The article's author, funded by the EPSRC to formalize a proof of Fermat's Last Theorem, said the Anthropic work does not make his project redundant because he also promised to make pull requests to Lean's mathematics library and create a dynamic document for humans to explore the modern proof. [1][8]
Anthropic announced that one of its internal models, using the prove2.me platform, formalized a complete proof of Fermat's Last Theorem in Lean, completing Freek Wiedijk's list of 100 formalization challenges. [2] Anthropic's researchers completed the task of formalizing Andrew Wiles' 1995 proof in 11 days using an internal research model. [3] The formalized proof was written in the programming language Lean and comprises 13 million lines of code, making it the largest-ever file of its kind. [4]
The codebase for the formalization is over 13.4 million lines of code and takes nearly 20 times as long to compile as Lean's mathematics library, according to the article's author who compiled it. [5] The formalized proof follows the Darmon-Diamond-Taylor 1995 exposition of the Wiles-Taylor-Wiles argument, using the Langlands-Tunnell theorem and Ribet's level-lowering theorem. [6] Kevin Buzzard, a mathematician whose work Claude used to generate the formalized proof, stated that AI autoformalization artifacts are now robust enough to be built upon. [7]En el autor del artículo, financiado por el EPSRC para formalizar una prueba del último teorema de Fermat, dijo que el trabajo de Anthropic no hace que su proyecto sea redundante, porque también prometió hacer solicitudes de extracción (pull requests) a la biblioteca de matemáticas de Lean y crear un documento dinámico para que los humanos exploren la prueba moderna. [1][8]
Anthropic anunció que uno de sus modelos internos, utilizando la plataforma prove2.me, formalizó una prueba completa del último teorema de Fermat en Lean, completando así la lista de 100 desafíos de formalización de Freek Wiedijk. [2] Los investigadores de Anthropic completaron la tarea de formalizar la prueba de 1995 de Andrew Wiles en 11 días utilizando un modelo de investigación interno. [3] La prueba formalizada fue escrita en el lenguaje de programación Lean y comprende 13 millones de líneas de código, convirtiéndose en el archivo más grande de su tipo. [4]
El código fuente de la formalización tiene más de 13.4 millones de líneas y tarda casi 20 veces más en compilar que la biblioteca de matemáticas de Lean, según el artículo citado por el autor que lo compiló. [5] La prueba formalizada sigue el modelo de Darmon-Diamond-Taylor de 1995 haciendo uso del argumento de Wiles-Taylor-Wiles, utilizando el teorema de Langlands-Tunnell y el teorema de reducción de nivel de Ribet. [6] Kevin Buzzard, un matemático cuyo trabajo fue utilizado por Claude para generar la prueba formalizada, afirma que los artefactos de autoformalización de IA son ya lo suficientemente robustos para construirse sobre ellos. [7]
Proof8 sources · 2 publishers
What this stands on
Anthropic PBC used its Claude model to create a computer-verifiable version of the proof for Fermat's Last Theorem. · SiliconANGLE
Anthropic announced that one of its internal models, using the prove2.me platform, formalized a complete proof of Fermat's Last Theorem in Lean, completing Freek Wiedijk's list of 100 formalization challenges. · Xena
Anthropic's researchers completed the task of formalizing Andrew Wiles' 1995 proof in 11 days using an internal research model. · SiliconANGLE
The formalized proof was written in the programming language Lean and comprises 13 million lines of code, making it the largest-ever file of its kind. · SiliconANGLE
The codebase for the formalization is over 13.4 million lines of code and takes nearly 20 times as long to compile as Lean's mathematics library, according to the article's author who compiled it. · Xena
The formalized proof follows the Darmon-Diamond-Taylor 1995 exposition of the Wiles-Taylor-Wiles argument, using the Langlands-Tunnell theorem and Ribet's level-lowering theorem. · Xena
Kevin Buzzard, a mathematician whose work Claude used to generate the formalized proof, stated that AI autoformalization artifacts are now robust enough to be built upon. · SiliconANGLE
The article's author, funded by the EPSRC to formalize a proof of Fermat's Last Theorem, said the Anthropic work does not make his project redundant because he also promised to make pull requests to Lean's mathematics library and create a dynamic document for humans to explore the modern proof. · Xena
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