> As part of our GitHub repository, we are sharing formalizations of many of the proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. We will update the repository with more formalizations as we obtain them.
Meaning they published all results before checking all of them, and intended to add more Lean proofs later. In the linked post they state ~42% of the posted results now have formalized proofs, some were added, some verified, and I assume this means that some results turned out to be wrong.
This is extremely disappointing. It means they are sharing unproven work for PR, forcing the mathematicians community to do the verification job for them, while so-called "accelerationists" surf on the hype and help with the pro-AI propaganda.
If your AI tool can help advance mathematical research, share the tool with mathematicians. Using it like this is irresponsible.
"AI will kill us all": no. Greedy humans will kill us all. With AI.
Every option is going to lead to someone shitting on OpenAI for what seems to be a pretty huge accomplishment. There have been opinions written by some mathematicians that OpenAI should just share the work that they have now so that people who are working on any solved problems can know. Which seems reasonable to me.
It’s a funny one. I’m not sure what a Lean-less LLM proof even is. LLMs are amazing at bullshitting and skipping key steps and details. I’d imagine a LLM non Lean proof to be generally hard to evaluate - harder than that of a human mathematician perhaps. And the scale effect is against OAI here - the firehose just keeps squeezing out proofs.
I don't think that's true. If what you're doing is building a fuzzer for mathematical proofs then just say that? The fact that it's doing some of the initial work on hard problems is cool. So is the fact that the promise of that new approach is having a social effect of crowd sourcing talented people to follow up on that work. No need to try to misrepresent it as more than that.
This technology has surpassed the the world's best mathematicians at the (explicitly and openly stated) goal by which they measure and reward mathematical progress. Such an advancement that it seems to have thrown the entire field into existential self-doubt. And then someone sits at their keyboard and says it is just a fuzzer.
Lean itself is very hard to get rigorously correct, if you have every tried it yourself. I am not surprised if some AI even tries to benchmaxx Lean 4 by some loopholes
They are not publishing Lean proofs. They are publishing proofs in natural language, and are not submitting to journals.
They are just putting out a bunch of weirdly written extremely long and technical papers and saying: Hey, here is the solution (we hope there are no mistakes).
But that exactly how human mathematicians do things. They upload their research to preprint services like arXiv as they await it to be peer reviewed and accepted into a journal. Why is it okay for mathematicians to publish preprint papers, but when OpenAI does it, it's irresponsible?
The difference is that human mathematicians wouldn't post it online, claim they have achieved some proof, and then check after publication and announcing the results to the world. You would always check your work first, then publish it. It's not about preprint vs peer-reviewed. That of course is normal practice, it's the high-profile claims that are being made that are the problem here. They just blindly published results produced by the LLM, with 0 due diligence.
Yes they would, in many fields it is (was?) normal to post a preprint and leave it up for the next year while the handful of other people working on the topic digest it and agree on whether it’s right or not, before even submitting to a journal. Sometimes the others would find an isssue in an argument and you hopefully manage to fix it or potentially retract / not submit to a journal.
You may want to read beyond the first part of a sentence. Yes, preprints have always been a thing. The claims and publicity around the potential findings are handled differently here. That's where the issue is.
What would’ve made you not complain about OpenAI’s papers?
They had over a hundred papers, they basically did a GitHub dump and a pretty bare blog post that mentions they have a retraction policy. Should they have done it anonymously? Is the blog post the problem? Is it that it’s on GitHub? Or what?
They should have posted the ones they actually confirmed. They don't have any time pressure to release hundreds of new proofs, they could do 10 a week for all I care, as long as they make sure everything is actually sound and properly checked. You know, do the due diligence with the results. Not only would that prevent them from having to do retractions, it also wouldn't be any less impressive. Just not as much shock marketing value.
It's really not that hard to understand. My issue is NOT with the fact that they publish results. It's purely about how it's done and what the misleading claims are that come along with them.
This goes back to the pre-print question then, which you just dismissed
> in many fields it is (was?) normal to post a preprint and leave it up for the next year while the handful of other people working on the topic digest it and agree on whether it’s right or not, before even submitting to a journal. Sometimes the others would find an isssue in an argument and you hopefully manage to fix it or potentially retract / not submit to a journal.
A pre-print has a chance to be incorrect. Pre-prints do sometimes end up incorrect and need adjustments or even retraction. It sounds like you define "confirming it before you publish" as being 100% certain it's correct. Nobody is 100% sure their pre-print is correct. If it was 100% correct and never retracted there'd be no need for this process of sharing and digesting it before actually submitting. You do your best and maybe someone else thinks about it in a new light you missed and it's suddenly wrong.
Is the rate of retraction and/or correction going to be worse for OpenAI than it would be in normal circumstances for a normal human author? Only time will tell, it's only been a few days.
But all these complaints really just look like pulling at whatever straw to deny what's happening.
They could've instead hired a select group of mathematicians to spend then next 6 months checking these works, trying to understand and refine them, build on them etc... You and the others here would have 100% complained. Even more bitterly. And then you would've perhaps been right: it would have looked like there's a select in-group of mathematicians that get to see and work on the new breakthroughs while the rest of the field is kept in the dark. Instead of now where it's public, anyone can do that. Maybe that's what will happen in the next release. It's not gonna be good though.
ok, that said there has alaways been a bunch of "maybe theorems" it's was a thing even in paul erdos books i think. now we have "maybe proofs". still better than "no proofs"
See DDOS. That's exactly how humans access a web page. Why is it okay for humans to access a webpage, but when a bot swarm does it, it's irresponsible?
That's an analogy among many others, but the point is that OpenAI should use their tools responsibly. If they have 700 potential ground-breaking but unproven results, they should share it in a way that they do not get free (possibly unwarranted) publicity for it.
The "irresponsible" part is about how orange buffoons in power will read this, and immediately defund all universities, and mathematicians will lose their jobs, leaving us with nothing but an AI tool that no one can keep in check anymore.
No, it's the exact opposite, actually. They were sharing them early on advice of mathematicians -- they were criticized for being opaque for too long with previous announcements. OpenAI is in ~bad faith, but this isn't a sound criticism.
Also you are deeply confused about what accelerationism is, I believe. Sorry.
Whom? Did they create their own board of mathematicians that would agree with them? See below Terence Tao's blog, sharing a statement from the Association for Human Mathematics.
> Mathematicians have a particular vision of progress that is informed by history and field-specific considerations.
really sounds like something a side-quest association would produce in a panic response to someone trying something different. It's just an _ad hominem_ and gatekeeping argument.
Sorry, I was unclear: they do indeed have their own board of mathematicians, but I was more getting at their stated reasoning matching with general mathematical sentiment (AFAICT), not permission from a particular group. The problem that that open letter is raising is the practice of setting an internal model on these kinds of problems in the first place, not the decision to release them earlier.
Also jeez just noticed their name... that's unfortunate. I guess mathematicians don't make great rhetoricians/politicians/marketers! Someone get a sophist or two over there to help them out STAT
AI is an incredible tool, and yes I am disappointed that every leader in this field is acting unethically and irresponsibly because they want to "win" a race that would make them slightly richer than the loser.
It were published proofs of unknown quality (how did they verify it) and unknown peer-review process. Its lower standards than usually accepted for math proofs.
> As part of our GitHub repository, we are sharing formalizations of many of the proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. We will update the repository with more formalizations as we obtain them.
Meaning they published all results before checking all of them, and intended to add more Lean proofs later. In the linked post they state ~42% of the posted results now have formalized proofs, some were added, some verified, and I assume this means that some results turned out to be wrong.