Fable 5 SOLVED 87-YEAR MATH PROBLEM

@vladojoinee

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Why it worked

The video explains a complex mathematical concept in an accessible way, using clear visuals and a narrative of a long-standing problem being solved. The use of an AI model as the solver adds a modern and intriguing element, making the breakthrough more compelling.

Summary

An AI model named Fable 5 has reportedly solved the 87-year-old Jacobian Conjecture, a complex math problem concerning polynomial maps. The AI found that a specific polynomial map has a constant Jacobian determinant of -2, disproving the long-held belief that such maps are always globally reversible.

Structure

1Introduction to the Jacobian Conjecture and Fable 5's role
2Explanation of polynomial maps and the Jacobian determinant
3The core question: reversibility of transformations
4How Fable 5 disproved the conjecture with a specific counterexample
5The significance of the solution and its implications

Product placement

Fable 5 ACTS - it is used to solve a math problem, and the result is confirmed by it. Removing it would change what happens in the video. Claude Fable 5 ACTS - it is used to solve a math problem, and the result is confirmed by it. Removing it would change what happens in the video.

Original caption

Fable 5 just cracked the Jacobian Conjecture, an 87-year-old math problem, revealing a polynomial map that breaks the long-held assumption about reversibility in complex spaces. This breakthrough could redefine how we understand polynomial transformations and complex geometry. #fable5 #jacobianconjecture #mathbreakthrough #complexgeometry #polynomialmaps

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On-screen text

FABLE 5 SOLVED 87-YEAR MATH PROBLEM Jacobian Conjecture Claude's Fable 5 Just Solved a Maths Problem That Was Basically Impossible to Solve for 87 Years Jacobian Conje its called the Jacobian conjecture imagine an infinite 3d complex space every point anywhere new only use addition subtraction or multiplication in other words use polynomial equations to build this entire system called a polynomial map single point you can zoom something called the Jacobian determinant think of local stretch factor that tells you around a point gets stretched squeezed or crushed flat become impossible to tell apart now suppose that number comes out to be some constant non zero value at every single entire space no matter where nothing ever gets flattened the question is does that guarantee the whole transformation is globally reversible that every final point came from exactly one starting point or could two completely different starting points in the exact same place even though everything looks perfectly fine that's the core of the Jacobian conjecture for 87 conjecture for 87 mathematicians believed the answer was yes but nobody could prove or disprove it then came fable the jacobian conjecture 1939-2026 det J = -2 everywhere and told to reason from first principles nobody was expecting a polynomial map determinant of minus where one point could be traced different starting points Fable 5 one that was enough to falsify an 87 year old mathematical belief first posted by the result still needs peer review holds up just settled biggest problems in mathematics you can talk it and watch it lose its mind

Transcript

Fable 5 just solved this problem that Jacobian Conjecture Claude's Fable 5 Just Solved a Maths Problem That Was Basically Impossible to Solve for 87 Years for 87 years it's called the Jacobian conjecture imagine an infinite 3d complex space every point anywhere new but you can only use addition subtraction or multiplication in other words you can use polynomial equations to build this entire system called a polynomial map at any single point you can zoom in and check something called the Jacobian determinant think of it as a local stretch factor that tells you whether the space around a point gets stretched squeezed or crushed flat so nearby points become impossible to tell apart now suppose that number comes out to be some constant non zero value at every single point in the entire space no matter where you zoom in nothing ever gets flattened the question is does that guarantee the whole transformation is globally reversible that every final point came from exactly one starting point or could two completely different starting points in the exact same place even though everything looks perfectly fine that's the core of the Jacobian conjecture for 87 conjecture for 87 years mathematicians believed the answer was yes but nobody could prove or disprove it then came fable the jacobian conjecture 1939-2026 det J = -2 everywhere and told to reason from first principles nobody was expecting a polynomial map determinant of minus two where one point could be traced different starting points Fable 5 one that was enough to falsify an 87 year old mathematical belief first posted by the result still needs peer review holds up just settled one of the biggest problems in mathematics you can talk it and watch it lose its mind