https://mashable.com/tech/anthropic-fable-5-disproves-jacobian-conjecture
While the rest of the world°hard word was watching the World°hard word Cup on Sunday evening, mathematician°hard word Levent°hard word Alp°hard wordöge°hard word casually°hard word announced on X that he had used Anthropic's°hard word Fable°hard word 5 to disprove°hard word the Jacobian°hard word conjecture°hard word.
hello there the jacobian°hard word conjecture°hard word is false thanx°hard word to my close friend akhil°hard word for asking about it and my other close friend fable°hard word for working during the world°hard word cup final
((1+xy°hard word)^3 z + y^2 (1+xy°hard word) (4+3xy°hard word), y + 3 x (1+xy°hard word)^2 z + 3 x y^2 (4+3xy°hard word), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian°hard word determinant°hard word -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°hard word conjecture°hard word is a long-standing°hard word open problem in algebraic°hard word geometry°hard word that's bedeviled°hard word highly accomplished°hard word mathematicians°hard word for almost 90 years. It was included°hard word in "Smale's°hard word problems," a list of unresolved°hard word math problems put forward by mathematician°hard word Stephen°hard word Smale°hard word in 1998.
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I'm only slightly qualified°hard word to comment°hard word on the mathematics of this. It is a solution that looks "easy to find" once you see it. And it is "inspired°hard word" by a failed°hard word attempt at a counterexample°hard word from 25-odd years ago. But: we have gone from "LLMs°hard word can't do arithmetic°hard word" to "LLMs°hard word are decent°hard word at AIME-level°hard word problems but might be cheating°hard word" to "LLMs°hard word 🔥 when assisted°hard word by a Harvard°hard word math expert can solve°hard word high-profile°hard word unsolved°hard word problems" in about 5 years.
Does it have any real-world°hard word applications°hard word? No.