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Why?
There will be more and more mathematical proofs provided by LLMs as they improve. If you assume every one is just a marketing tactic, you'll drive yourself insane.
The poster works at Anthropic, so they likely have internal access to the next generation of Fable. Their internal model is probably an absolute beast at mathematics, and the upcoming benchmark results will likely set a new record for maths performance. I suspect this is what happened, because the poster is coy about sharing the actual prompt / reasoning trace used to reach this result. That would be covered by an ND…
Sol is able to find the same counter example independently [1], so no reason to conclude in the existence of a benchmark destroying math beast Fable 6.
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Wikipedia's gonna Wikipedia. Unless there's a material debate over the Jacobian Conjecture itself, there's really no open question here. This isn't a complicated proof; it's a straightforwardly checkable certificate of a solution.
I removed the "claimed" weasel wording, and now others have followed up. The editors that don't understand math and don't realize how easily this counterexample can be confirmed have lost the debate -- not that there really ever was one.
Luckily there is now a New Scientist article to link to, so, the issue should now be resolved.
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If we don't ask for proof when someone claims something, the next few years are going to be rough for everyone. We can't trust anything nowadays
They have provided a literal mathematical proof.
Remember when Anthropic wouldn't release Fable because it would be "the end of cyber security as we know it"? Yet here we are
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The field now favors into the view that symbolic manipulation is not the mechanism of general intelligence, but rather an emergent byproduct of learning. So the fact that a connectionist machine (neural network) got so good at symbolic manipulation actually supports the view that we are closing the gap to general intelligence. Through the rote work, the machine really internalizes those rules and the symbolic manipul…
I am not confused. Because herein these forums, I predicted everything that was going to happen years ago. And the "insane inefficiency" of deep learning is fully to be expected from how it works. As well, there are provably no—literally no—emergent properties in these models. The choice of metric was a convenient, sloppy, and embarrassing fault of the field. It should be discredited; the field should be embarrassed;…
I mean, lol.
This is so unreasonable! As @__alpoge__ himself notes this is classic crank graveyard territory and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search. Wild!
> and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search Is that true? Even restricting this to f(x,y,z) and coefficients and powers to 1 ≤ x ≤ 10, there are a lot of polynomials to check, and checking requires checking the Jacobian determinant and, if it’s a non zero constant, finding two points for which the polynomial produces the same value. Or is there a way t…
Be fun to ask Fable to write a search program to find more counter examples using only early grad theory to guide the search.
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I told GPT5.6 I came up with this walking down the street. "Jesus Christ" was its response.
Lol, you must have some custom instructions on that beast, lol
A little over 10 years ago I remember meeting a postdoc who believed he had something close to a counterexample to the Jacobian Conjecture. He and another person was bruteforcing polynomials in about 16 variables, something like 80 - 700 terms each, using binary trees for mapping coefficients. They were guessing, at the time, that the lower bound of a counterexample (P, Q) for max(deg(P), deg(Q)) would go up to 200.…
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So many mathematicians over the years tried hard and failed, but now Anthropic just for some PR magically did it? And this after LLMs obtaining different math wins? What is your logic here really escapes my understanding.
The parent's absolutely nonsensical post highlights how polarized AI (as everything else) is today. I can understand someone being opposed to AI on moral, cost-benefit or productivity grounds. But we're seeing a lot of extremist "AI is good for nothing" posts out there nowadays.
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They have provided a literal mathematical proof.
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
Additionally, posting this during the World Cup would be the most inefficient way to do marketing.