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How An AI math breakthrough ignited a controversy

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Re: How An AI math breakthrough ignited a controversy

#71

Post by aenis »

lemoncookiechip wrote: post #46

This right here, or at least the thought of this, is why in the not so far future, businesses can't (won't?) be using these LLMs services. You cannot risk companies like Anthropic, OpenAI or their business partners like Microsoft having unfettered access to proprietary data on your company/businesses. It it likely that they or rogue employees will use the information to make a profit? It's pure speculation, but I'd s…

Its not "in the future", its already here, right now. Sensitive IP gets processed on rented or local GPUs running open weight models. Sometimes its required due to data privacy laws, sometimes its because the people running those shops are not trusting OpenAI/Anthropic ZDR policies being observed. Normal, boring, US and EU-domiciled enterprises do this on a regular basis, and there is an industry of companies helping said boring companies set things up.

Re: How An AI math breakthrough ignited a controversy

#72

Post by zero-sharp »

impendia wrote: post #30
zero-sharp wrote: post #5

Moving forward, I can't imagine other mathematicians wanting to have this kind of experience. So there has to be a shift away from these services.

I'm a mathematician. I have a lot of trepidation about these tools and what they mean for the future of the profession. That said... most of us are not working on problems as famous as Navier-Stokes. Even if OpenAI could scoop me based on my back-and-forth with ChatGPT, which I presume they could if they threw $15 million worth of compute at it, I highly doubt they'd bother.

I think they spent millions pursuing strategies to attack that particular problem? I don't think it takes 15 million for their model to get trained on your chat logs. This is probably all automated internally. If they did scoop your ideas, it would likely get incorporated into their model without any conscious decision making. And if you're not a high profile academic, nobody will hear about it.

Re: How An AI math breakthrough ignited a controversy

#74

Post by elgertam »

huurtehoog wrote: post #10
afavour wrote: post #7

The core section: > However, communications quickly became contentious. According to Buckmaster, OpenAI offered to give him sole authorship on the Navier-Stokes solution—but only if Alpöge’s name was removed from the work and if the write-up would acknowledge the problem had been resolved by an internal OpenAI model. Buckmaster refused, in part because he was troubled by the question of what OpenAI's system had actua…

So, this company wants everyone and every organization on Earth to use their software, and reserve the right to then tell anyone how the resulting work can be published and credited? Real solid business model there, how could it ever fail?

The site should have a disclaimer at the bottom: "A Sam Altman Production."

Re: How An AI math breakthrough ignited a controversy

#75

Post by sebzim4500 »

JohnKemeny wrote: post #50
sebzim4500 wrote: post #36

Earlier quoted context omitted.

Are you asking if it uses additional axioms of `sorry` in the proof? It's easy to check that it doesn't by compiling it and telling lean to list the axioms.

It's highly non-trivial to confirm that the theorems written in Lean are actually the same as the Navier–Stokes (non-)theorem.

Is it? Clicking around the code it looks like a pretty mechanical translation of the statement on the millennium problem website. Assuming of course that you are willing to trust that e.g. the real numbers definition and API included in MathLib4 is correct, but that feels very safe to me.

I'm not claiming to be an expert on Lean4 (although I have contributed tactics) but this is one of the most direct formalisations I've seen of a serious result (second only to FLT of course, which has a horrible proof but it is trivial to verify the statement)

Re: How An AI math breakthrough ignited a controversy

#76

Post by code51 »

ltononro wrote: post #61
mrbungie wrote: post #27

Earlier quoted context omitted.

They represent different AI usage patterns. OpenAI wants everyone to believe that it was done with a practically autonomous network of thousands of agents with little to no human intervention for 88 hours, while Buckmaster/Alpöge were using AI in a more guided way for months. If OpenAI actually used anything from Buckmaster/Alpöge work they would be misleading the public.

Agree! Not sure I believe that Buckmaster/Alpöge were guiding the AI. This is just their way of saying that they had something in the process and deserve merit.

So you believe they're like "solve navier-stokes make me rich make no mistakes" despite being mathematicians of top ability? Occam's Razor for sure.

Re: How An AI math breakthrough ignited a controversy

#77

Post by jeanmichelselli »

AI models and in particular LLMs are not capable of logic reasoning. See for example this paper:

https://arxiv.org/abs/2506.06941

Ergo, they can't prove any theorem whatsoever. How do people at OpenAI expect that we believe in claims like that? This is yet another before-the-IPO stunt in my opinion..

Personally, I won't believe any of these claims until the community of mathematicians says otherwise.

Re: How An AI math breakthrough ignited a controversy

#78

Post by Gabrys1 »

JohnKemeny wrote: post #37
afavour wrote: post #7

The core section: > However, communications quickly became contentious. According to Buckmaster, OpenAI offered to give him sole authorship on the Navier-Stokes solution—but only if Alpöge’s name was removed from the work and if the write-up would acknowledge the problem had been resolved by an internal OpenAI model. Buckmaster refused, in part because he was troubled by the question of what OpenAI's system had actua…

> but only if Alpöge’s name was removed This is blatant scientific misconduct.

Any idea why OpenAI cared about this name removed from the paper?

Re: How An AI math breakthrough ignited a controversy

#79

Post by Tenemo »

greggoB wrote: post #28
olmo23 wrote: post #24

Earlier quoted context omitted.

> While unlikely, we cannot rule out that de-identified data derived from [Buckmaster and Alpöge’s] usage of our products helped improve our models. Well yeah, if you use the free product they train on your data, ... I thought this was widely understood?

If you read Buckmasters statement, he specifically notes that they used the paid subscriptions, iirc.

Paying for an account doesn't opt you out by itself, right? Has he stated anywhere that he actually opted out? But if not, then I also don't understand why OpenAI's communications about this have been so vague, they could've just said that he didn't opt out, using those chats in training data follows their ToS and that's it (whether that's "fair" is a separate discussion).

Re: How An AI math breakthrough ignited a controversy

#80

Post by igleria »

mrngld wrote: post #42
rrhjm53270 wrote: post #9

My impression: the re-aristocratization of scientific research seems inevitable.

Your local trailer park was never going to be able to afford sponsoring high energy particle physics experiments projects that hollow out a mountain and use up a ton of xenon to try to detect a stray particle. High end science has required deep pockets for a long time. But given the cost of a college textbook this is a pretty silly complaint to lobby against a subscription that's $200 a month, in the context of the c…

> Your local trailer park was never going to be able to afford sponsoring high energy

taxes.

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