The Millennium Problems are a set of the most important open problems in mathematics. so far only 2 have been solved: the Poincare Conjecture by Grigori Perelman in 2010 and today OpenAI released this https://openai.com/index/navier-stokes-solution/

The only problem is, that their AI didn't even come up with the solution itself. Mathematicians working on the same problem recently made big strides in solving the Navier Stokes equations, and their chat logs were scraped and used in training data before they could release the proof themselves.

Here is the unpaywalled statements of the Mathematician: https://mastodon.social/@tristanbuckmaster/117233413705701198

Western AI companies have been tackling a bunch of open problems and techbro chuds cannot shut up about it, this is just Marketing and the fact they have to steal real people's work to do so just proves it. They really want that IPO moneyyy capitalist-laugh

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[–] 16 points 2 days ago* (2 children)

may indicate same problem as fermat that some proofs are just too long to be fit in couple of people's heads.

I wonder if it's a "fish doesn't know what water is" kind of situation. The limits of our own brain likely leave us with a lot of blind spots for solutions that seem.... not exactly "obvious in retrospect", but just unintuitive enough that we might never have figured it out. Even if "AI agents" are only really doing intern-level work, they are interns that have some capabilities that are unmatchable by humans.

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  • [–] 15 points 2 days ago* (1 child)

    Honestly, most of this just seems to be showing how impressive modern compilers are.

    Having a logic engine that can basically instantly tell you at compile time if your proof works is what's making these discoveries possible.

    The LLMs would basically be useless without that tooling. Also seems like having a proof is enough of a starting point to begin the process of optimizing.

    Now is it worth the millions of dollars? Who knows. If it turns out that this leads to something maybe, but for now it's just a research novelty that could also be achieved the "folding at home" way, or by just having a bunch of undergrads spend a few weeks churning out Lean proofs until one works.

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  • [–] 8 points 1 day ago*

    I'd agree with this. The major advancement in technology here is the invention and refinement of Lean. Without LLMs we'd just be pumping slightly differently algorithms to brute-force and test proofs.

    These discoveries would be made by chucking millions (or billions?) of dollars into almost any algorithm trying stuff against Lean. AI is tangentially relevant at best. Like inventing a teleporter and then giving the invention credit to the company who made your shirt - Yeah it was there, but it's actual contribution was minimal.

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