Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Claude Fable produced a counterexample to the Jacobian Conjecture

xcancel.com

Post reply on HN
Print view View original

51–60 of 562 posts

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#51

Post by ViscountPenguin »

mathisfun123 wrote: post #44

The funniest thing about LLMs is the cognitive dissonance they cause people. People clearly recognize (and bemoan) the fact that LLMs produce derivative breathless prose ie they fundamentally fail at "unstructured creativity" (something the might accurately labeled intelligence ) but are then shocked that the same LLMs can do math. It's reasoning from a flawed premise that math universally requires intelligence and c…

I dunno, this screams of goal post moving. Even if LLMs lack whatever nebulous definition of "creativity" that someone favours, there's no inherent reason for "creativity" to be required to solve any problems at all, "creativity" could just be a human method for solving problems that evolved because of it's broad applicability but is suboptimal at any given task.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#52

Post by tptacek »

SyzygyRhythm wrote: post #49
gnarlouse wrote: post #23

Anybody can ELI5?

Are you at least a little familiar with linear algebra? If so, you've probably heard of the determinant. It's a certain way of "summarizing" a matrix with one value. The determinant in this case is of the Jacobian, which is a matrix you can construct from a multi-variable function. Each term is the partial derivative with respect to each variable (x, y, z, etc.), with one line per output variable (vector element). Th…

Nice!

(It's gotta be a nonzero constant, right, a nonsingular matrix).

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#53

Post by tomjakubowski »

cyphar wrote: post #28
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.

I don't think the (fairly factual) description of these systems as stochastic parrots means that they will never do useful work, just that they are not intelligent in the way we believe animals to be (to "push back" on your anecdata, I've also heard fewer people claiming that LLMs are actually conscious in the past year -- maybe we're reaching the happy medium?). That was the point the stochastic parrots paper and Ch…

Agreed totally. When past computer-assisted proofs were published, nobody (or hardly anyone) waxed about this being evidence of Rocq or Coq as superintelligent or even conscious beings of some kind, as people have said about LLMs.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#55

Post by rowbin »

rvz wrote: post #48
kmaitreys wrote: post #42

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

I'd rather wait for independent seasoned mathematicians to verify such claims first before someone at said AI lab posting a claim about solving a proof online. Let this be a lesson to those who fell for such AI psychosis and to not believe everything you see on the internet as real.

Maybe have a seasoned mathematician check if the counterexample is really bogus before saying people fell for ai psychosis.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#56

Post by tptacek »

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? :)

I told GPT5.6 I came up with this walking down the street. "Jesus Christ" was its response.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#57

Post by slopinthebag »

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.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#58

Post by mathisfun123 »

ViscountPenguin wrote: post #51
mathisfun123 wrote: post #44

The funniest thing about LLMs is the cognitive dissonance they cause people. People clearly recognize (and bemoan) the fact that LLMs produce derivative breathless prose ie they fundamentally fail at "unstructured creativity" (something the might accurately labeled intelligence ) but are then shocked that the same LLMs can do math. It's reasoning from a flawed premise that math universally requires intelligence and c…

I dunno, this screams of goal post moving. Even if LLMs lack whatever nebulous definition of "creativity" that someone favours, there's no inherent reason for "creativity" to be required to solve any problems at all, "creativity" could just be a human method for solving problems that evolved because of it's broad applicability but is suboptimal at any given task.

> 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 intelligence or just computation.

What's more reasonable?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#60

Post by krackers »

SyzygyRhythm wrote: post #49
gnarlouse wrote: post #23

Anybody can ELI5?

Are you at least a little familiar with linear algebra? If so, you've probably heard of the determinant. It's a certain way of "summarizing" a matrix with one value. The determinant in this case is of the Jacobian, which is a matrix you can construct from a multi-variable function. Each term is the partial derivative with respect to each variable (x, y, z, etc.), with one line per output variable (vector element). Th…

I think another way to understand it is the generalization of the inverse function theorem. The inverse function theorem gives you local invertibility, but even being "locally invertible" everywhere does not imply global invertibility (you don't need too pathological an example to see this, a periodic function serves iirc).

The Jacobian conjecture roughly asks what whether local invertibility gives you global invertibility when you restrict only to polynomials (which we might hope "behave nicely"). Apparently for polynomials over reals this was disproved a while back, but up until now the general case of polynomials over complex numbers was open.

Post reply on HN