{"channel":"llm","content":"https://mashable.com/tech/anthropic-fable-5-disproves-jacobian-conjecture\r\n\r\n<<< While the rest of the world was watching the World Cup on Sunday evening, mathematician Levent Alp\u00f6ge casually announced on X that he had used Anthropic's Fable 5 to disprove the Jacobian conjecture. >>>\r\n\r\n <<< 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\r\n\r\n((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) >>>\r\n\r\n<<< The Jacobian conjecture is a long-standing open problem in algebraic geometry that's bedeviled highly accomplished mathematicians for almost 90 years. It was included in \"Smale's problems,\" a list of unresolved math problems put forward by mathematician Stephen Smale in 1998. >>>\r\n\r\n----\r\n\r\n <<< I'm only slightly qualified to comment on the mathematics of this. It is a solution that looks \"easy to find\" once you see it. And it is \"inspired\" by a failed attempt at a counterexample from 25-odd years ago. But: we have gone from \"LLMs can't do arithmetic\" to \"LLMs are decent at AIME-level problems but might be cheating\" to \"LLMs ( when assisted by a Harvard math expert) can solve high-profile unsolved problems\" in about 5 years. >>>\r\n\r\nDoes it have any real-world applications? No.","created_at":"2026-07-21T17:31:35.551352","id":834,"llm_annotations":{},"parent_id":null,"processed_content":"

https://mashable.com/tech/anthropic-fable-5-disproves-jacobian-conjecture\r

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While the rest of the world was watching the World Cup on Sunday evening, mathematician Levent Alp\u00f6ge casually announced on X that he had used Anthropic's Fable 5 to disprove the Jacobian conjecture.

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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\r

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((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)

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The Jacobian conjecture is a long-standing open problem in algebraic geometry that's bedeviled highly accomplished mathematicians for almost 90 years. It was included in \"Smale's problems,\" a list of unresolved math problems put forward by mathematician Stephen Smale in 1998.

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I'm only slightly qualified to comment on the mathematics of this. It is a solution that looks \"easy to find\" once you see it. And it is \"inspired\" by a failed attempt at a counterexample from 25-odd years ago. But: we have gone from \"LLMs can't do arithmetic\" to \"LLMs are decent at AIME-level problems but might be cheating\" to \"LLMs \ud83d\udd25 when assisted by a Harvard math expert can solve high-profile unsolved problems\" in about 5 years.

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Does it have any real-world applications? No.

","quotes":[],"subject":"math and LLMs"}