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How An AI math breakthrough ignited a controversy

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Re: How An AI math breakthrough ignited a controversy

#191

Post by 00ze »

rsfern wrote: post #18

Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development. Those problems can’t be formally verified with an automated theorem prover. We have a lot of physics bas…

Solve logically? Sure.

Solve for how to implement and synthesize physically? Not likely.

Humans solved for launching rockets to the Moon on paper decades before it happened.

Pareto type thing; the logical work is the easy 80%. The last 20% is fighting physics.

There is no beating physics but there is still plenty of room for us to improve our understanding of it.

Which we weren't focused on at all sitting millions primates at well understood physical computers searching for Shakespeare Python and Ruby code yet merely getting same old contemporary software outputs.

Re: How An AI math breakthrough ignited a controversy

#192

Post by hunterpayne »

whimsicalism wrote: post #163
rakejake wrote: post #44

Earlier quoted context omitted.

Yeah, I think you can't just throw money randomly at problems and expect results unless you know a line of attack that can get you all the way. OpenAI chose the line of attack only after it became known to them via rumors. They "front-ran" the researchers.

but the researchers were also largely relying on AI

The researchers were driving prompts and trying to actually do math.

The OpenAI effort was a pure brute force attempt. I'm not even sure an LLM was actually involved. I think they just used their hardware to run the matrix multiplies required by the search for a counter example. Perhaps some clever approach guided the search but that seems to be about it.

Re: How An AI math breakthrough ignited a controversy

#193

Post by vonneumannstan »

eieje1 wrote: post #184
rakejake wrote: post #44

Earlier quoted context omitted.

Yeah, I think you can't just throw money randomly at problems and expect results unless you know a line of attack that can get you all the way. OpenAI chose the line of attack only after it became known to them via rumors. They "front-ran" the researchers.

You can’t do anything novel with these models from scratch and let it fly. I’ve observed something over the past few months Work on something novel -> llm is kinda useless and low value-add -> Keep at it and in the process feed it more information -> keep doing this periodically -> a few months go by and you realise the model outputs are almost like-for-like regurgitations of what was inputted in some prior period. O…

This doesn't follow for me. There are what, Dozens or Erdos tier problems that got solved with no progress for decades? How does that factor in to your view?

Re: How An AI math breakthrough ignited a controversy

#194

Post by jrflo »

u1hcw9nx wrote: post #96
rsfern wrote: post #18

Regardless of what you think of the priority dispute issue discussed on sibling threads, I’m highly skeptical of the closing quote that this Navier Stokes result means that the same approach of casually spending a few million on agentic computation is going to solve end to end materials design or drug development. Those problems can’t be formally verified with an automated theorem prover. We have a lot of physics bas…

For any practical application, numerical solvers for Navier-Stokes already exist and do a good job. This proof is just checking the boxes for mathematicians.

The efficacy of applied NS was never in doubt. "Checking the box" is downplaying the magnitude of the discovery quite a bit as it has been unsolved for almost 100 years. Yes, this particular problem with NS no real-world applications, but that's true for 99.9% of math research.

Re: How An AI math breakthrough ignited a controversy

#196

Post by zeroonetwothree »

dguest wrote: post #188
rocqua wrote: post #151

Earlier quoted context omitted.

It seems very hard for OpenAI to prove that independence. Since they seem unable to exclude the possibility that their model was trained on transcripts by the two mathematicians.

If that's true, either they both deserve credit or neither of them do. You don't just average 0 and 2 and decide that = 1 person deserves credit.

And yet it happens constantly in the history of science

Re: How An AI math breakthrough ignited a controversy

#197

Post by zeroonetwothree »

timmg wrote: post #23

I think it was a pretty questionable thing to do by trying to front-run these researchers even if they didn’t make use of their techniques. The fact that they may have inadvertently “borrowed” their work via training data makes it much worse. OpenAI’s behavior here — even if you only consider [their] side of the story — was (at best) in bad taste.

Isn’t that how research works? You build on what others have done. I don’t understand the big deal. I’d rather have the result available sooner than later just to assuage some egos

Re: How An AI math breakthrough ignited a controversy

#198

Post by jrflo »

afavour wrote: post #7

The core section: > However, communications quickly became contentious. According to Buckmaster, OpenAI offered to give him sole authorship on the Navier-Stokes solution—but only if Alpöge’s name was removed from the work and if the write-up would acknowledge the problem had been resolved by an internal OpenAI model. Buckmaster refused, in part because he was troubled by the question of what OpenAI's system had actua…

I could see their comment on user training data as a bit of a CYA statement, but removing Alpoge from the paper is awful. Has really soured what could have been a huge moment for AI progress.

Re: How An AI math breakthrough ignited a controversy

#199

Post by lackoftactics »

dgellow wrote: post #143
JohnKemeny wrote: post #45

Earlier quoted context omitted.

It's one of the seven most important problems in mathematics. Pick a better analogy.

If you want to be pedantic it’s one of the 7 problems a specific institute considers to be the most important in mathematics: https://en.wikipedia.org/wiki/Millennium_Prize_Problems (Not that I think the comparison to pi digits make sense)

are we really moving the goalpost after solving Millenium Prize Problem? Six years ago that would be something, but today let's move the goalpost

Re: How An AI math breakthrough ignited a controversy

#200

Post by hunterpayne »

nayroclade wrote: post #117
harhargange wrote: post #68

Earlier quoted context omitted.

I’m pretty sure that OpenAI has some of the best mathematicians prompting the models and analysing the results. While they are marketing as if the model solves problems themselves.

Prompting them yes, suggesting potentially fruitful research directions and so on, but the actual research was conducted by hundreds of agents swapping millions of messages and using billions of output tokens over 88 hours. The result being a huge Lean proof: https://github.com/openai/NavierStokesAndEuler . It's not just possible for humans to manually guide such a process in a meaningful way. They can set the direct…

The OpenAI team didn't make a Lean proof. They brute forced a counter example. The "other" team was doing what you described but they haven't "finished" their work yet. Also, their Lean proof was for a simpler version of the problem, not the full NS.

Also, OpenAI wanted the actual mathematician taken off the resulting paper. I'm not sure I would describe what OpenAI did as research. What the other team was doing does seem to be more like research but the hardware was still in those cases mostly brute forcing things and then doing something like a genetic algorithm to compose an actual proof based upon the results of a large set of brute force attempts.

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