https://mashable.com/tech/anthropic-fable-5-disproves-jacobian-conjecture
While the rest of the world was watching the World Cup on Sunday evening, mathematician Levent Alpöge casually announced on X that he had used Anthropic's Fable 5 to disprove the Jacobian conjecture.
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)
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 🔥 when assisted by a Harvard math expert can solve high-profile unsolved problems" in about 5 years.
Does it have any real-world applications? No.