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No one really knows a viable approach towards P vs NP so we can't say for sure, but LLMs have created plenty of significant complexity theory results so I wouldn't say there's no progress.
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Interesting, that does look relevant. I don't have any sense how significant this is though (do you?)
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No idea, not a physicist. But I thought I should draw attention to it because it may escape people.
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I've read that another mathematicians work potentially has been incorporated into the training data with the work done on the Navier-Stokes equations so we should likely asterisk this one. Still it's mad these systems are this good that mathematicians are now using them to see further and probably to check their own work and understanding.
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You are being downvoted for this because OpenAI subsequently checked and clarified than none of the relevant conversations were in the training data in anyway for the Navier-Stokes result.
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> because OpenAI subsequently checked and clarified than none of the relevant conversations were in the training data in anyway for the Navier-Stokes result.

could you give link? Because I remember they said they couldn't verify:

"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

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Sure.

> Following an investigation, we have confirmed that Buckmaster’s Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training.

https://openai.com/index/navier-stokes-solution/

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for 2 months prior. Not any of the relevant conversations. For a cutoff date a couple months before the announcement. They said they had been working on that problem for a year or more
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Thanks, it's hard to stay up to date. However, we are just meant to believe that the mathematicians were going about the proof independently in the exact same way as the machines did it. It seems like a very odd coincidence to me.
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> Our proofs also differ significantly. In the Euler case, Alpöge and Buckmaster proved a result with external forcing, while OpenAI’s system proved a result without external forcing.

https://openai.com/index/navier-stokes-solution/

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True. They investigated themselves for one day.
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Oh, well if notorious liar Sam Altman and his company notorious for lying says so…
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Great that they're so transparent and honest, BTW, can you ask them if they trained on any copyrighted data that they pirated?
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Courts have rejected the "training is piracy" interpretation.

I agree with the courts. I don't think learning from something is piracy in anyway.

Obviously though this is a very different issue to what the OP was claiming. In that case there is no legal argument at all that they could train on it and the argument is there about moral rights.

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Buying and copying one training manual and distributing it to 1000s of human workers is considered illegal, but somehow scanning one book and sending it to 1000s of distributed training instances is not?

Also, you learning something is different than a model learning it, because a model is not a person. You can learn from a book and sell the skills you gained from it, but you can only be in one place at a time. The model can serve that knowledge to every person on the planet simultaneously. We obviously need new laws since this is a fundamentally different situation.

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As you point out, a model is not a person, so your second argument invalidates your first sentence. We can't assume that they're the same thing; that's for the courts to decide. It ultimately hinges on whether or not the courts consider a given use of copyrighted material as "transformative" or otherwise constituting fair use under copyright law.
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The model seems to be a person when it's advantageous and not a person when it isn't...
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There's a lot of anthropomorphizing on all sides of the debate. Personally, I think we should just call it a piece of software and leave it at that.
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I was making two separate points:

A model is not a person -> we need to write new laws. This is not a job for the courts but for us as a society.

The rest of my argument -> information that helps the courts decide, which generally will look at precedent with humans as that is the closest proxy. When you extrapolate from the law as it pertains to humans, the duplication of books for distributed training seems illegal.

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Training a model is not "learning something". Only people learn things. Whether training is a fair use is debatable, but it has nothing to do with the justification that people are allowed to learn from books.
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> No sign of P vs. NP

Check out my other top level comment in this thread.

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