AI/LLMs Can LLMs Think? - The Debate

[FrogReaver]

Proof is now public

https://openai.com/index/navier-stokes-solution/

Fascinating. Waiting on top tier mathematicians to validate. But very interesting. Given the method was multiple ai agents working in concert I’m not sure how relevant to thinking it is. But absolutely fascinating if verified.

 

[Umbran]

I mean, I don't at think this is the wrong place for us, given the extreme breach of trust.

I know what comes to mind....


A song, by the way, which is in the public domain...

 

[Justice and Rule]

The important point imo is that in no circumstance is it taking a year of a human's work. All of that work was done with AI--that's what codex is for. So whatever the behind the scenes details, AI played a crucial role in solving a Millennium Problem.

No, it's not just done with AI. It absolutely was assisted, but you can't remove that part of the equation and how it was directed. It certainly helped, but this wasn't just putting the equation in and forcing an answer with a prompt, but rather something that was built upon a whole lot of directed work that ended up being stolen by one of the AI companies in question, which is now attempting to strong-arm the person whose work they stole.

This isn't denying that AI has uses and certainly played its part here, but this wasn't just the system solving the problem (though OpenAI definitely would like that to be how people view it).

 

[FrogReaver]

American Mathematical Society’s statement:

"The news today of progress on resolving the Navier–Stokes problem, one of mathematics' great longstanding challenges concerning the equations that govern the flow of fluids, represents a milestone advance in human knowledge. This story began with Navier, Stokes, Leray, and Ladyzhenskaya and has culminated in the recent breakthroughs of Córdoba and Martínez-Zoroa, then — assisted by new technologies — Alpöge and Buckmaster, with the final steps taken by OpenAI mathematicians. The purpose of mathematics is human understanding, and this achievement, and the process that led to it, will bear fruit for a long time to come."

https://www.ams.org/news?news_id=7686

Thanks for this. Proof isn’t officially validated but this is quite the statement in favor of it being legitimate.

 

[The Firebird]

This isn't denying that AI has uses and certainly played its part here

That was the extent of my point.

 

[Umbran]

I read an interesting article today, that brought me to a basic consideration - why are we so interested in making machines think, when the most obvious use is to have it think not to serve you, but instead of you.

"We'd never do that!" you figure? It would be restricted to merely assistive use?

Bullpucky. There's a guy out there now, making any app called "Cluely" that is intended to remove your neednto think. No need to carry on a conversation - Cluely will tell you what to say!

Child’s Play, by Sam Kriss

Tech’s new generation and the end of thinking

harpers.org

Whether or not it can think, if it can produce a good enough facsimile, your own ability to think becomes superfluous.

 

[Umbran]

That was the extent of my point.

Yes, but it wasn't free. Reportedly, it took them $22 million dollars of computing time to try to scoop the human mathematicians.

$22 million.

At a salary of $125k, that would be... 176 mathematicians for a year. Or 17 mathematicians for a decade.

Was that one proof worth more to human knowledge than the output of 17 mathematicians for a decade?

 

[Justice and Rule]

Yes, but it wasn't free. Reportedly, it took them $22 million dollars of computing time to try to scoop the human mathematicians.

$22 million.

At a salary of $125k, that would be... 176 mathematicians for a year. Or 17 mathematicians for a decade.

Was that one proof worth more to human knowledge than the output of 17 mathematicians for a decade?

Plus that's with the homework of someone having already worked on the problem. They didn't just input something as much as tag an entire team and a massive amount of compute using the notes of the people who actually seemed to crack the code.

I'm not trying to understate what was done, but it's got a good amount of caveats. I also wonder how much this is going to throw cold water on the usage of things like Codex if you know that the company will throw its unlimited compute at it once you get close enough so that they can steal the credit and a headline.

 

[FrogReaver]

I think it's important to take a step back to appreciate exactly what the Millennium problems represent and all the human capital that has been spent working on them over the years. While the prizes were formally established in 2000, many of the problems originated much earlier. For many, if not all of these problems, entire careers have been spent on partial progress, new techniques, and failed approaches, without meaningfully getting closer to a solution.

The Clay Mathematics Institution - Millennium Problems

In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.

 

[briggart]

I stumbled on this video which I think would be of interest here.

The TL;DR: the speaker is a theoretical physicist who transitioned to AI and now works for Google/Deepmind. His point is that in six years AI/LLM went from a preschooler level to consistently solving non-trivial science problems at the level of good graduate students on their own. Now we are moving into a regime where, under human supervision, they are performing novel math research. At the same time, the cost/resources required for a given level of intelligence have decreased by several orders of magnitude, and he doesn't believe both trends are not going to stop anytime soon.