501–510 of 1001 posts
I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able…
To be fair, I think it's still an open question about how far it might surpass human capabilities.
I think it's clear that its speed of development will be significantly faster, but it's technically not proven that the frontier and problems don't themselves become increasingly difficult faster than any acceleration in intelligence past the point of human training, data and existing knowledge.
Should this be the case, we would see a rapid broadening of development, and a slow advance in the frontier in such a way that might surpass the collective capabilities of people, but not by very far.
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The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”. [1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/
Compute will always be the bottleneck even if this were true.
Bit apples to oranges, but it reminds me of all the fiber we installed in the late 90s, certain that per-strand capacity increases were years or decades out, only to get massively rugged
Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
The singularity happening under trump? We could have had star trek, instead we're getting the combine.
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Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof. https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310 A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.
Their own claim is that they wanted Buckmaster without Alpöge to lead a rewrite of OpenAI's Navier-Stokes work, not of Alpöge-Buckmaster's Euler work. No one can know if that's correct without proof but I don't know how you're reading it so differently.
Just suggesting to a mathematician to dissociate with their collaborator for a follow-up work, because their collaborator “is inappropriate to author OpenAI’s work”, is completely against the norm of mathematical research. As charm137 puts it in a comment below:
> This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that!
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Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…
To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effec…
If the internal OpenAI model is as capable as you claim (being able to solve a Millenium problem without using unpublished insights built on years of work from mathematicians), then it should be able to demonstrate this capability again.
How about OpenAI solves another Millenium problem within the next two weeks, that doesn't coincide with the parallel discovery/solution of other teams of mathematicians, using ChatGPT for preliminary proofs & write-ups.
It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774
woah, this gives some credit to the rumor that openai finetuned a model over the course of a few days for this task, and maybe trained on the Chatgpt/codex history of the authors, including drafts of this research.
It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774
Buckmaster: > "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer." OpenAI (i.e. this OP): > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helpe…
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> WOW This. I do dislike the AI oligarchs as much as the next person, but I do find the thread full of complaining a bit depressing still. If the result holds (and it looks it does), this may be one of the, if not the, biggest things to happen in computing to date. A lot bigger than e.g. Deep Blue beating Kasparov in chess or AlphaGo beating Sedol in Go.
Seeing mathematicians such as Terry Tao being unhappy with open problems being solved makes me sort of question the usefulness of any of this pure mathematics. If we're not happy that the problems are being solved, why care about this field at all?