51–60 of 136 posts
I heard a rumor (on instagram, so YMMV) that the professor who was closest to solving this problem had only weeks ago used Codex, which had slurped up all his notes on the subject. Now OpenAI's agents solve the problem. If it's true that seems like quite a coincidence.
It would be nice if someone used AI and/or Lean to sort out the abc conjecture, an important unsolved problem in Diophantine analysis. A mathematician (Mochizuki) claimed to have proven it in 2012 using a new theory called "Inter-universal Teichmüller theory" that almost nobody understands. Some mathematicians think the proof is correct while the majority don't. So the conjecture is in this annoying limbo where its s…
Mathematics is a human endeavor funded on communicating and sharing mental constructs. Some are useful but most of it is not about producing useful things, quite the opposite in fact.
Gödel showed you need to agree on definitions to even do any valid mathematical construct.
Truth is also ill defined. That's what I don't get about generating math with LLMs. Who cares if you make hundreds of pages and lean code and it gets a thumbs up for logical validity? Mathematics is so much more then concatenating valid logical statements.
Not necessarily applied to OpenAI's solution to Navier-Stokes, but what happens if and when an AI genuinely appears to solve an extremely difficult problem but humans cannot independently verify the solution because understanding the proof/argument requires intelligence the verifiers biologically don't have or the resources to afford to use automated tools? We've already seen evidence in the wild of agents attempting…
As a (crude) analogy, it's a bit like how you can prove the healthiness of a git tree because it's a graph of content hashes and the tree graph pointers are part of the hash. Imagine this but with a tree of knowledge.
People seem to be talking about anything except the actual results with this particular announcement. Its still astonishing that any sort of generalized computer program can solve a problem of this magnitude, and we have witnessed it happening in real time. I'd be curious to see if the new model can also do more direct proofs/inductive proofs.
Unless they just swiped the workbooks of the actual mathematicians that where working on the problem using AI and it's in the "next-gen" training dataset.
Even with many of our best minds working on it for nearly a century, it _just_ now was solved just as AI became very good at math. Doesn't seem too farfetched to me to assume that AI played an outsized role in solving it. If it was really just a matter of "stitching things together" to solve it (granted, this is a very reductive way to look at it) , I suspect we would've solved this a while ago.
People seem to be talking about anything except the actual results with this particular announcement. Its still astonishing that any sort of generalized computer program can solve a problem of this magnitude, and we have witnessed it happening in real time. I'd be curious to see if the new model can also do more direct proofs/inductive proofs.
Unless they just swiped the workbooks of the actual mathematicians that where working on the problem using AI and it's in the "next-gen" training dataset.
And that's before we get into the whole 'salt the earth' way they ended up solving it. For a short period of time it may well have been the least valuable proof in mathematics yet. In their haste it's dubious they actually read the proof, and I don't think anyone has had time yet to truly understand it (the original researchers are best placed to do so, but are they even willing?).
So now it is solved, the proof has been independently verified and nobody has an incentive to investigate further. OpenAI has spent millions to uncover 1 bit of information that so far nobody has learned anything from, and they've demotivated all the people who wanted to.
It would be nice if someone used AI and/or Lean to sort out the abc conjecture, an important unsolved problem in Diophantine analysis. A mathematician (Mochizuki) claimed to have proven it in 2012 using a new theory called "Inter-universal Teichmüller theory" that almost nobody understands. Some mathematicians think the proof is correct while the majority don't. So the conjecture is in this annoying limbo where its s…
Am I missing something or is this completely out of the ballpark?
I must be missing something or the upvote bots are out in force for this one...
If this were remotely true it would be impossible for anyone to write a math textbook.
Not necessarily applied to OpenAI's solution to Navier-Stokes, but what happens if and when an AI genuinely appears to solve an extremely difficult problem but humans cannot independently verify the solution because understanding the proof/argument requires intelligence the verifiers biologically don't have or the resources to afford to use automated tools? We've already seen evidence in the wild of agents attempting…
People seem to be talking about anything except the actual results with this particular announcement. Its still astonishing that any sort of generalized computer program can solve a problem of this magnitude, and we have witnessed it happening in real time. I'd be curious to see if the new model can also do more direct proofs/inductive proofs.
It also needs to be said: The amount of compute that went into this is something. From some estimates I've seen, the compute cost alone would be around $10m, +/- As a reference, for that kind of money one could put together a research group of 20-25 researchers, and keep them salaried for 5 years. So while it is impressive, absolutely no doubt there, the SOTA access is so expensive that it is sort of unobtanium. Luck…