‘hello there the jacobian conjecture is false thanx’: why a tiny social media post has mathematicians rethinking AI

Per The Conversation, mathematician Levent Alpöge at Anthropic announced this week that he solved a century-old puzzle in algebraic geometry using Anthropic's recently released Fable 5 language model. The Jacobian conjecture, posed in eighteen eighty-four, has resisted proof for generations. His counterexample is remarkably simple—short enough for a social media post—and proves it false for all dimensions beyond two. The discovery illustrates how large language models can excel not just at intricate reasoning, but at navigating vast search spaces to find unexpected solutions that humans couldn't efficiently uncover alone.

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