alt Hacker NewsClaude Fable produced a counterexample to the Jacobian Conjecture
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Related:
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I just fed this to GPT 5.6 Sol:
Counterexample to Jacobian conjecture:
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
"As written, this is an explicit counterexample to the Jacobian conjecture. I checked it using exact symbolic algebra.
I do not see an algebraic catch in what you typed. Unless a term or exponent differs from the intended expression, it appears to disprove the conjecture. This deserves serious independent checking rather than casual dismissal."
Waiting for someone to write the Lean proof.
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For the people saying goalposts have moved etc, whats your endgame?
Actual tweet:
>> hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
So where does it say that Fable "produced" the counterexample? The tweet says it was a collaboration between two people, using Fable.
What’s more Impressive you got Fable to do anything useful.
The model is still useless for real data to day work, no matter how many parlor trucks it performs.
A counterexample to the Jacobian Conjecture - and also a counterexample to “AI will never be smarter than humans.” Even the most dyed-in-the-wool AI hater at this point must acknowledge that it is more intelligent than any human. The other day I found out that Fable could read seal script! The small seal, standardized stuff no prob, but I found it even did OK at the hardest you can get, Warring States regional scripts. That’s something maybe 2,000 academics worldwide can do and nobody’s even talking about it because it’s just one more item in a very long list.
It’s a strange feeling, to be overtaken by our own creation. Top dog for millions of years and then in the blink of an eye we go from “how many Rs in strawberry” to this.
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 creativity. It does not. Anyone that's proved things via "diagram chasing" can affirm that. The conclusion you should draw is that math (at least the kind they excel at) isn't actually a creative endeavor.