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OpenAI’s Navier-Stokes release included a Lean 4 formal proof

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151–154 of 154 posts

Re: OpenAI’s Navier-Stokes release included a Lean 4 formal proof

#151
post #7

It's kinda funny to realize that Lean is apparently so slow that for Fermat's Last Theorem proof verification runs only 1 order of magnitude faster than agents could generate the Lean code (15h verification with 230GB of RAM vs 11 days to generate it). To what extent can you optimize Lean? It has to be simple enough to be auditable, does that mean you cannot use opaque optimizations to make it run faster?

Does it really matter? You really only need to run it once.

Re: OpenAI’s Navier-Stokes release included a Lean 4 formal proof

#152
post #35

Earlier quoted context omitted.

Because the core of the issue is that it may well not have solved it, but instead plagiarised the significant step of the result from other researchers That's why nobody's talking about how impressive this is, because its not nearly as impressive of a piece of work to simply cobble together other peoples' work that didn't know you were doing it. I could have republished relativity from einstein's notes, but people wo…

It is very unlikely to be plagiarized, and claims of plagiarism are largely unfounded and show a lack of understanding of the situation. They fall apart when reviewing the timeline, and what was actually solved. This is the timeline: On June 29, Buckmaster opted out of model training, and stopped allowing his chats to be used as training data with OpenAI https://mastodon.social/@tristanbuckmaster/11723341370570119...…

It doesn't seem like you're familiar with how mathematical research is done. Taking 6 weeks between a major breakthrough on a huge proof, and making your proof public, is not unusual.

It takes a lot of time to finish a proof and figure out the best way to present it. I would personally be surprised if Buckmaster had not gotten it mostly cracked before June 29th.

Re: OpenAI’s Navier-Stokes release included a Lean 4 formal proof

#153
post #7

It's kinda funny to realize that Lean is apparently so slow that for Fermat's Last Theorem proof verification runs only 1 order of magnitude faster than agents could generate the Lean code (15h verification with 230GB of RAM vs 11 days to generate it). To what extent can you optimize Lean? It has to be simple enough to be auditable, does that mean you cannot use opaque optimizations to make it run faster?

Sure, but to clarify the article is describing formalization (writing a correct program), not verification (compiling said program). The author is not making the same comparison.

Verification is also open ended (not sure about lean specifically) - you could in theory give lean just the Navier-Stokes problem definition to an ATP and let it run.

Re: OpenAI’s Navier-Stokes release included a Lean 4 formal proof

#154
post #138

Earlier quoted context omitted.

It is very unlikely to be plagiarized, and claims of plagiarism are largely unfounded and show a lack of understanding of the situation. They fall apart when reviewing the timeline, and what was actually solved. This is the timeline: On June 29, Buckmaster opted out of model training, and stopped allowing his chats to be used as training data with OpenAI https://mastodon.social/@tristanbuckmaster/11723341370570119...…

I’m unsure or not if this is true but I did see some people saying that that checkbox when off only anonymizes your data, but it still may be trained on. Someone correct me if I am wrong

Even if it does use your data with or without anonymization, it doesn't have to be intentional, it could just be a glitch, or a bug, or something we'll catch in the next update, it's all good man, just a normal computer error.
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