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Claude Fable produced a counterexample to the Jacobian Conjecture

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Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#71

Post by sosodev »

NitpickLawyer wrote: post #38
bigyabai wrote: post #26

Earlier quoted context omitted.

https://en.wikipedia.org/wiki/Sycophancy_(artificial_intelli...

To be fair to the sycophancy tendencies, this was an open conjecture that held for 85 years, and not for lack of trying. So, maybe a bit warranted here? :)

That’s the worst thing about sycophancy. You can never tell when it’s warranted or not. I imagine that many AI chats have had real gold in them and yet we’ll never know.

The same was obviously true historically. People have had many revolutionary thoughts or even writings that nobody noticed. I think in this case it just feels worse because the AI could be the perfect tool for discerning the diamonds in the rough.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#72

Post by ignoramous »

scarmig wrote: post #19
aurareturn wrote: post #12

Earlier quoted context omitted.

The goal posts have moved. People generally stopped saying this stuff now. Even if you go to the ultimate anti-AI subreddit r/betteroffline, they've changed from "AI is useless" to "AI is good but the AI bubble will collapse soon" over the last 6 months.

Some quotes from a day ago, https://news.ycombinator.com/item?id=48957779 : > I hold my stance that LLMs are stochastic parrots... Making the parrots ever more complex and training > Except solving problem is probably the least (even though it's important) interesting thing in research. > Can we use AI to get a cure for cancer yet? Or is math-turbation the only thing these things are good for? > Train on enough examp…

Don't think HN is anti-AI but experts of course may have a different perspective. A comment in this discussion points out that LLMs have been doing math that's been long overlooked in favour of perhaps more impactful work: https://news.ycombinator.com/item?id=48974274

  There isn't a lot of money in academic math, and the ones that love it don't look for low value findings. Proofs like these are ... usually the domain of hobbyists ...

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#74

Post by whateveracct »

aurareturn wrote: post #12
scarmig wrote: post #11

"Any idiot could have done this, it's just high school calculus and just a counterexample anyway. Stochastic parrot, spicy autocomplete, AI psychosis. Wake me up when an AI does something real."

The goal posts have moved. People generally stopped saying this stuff now. Even if you go to the ultimate anti-AI subreddit r/betteroffline, they've changed from "AI is useless" to "AI is good but the AI bubble will collapse soon" over the last 6 months.

the ROI just isn't there. they aren't making these capital investments back in the next decade even.

not to mention the trillions yet to be spent.

it kinda all works but it's an earth-scale blood from a stone. the resources needed to even do these parlor tricks is nutso.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#76

Post by userbinator »

sobellian wrote: post #67
jdw64 wrote: post #46

I've come to understand that while an LLM is a parrot, it's a parrot that's smarter than I am.

If you have to be a parrot of another man's thoughts, at least let that man be a synthesis of all human endeavor to date.

"If I have seen further it is by standing on the shoulders of Giants." -Isaac Newton

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#77

Post by mathisfun123 »

gmadsen wrote: post #70
mathisfun123 wrote: post #58

Earlier quoted context omitted.

> could just be a human method for solving problems that evolved because of it's broad applicability but is suboptimal at any given task. Ya sure let's just posit another random hypothesis about evolutionary biology in order to substantiate the claim that LLMs are intelligent. Or (bear with me) you can recall your (likely) experience proving stuff like SAS triangle identities and reflect on whether that required inte…

Why is your example SAS triangles and not something like the modularity theorem?

Because SAS triangle identity proofs are relatable and I'm trying to make a point...?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#78

Post by omaranto »

slopinthebag wrote: post #57
kmaitreys wrote: post #42

Maybe not? https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...

The author has a PhD in math from Cambridge. If it turns out to be a false claim it is an interesting case study on AI's sycophancy causing even experts to drop their guard and make mistakes.

Who do you mean? The author of the tweet is Levent Alpöge, who does not have a PhD in math from Cambridge... but does have a PhD in math from Princeton. And his advisor was Fields Medalist Manjul Bhargava.

Also, there is no way this counterexample is wrong. You can very easily check it for yourself. (I did, I don't know why, obviously Levent wouldn't be wrong about this, but I guess I was in shock.)

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#79

Post by EagnaIonat »

slopinthebag wrote: post #57
kmaitreys wrote: post #42

Maybe not? https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...

The author has a PhD in math from Cambridge. If it turns out to be a false claim it is an interesting case study on AI's sycophancy causing even experts to drop their guard and make mistakes.

[flagged]

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#80

Post by tptacek »

whateveracct wrote: post #74
aurareturn wrote: post #12

Earlier quoted context omitted.

The goal posts have moved. People generally stopped saying this stuff now. Even if you go to the ultimate anti-AI subreddit r/betteroffline, they've changed from "AI is useless" to "AI is good but the AI bubble will collapse soon" over the last 6 months.

the ROI just isn't there. they aren't making these capital investments back in the next decade even. not to mention the trillions yet to be spent. it kinda all works but it's an earth-scale blood from a stone. the resources needed to even do these parlor tricks is nutso.

Am I reading you right that you're claiming solving one of Smale's open problems is a "parlor trick"?
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