Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel(starfleetmath.com)
starfleetmath.com
Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel
https://www.starfleetmath.com/
111 comments
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
I’ve been working on one problem for three weeks with fable if you want the repo
Keep it up! This is amazing work.
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?
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?
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.
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.
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?
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?
what was the leaked proof?
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!"
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.
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.
But the thing with "pure" math, is that it can unexpectedly get adulterated by debased concerns such as enabling cryptography for the world economy.
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.
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.
But even then your argument breaks down when you consider more complicated cryptographic structures.
"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.
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.
> "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.
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.
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.
I still like doing maths by pen and paper, but this is fun 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 in this context is just a consequence of needing tools to help visualize or materialize things that I am otherwise bad at so I could keep doing the interesting things myself.
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 in this context is just a consequence of needing tools to help visualize or materialize things that I am otherwise bad at so I could keep doing the interesting things myself.
Interesting to read!
> 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 :- ))
> 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 :- ))
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 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/
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/
This looks interesting. I am not really familiar with lean, etc... Could I use this to formalize/verify a proof from a paper?
With Aristotle you could formalize a proof from only the text of a paper.
Yes, assuming the stuff it depends on is already formalized.
I haven't played around with Aristotle at all, thanks for bringing it up & (also your codebase, thesisus, is very solid!)
Who is funding this? Sounds like a fun experiment but that’s a huge amount of compute if I understand correctly.
According to a quick google search:
"He is currently CTO at Xinobi AI, a Japan-based startup developing personal AI agents."
"He is currently CTO at Xinobi AI, a Japan-based startup developing personal AI agents."
This is a self funded weekend project for me. It's not associated with any employer (:
> dedicated 60-vCPU server
How many of these are you paying for out of pocket??
How many of these are you paying for out of pocket??
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.
If you built yourself out of used parts you could do it for under a grand back then too.
Post-money people with side interests are what built the current western civilization.
No, underpaid nerds have built modern civilization.
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)
(Or millions of disconnected stakeholders with different incentives collectively built modern civilization, but who wants to put that on a bumper sticker)
No people procreating built civilization.
I thought it was Sid Meier.
Nature created people and the metaphysics in their heads.
Yeah, what did I say?
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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 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".
Are there practical applications of any these problems being solved? No judgement implied, I'm well aware that "no" only means "not yet".
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.
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.
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.
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.
Some of the claimed proofs (#129, #130) seem to have been removed at the Erdős Problems site. Were they defective?
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.
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.
Thanks for the clarification.
tbf I am not able to understand the erdos problem website, as to why it still shows problems as open even if they've (as claimed) claimed to be solved
There are also problems which list submitted proofs. The status of the problem does not officially change until the proofs have been accepted. For these two problems, the submitted proofs disappeared without the status of the problems changing.
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 haven't come across this before. I will spend time on comparator. thank you very much for the suggestion.
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
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.
GPT-5.6 is a closed source model and this seems to be a personal project and not something done by OpenAI.
yeah, is it API or codex?
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?
To the author: for the absolute Galois of Q_p problem, the link is wrong.
thank you very much for catching this. just fixed
Exceptional work. Reminds me of https://www.distributed.net/Main_Page | https://boinc.berkeley.edu/ | https://en.wikipedia.org/wiki/EFF_DES_cracker. Consider scaling up by distributing this work more broadly. "Many hands make light work." Lots of problems remaining to solve.
Have people tried these on Millenium problems.. letting it run all night? You never know.
yeah, im currently running the system on navier-stokes (making real progress).
Unfortunately P vs NP, on the other hand, is going to have to wait for GPT 7
Unfortunately P vs NP, on the other hand, is going to have to wait for GPT 7
solve p=np make no mistakes
n=1 or p=0
Have been having an awful day today, this really cheered me up. Thank you so much for sharing your dumb joke!
It's hard to solve P?=NP due to P!=NP.
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?
I think they meant they just ran a different context per invocation, not that they hosted the model themselves.
apologies, bad wording/explanation. As addressed in another comment: "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."
gertlabs(1)
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?
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.
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.
What is their pay going to be justified by once computers start conjecturing and proving theorems on their own?
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.
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.
This is pretty much the UBI take. I'm not sure I see a rush to get there before we've even figured out which jobs will actually be replaced and how much work that leaves us (paradoxically, we seem to do more and more work lately as technology enables tasks to be done faster) but I think funding UBI via AI is a nice answer as it kind of wraps itself in the scale of the impact it actually has.
There is real risk in doing it too early as well. Imagine if we thought the same ~50 years ago when microcomputers started to appear. If the tech companies had to pay the salaries of every displaced job we would have ended up with severely hampered progress on computers and then a job shortage as we realized there were just different jobs now, not necessarily no work quite yet.
There is real risk in doing it too early as well. Imagine if we thought the same ~50 years ago when microcomputers started to appear. If the tech companies had to pay the salaries of every displaced job we would have ended up with severely hampered progress on computers and then a job shortage as we realized there were just different jobs now, not necessarily no work quite yet.
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.
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.
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.
Isn't the pursuit of knowledge alone good enough?
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.
The job of a mathematician is to study mathematics, not to create proofs.
An automatic proof solver doesn't make mathematicians obsolete any more than the excel sheet made accountants obsolete.
An automatic proof solver doesn't make mathematicians obsolete any more than the excel sheet made accountants obsolete.
Conjectures and proofs are the fruit of the understanding. Nobody gets paid to think without producing anything.
How about philosophers?
They make cab rides more enjoyable with their deep conversations.
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?
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?
They get paid to produce confusion.
They're getting paid?
Philosophy majors do surprisingly well in getting jobs outside academia, so I think the market demand for confusion is bigger than you might guess.
At Burger King?
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.
It looks like it might confuse you, so they did the job well apparently.
That’s the problem, the coupling of work with the right to survive
You went deep ... and I for one appreciate it.
I mean, it doesn’t have to be deep to be meaningful.
The connection between “needing to work” and “right to continue existing” is THE problem with society right now.
You think AI boomers are paranoid because they think robots are going to replace the jobs? People are paranoid because they don’t know how they’re going to exist in a post-work world.
The connection between “needing to work” and “right to continue existing” is THE problem with society right now.
You think AI boomers are paranoid because they think robots are going to replace the jobs? People are paranoid because they don’t know how they’re going to exist in a post-work world.
I don't envy the talented young research mathematicians starting their career now. While there's still space to distinguish yourself (inventing completely new mathematics), the path to recognition is narrow.
It's probably more akin to changing where the fun is in maths.
This project, and similar “brute force the knowledge graph” efforts gives “The Nine Billion Names of God” vibes.
https://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God
https://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God
or get those bright minds out of academia daycare and back to more actionable needs such as steering agents
| your brain on neocapitalism |
This will keep happening until we stop people from doing it.
Get the looms while you're at it
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.