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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

#511

Post by latexr »

minimaxir wrote: post #406
pred_ wrote: post #332

Earlier quoted context omitted.

I don't think it is nonsensical at all. The author and his collaborator both appear to be bright people, so there's a good chance they had to offer non-trivial insights to guide the LLM, yet it's clearly in the interest of his employer to downplay whatever personal contribution they provided. Edit: Now the OP is flagged/dead for some reason. You could disagree on their take (calling it a marketing stunt is maybe a bi…

> I think the argument is sound They got flagged because it is a literal conspiracy theory that assumes bad faith.

> literal conspiracy theory

The strongest words they used were “marketing stunt”. Calling that a conspiracy theory is quite the stretch.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#512

Post by redsocksfan45 »

bonzini wrote: post #147
tptacek wrote: post #98

Earlier quoted context omitted.

I'm not complaining about Wikipedia here, just noting for the thread: it's a vector of polynomials. It has a nonsingular Jacobian. Provided with it are 3 distinct points it sends to the same point; it can't be invertible. What Wikipedia says about this doesn't matter, does it?

Wikipedia does have a rule allowing "routine calculations" https://en.wikipedia.org/wiki/Wikipedia:No_original_research... Of course given the magnitude of the statement a bit of care is warranted, but the rules do allow it.

[dead]

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#513

Post by latexr »

minimaxir wrote: post #420
gonzalohm wrote: post #414

Earlier quoted context omitted.

Proof that an LLM did it and that this is not yet again another marketing stunt. Remember when Anthropic wouldn't release Fable because it would be "the end of cyber security as we know it"? Yet here we are

This proof was posted by an individual researcher, Anthropic has not used it in any of their marketing. Additionally, posting this during the World Cup would be the most inefficient way to do marketing.

> posting this during the World Cup

The World Cup is over. This tweet was the day after.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#514

Post by mw888 »

nxtfari wrote: post #424
kelseyfrog wrote: post #131

Earlier quoted context omitted.

Same result. Public share https://claude.ai/share/19fd1a34-d63b-4a16-8d83-60d5b79e7747 It did the multiple verification sequence before expanding to internet search where it found this thread.

Everyone using Claude Fable to verify this proof is so funny. If you read the definition of the Jacobian Conjecture and (I am not exaggerating this) have passed a college Calc 3 class, you can just verify the proof yourself in 30 seconds. The problem was very hard to solve but the counterexample is very easy to verify! --- edit, adding an explanation: To summarize it, the conjecture says if you have any multi-variabl…

Something something pedantry.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#515

Post by Fredkin »

Lots of other point collisions too: {{{-1, 3/2, 13/2}, {1, -3/2, 13/2}, {0, 0, -1/4}}, {{0, 7/8, -(3479/1152)}, {48/7, 0, 49/1152}, {-(48/7), 7/16, 539/2304}}, {{-1, 7/8, -(40523/648)}, {160/7, 0, 49/5184}}, {{-2, 7/8, 2989/1296}, {32/21, 0, -(49/192)}}, {{1/63 (-120 - 16 Sqrt[3]), 7/8, 0}, {4/7 (-1 + 3 Sqrt[3]), 0, 49/288 (5 + 3 Sqrt[3])}} }; Next steps would be a simpler counterexample or family of polynomials where the conjecture breaks.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#516

Post by cornholio »

abernard1 wrote: post #456
snarkconjecture wrote: post #435

Earlier quoted context omitted.

Current LLMs can absolutely multiply floats without a tool call. In fact, that's a much more rote symbol-manipulation task than doing original math research.

With what accuracy? And with how many intermediate tokens? We can replace multiplication with any class of problems which should go from 0->100% solution almost immediately if there was actually a concept learned. There is not. Because they are plain ol' fits. And there are no "emergent" features that pop out without having a sufficient set, where "sufficient" is absolutely gigantic and equivalent to memorizing enoug…

> With what accuracy? And with how many intermediate tokens?

So you are arguing here that LLMs should just "know" the result of a multiplication when the operands are in context, ie, that a hidden multiplier circuit should emerge in their weights.

Is this how you do multiplication, if I give you two 12 digit numbers, does the 24 digit multiplication result just pop in your head? Don't you have to follow a learned algorithm through a tedious system 2 effort? Don't you need to write down the results on paper because you can't actually hold in your head the dozen partial results, each with a dozen digits? How many visual, tactile and reasoning tokens does this consume, moving the hundreds of muscles that make up your hand to draw each number under visual feedback, then reading all those numbers back and transforming ocular activation data into numeric symbols?

It seems to me your system 2 is just following a symbolic algorithm for multiplication, and it does roughly the same steps as the LLM trace I showed you previously.

So if you think this is the mark of your intelligence, why wouldn't it apply to the machine too? Why is it implausible that, following a similar algorithm learned from some mathematical paper, the LLMs has reasoned a new solution to a problem in another math field? Why couldn't the machine combine and morph these algorithms for symbolic manipulation, to yield entirely new and original results? How would those results differ from results human mathematicians generate, using recipes they learned in university?

The emergent behavior that we talk about isn't that the machine can do multiplication in its "head" after knowing the multiplication algorithm. What emerges is the ability to follow any other algorithm, even algorithms that were not in the training set, even algorithms to create other algorithms, which it then executes. This is the emergent behavior that matters for AGI; once it can do that, it's a trivial exercise to create a non-AI tool to automate and accelerate the mechanical tasks - just like we humans do it.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#517

Post by jacv »

kelseyfrog wrote: post #131
aizk wrote: post #112

This is a rare instance where feeding this groundbreaking information into an LLM gives _them_ psychosis. I fed this to claude code and watched it verify the result in 7 different ways to be 100% certain, and it was just flabbergasted. Quite remarkable.

Same result. Public share https://claude.ai/share/19fd1a34-d63b-4a16-8d83-60d5b79e7747 It did the multiple verification sequence before expanding to internet search where it found this thread.

[flagged]

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#518

Post by thin_carapace »

handoflixue wrote: post #468
thin_carapace wrote: post #169

Earlier quoted context omitted.

I've seen plenty videos of locals being violently removed from town halls due to displaying of anti AI sentiment. I wouldnt consider it fair to use these examples to tar the entirety of the pro AI camp. the way objectivity and subjectivity are intertwined in your comment is spectacular, ever considered a career in propaganda?

Accuse the enemy of propaganda; insist there's plenty of evidence without linking a single source... Have you considered maybe reading this comment out loud in front of a mirror?

umm have you considered that you can go to youtube and verify my claim whereas the other interlocutor explicitly refers to unverifiable personal anecdotes? and did you want to verify that I explicitly accused someone of propaganda?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#519

Post by [deleted] »

auggierose wrote: post #319
rowanG077 wrote: post #251

Earlier quoted context omitted.

Does anything truly better exist? I'm not a mathematician but I did use Rocq and Lean during university. And I found lean to be better.

No, something truly better does not exist yet, but that doesn't mean that it won't. Lean is young compared to Isabelle or Rocq, but actually quite old in absolut terms (and especially in AI terms).

[deleted]

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#520

Post by oska »

abc42 wrote: post #418
0x1ceb00da wrote: post #245

Earlier quoted context omitted.

[flagged]

This anti-AI sentiment is getting borderline insane.

1. There is no such thing as "Artificial Intelligence" (but yes, machine learning and LLMs are real and powerful things)

2. Calling LLMs 'AI' is part of the grifting hype that has been wildly prevalent in the US corporate space. It's very natural and also very good that there is now backlash to and scepticism around all of the hype that is has been generated over the last 5 or so years

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