Claude Fable produced a counterexample to the Jacobian Conjecture
摘要
帖文称 Jacobian 猜想为假，归功于 Claude Fable 生成的反例；给出显式映射 ((1 + xy)^3 z + y^2 (1 + xy)(4 + 3xy), y + 3x (1 + xy)^2 z + 3x y^2 (4 + 3xy), 2x - 3x^2 y - x^3 z) : C^3 → C^3，其 Jacobian 行列式为 -2，并列出三个点 (0,0,-1/4)、(1,-3/2,13/2)、(-1,3/2,13/2) 均映射至 (-1/4,0,0)；附带 Wolfram Alpha 行列式与求值链接供验证。
荐读理由
帖中给出可验证的多项式反例及Wolfram链接，帮你更新对Claude Fable类AI在构造原创数学反例上能力的判断，尽管复数域完整有效性仍有讨论
原文
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 ((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)
Jul 20, 2026 · 2:19 AM UTC
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wolframalpha.com/input?i=Det… jacobian determinant in wolfram alpha
Det[D[{(1+x y)^3 z + y^2 (1 + x y) (4 + 3x y), y + 3x (1 + x y)^2 z + 3x y^2 (4 + 3x y), 2x - 3x^2...
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
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wolframalpha.com/input?i=%28… wolframalpha.com/input?i=%28… evaluating at two of those points in wolfram alpha
((1+x y)^3 z + y^2 (1 + x y) (4 + 3x y), y + 3x (1 + x y)^2 z + 3x y^2 (4 + 3x y), 2x - 3x^2 y -...
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
wolframalpha.com
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Sort replies: Relevant Recent Liked
Replying to @alpoge
Thank you blessed math fairy
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This is the most hilarious / horrifying problem because it is like the canonical crank graveyard. Ty 4 investment🙏
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Replying to @alpoge
is this the same as in Yitang Zhang's thesis? math.purdue.edu/~ttm/Zthesis…
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Yo he is so incredible. i was at his first talk on small gaps:D the story was that he relied on a result which had a gap right
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Squeedallyboopbop@Squeedally99517
Replying to @alpoge
What a time to be alive, open up twitter before bed to see the latest clips of soccer hooliganism, find a disproof of a century old conjecture that fits in a single tweet instead
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Replying to @alpoge
Congrats!! Insane stuff... Do you think there are other counterexamples? An infinite family? Might there be a suitably refined version of the conjecture that is true?
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Replying to @alpoge
Correct me if I’m wrong but isn’t this only a valid example over the reals? Unfortunately for the complex case we need the function F to be proper (essentially all points that rush off to infinity need to be evaluated at infinity).
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Replying to @alpoge
Can you provide the full solution, thanks
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Replying to @alpoge
the speed at which certain parts of Wikipedia get updated never fails to be funny
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Replying to @alpoge
holy chet mane
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Replying to @alpoge
damn bro thats crazy
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Replying to @alpoge
investing early
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Replying to @alpoge
lmao
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Replying to @alpoge
gemini 3.1 pro says it's true so it must be. Also love the GLM-5.2 thinking trace. Do you need special tricks to convince models to work on a problem it knows is open?
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Replying to @alpoge
what was the prompt? this is crazy
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Replying to @alpoge
Congratulations!
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Replying to @alpoge
congrats
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Replying to @alpoge
is this going on the bio or nah
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Thelonious Oditamo@originaldint
Replying to @alpoge
artificial super counterexample finder confirmed my goodness
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Replying to @alpoge
Impressive
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Replying to @alpoge
🤯 Context: en.wikipedia.org/wiki/Jacobi…
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Replying to @alpoge
ok this is something that I have heard of and understood actually. Holy shit. Here before this blows up and goes down in history
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