SockOlm [she/her]
newsThe 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
This is a weird one, the researchers made heavy use of Codex and Claude agents to iterate on their proof, then the companies stole their work and just smashed 10x the compute at it so they could "solve it first".
The original idea was definitely the researchers, and it will likely end up being attributed that way, but OpenAI saw a chance to hop in and steal someone else's spotlight for a PR win.
This really should wake people up to how dangerous these companies are. The second you input anything into a chatbot, it's no longer yours. They're setting the precedent that they own anything that touches their models. Why would anyone want this?
Oh. This also goes for anything you didn't directly input into their chatbot, but that it managed to discover about you eitehr through corporate espionage (someone in HR putting your private info into it), or blatant scraping of the commons.
It solved a Millennium Puzzle?
Seto Kaiba already had the Millennium Puzzle solved in DSOD using a machine inside a space station
Every mathematical problem in the world belongs to America
tbh, whether it is mathematicians prompting chain proof machine or "ai agents" prompting chain proof machine, it's very impressive. may indicate same problem as fermat that some proofs are just too long to be fit in couple of people's heads.
nobody will publish couple of lemmas which will indicate your direction of problem proof, and correct chain can be dozens conjectures long, so that's what we get.
(i mean just look at the openai published concept of a proof, it's a painful construction of a force field which will break navier stokes, while satisfying it's conditions)
i think it's entirely possible they've done this as well; providing a lean formalization is at least something that can be readily checked. i think that's the other half of what's interesting about this actually. the magic here might be applying something that can spit out a great many outputs, most of which are nonsense (LLMs), to something that is basically verified to be correct if it works at all (the lean proof verifier).
also notable here is that the solution they claim to have proven follows from the kind of progress that Terry Tao published a few years ago that suggested finite-time blowup for the navier-stokes equations.
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.
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.
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.
Yes, the human intellect is very impressive, stolen or not
i think with "chain proof" he is talking about the programming language lean, which can be used to verify mathematical proofs. it can also be used to generate a bunch of proof attempts to brute force the solution and that's basically also what the chat-bots do (with the help of millions of $ in compute), but those proofs end up being incomprehensible and really long.
AI is just a more obfuscated Mechanical Turk.
