize, and the scrutiny worked exactly like it should. Happy to take any feedback and make them better.
I feel like I'm seeing a maths+AI change from "let's test the limits of LLMs by seeing if they can do useful math" to "LLMs can do useful math, now let's solve lots of problems!", or put a different way the goal has shifted from "interesting exercise for AI" to "making a big difference in math". Am I correct?
Are there practical applications of any these problems being solved? No judgement implied, I'm well aware that "no" only means "not yet".
I don't disagree with you zingar. I think Erdős problems are great for testing a system's capability on genuinely hard math, which has value as a benchmark in itself, and maybe as a stepping stone toward more real-world impact. Your sentiment is well put.
To answer your question directly: most Erdős problems don't have practical applications on their own; the value is the techniques and the machine-checked proofs they leave behind. But there's more real world value in solving some of the FrontierMath Open Problems or Millennium Problems. There's a Venn diagram of "hard problems" and "real world impact" for sure.
At some point the effort shifts from proof of concept to exploration of impact. Of course doing proving at large scale provides further feedback for improving the AIs. Visual reasoning, for example, may still need work.
The big impact will be with scaling, for example complete autoformalization of existing math, and automatic exploration for new conjectures, with emphasis on how interesting they are. Automatic conjecture generation goes way way back, to the days of Lenat's AM system. Modern AI should do a far better job.
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[ 0.31 ms ] story [ 14.0 ms ] thread"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)
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.
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?
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 that.
If you could roughly sketch out your agentic harness loop, 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?
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.
But also: so what? We do all sorts of enjoyable activities with no benefit other than the enjoyment.
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.
So whuch 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 you 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 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.
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.
Put differently: There is no natural law of the universe of why we pay people to do work. It just works well for us currently. If it stops making sense we do something else that works well for that new currently.
An automatic proof solver doesn't make mathematicians obsolete any more than the excel sheet made accountants obsolete.
Mathematicians will soon be left only to conjecture, with proofs being automated. The issue I see is that AI will devise proofs that are beyond our comprehension, since humans are already taxing each other (cf. Wiles, Mochizuki, Perelman, etc.) Once humans lose grasp of the proof, how will they propose new conjectures?
I still like doing maths by pen and paper, but this is fun too.
I designed and stood up a sovereign inference/compute on my intranet. It uses a trust model that allows for a controller (me) to spin up untrusted inference/forge machines for Lean, Sage, or other runtimes. Untrusted sandbox workers integrate directly into my custom harness as first class “attachments.” This is the “orchestration” layer. It’s mostly on open weights, by design.
I haven’t yet started SFTing since my examples corpus isn’t quite where I’d like it.
I have solved and formalized a one non-Erdos conjecture. I have formalized several pieces of another subfield that does not exist in Mathlib yet.
As for what I am currently working on, I have an idea I want to build out about how we might think about sieving algebraic structures to generating new, insightful conjectures.
Using LLMs and distributed compute here and just a consequence of tools I needed to build to help visualize or materialize things that I am otherwise bad at so I could keep doing the interesting things myself.
> contributions
One thing I think you and the other "AI math builders" have done, is to show how good the top models are at logics and reasoning.
I didn't realize how good they are, until they solved an Erdös problem. And now lots of Erdös problems!
(Plus verified that the AIs actually did solve the problems, that's not easy :- ))
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/
Unfortunately P vs NP, on the other hand, is going to have to wait for GPT 7
GPT-5.6 is a closed source model and this seems to be a personal project and not something done by OpenAI.
We ran it through our multi-agent coding evaluations at https://gertlabs.com/rankings
1) For #129 a couple people pointed out that the report was very confusing. And I agree. So I'm currently attempting to improve it.
2) For #130, a person pointed it out as being a partial solution. This seems correct, so I'm currently working on making it fully end to end.
These are put out as "proposed solutions" for the mathematics community to scrutinize, and the scrutiny worked exactly like it should. Happy to take any feedback and make them better.
Are there practical applications of any these problems being solved? No judgement implied, I'm well aware that "no" only means "not yet".
To answer your question directly: most Erdős problems don't have practical applications on their own; the value is the techniques and the machine-checked proofs they leave behind. But there's more real world value in solving some of the FrontierMath Open Problems or Millennium Problems. There's a Venn diagram of "hard problems" and "real world impact" for sure.
The big impact will be with scaling, for example complete autoformalization of existing math, and automatic exploration for new conjectures, with emphasis on how interesting they are. Automatic conjecture generation goes way way back, to the days of Lenat's AM system. Modern AI should do a far better job.