Alex J Best, C. Birkbeck, Riccardo Brasca, Eric Rodriguez Boidi
{"title":"Fermat's Last Theorem for regular primes","authors":"Alex J Best, C. Birkbeck, Riccardo Brasca, Eric Rodriguez Boidi","doi":"10.48550/arXiv.2305.08955","DOIUrl":null,"url":null,"abstract":"We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \\emph{Lean} theorem prover and its mathematical library \\emph{mathlib}. This is an important 19th century result that motivated the development of modern algebraic number theory. Besides explaining the mathematics behind this result, we analyze in this paper the difficulties we faced in the formalisation process and how we solved them. For example, we had to deal with a diamond about characteristic zero fields and problems arising from multiple nested coercions related to number fields. We also explain how we integrated our work to \\emph{mathlib}.","PeriodicalId":296683,"journal":{"name":"International Conference on Interactive Theorem Proving","volume":"92 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Interactive Theorem Proving","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2305.08955","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{mathlib}. This is an important 19th century result that motivated the development of modern algebraic number theory. Besides explaining the mathematics behind this result, we analyze in this paper the difficulties we faced in the formalisation process and how we solved them. For example, we had to deal with a diamond about characteristic zero fields and problems arising from multiple nested coercions related to number fields. We also explain how we integrated our work to \emph{mathlib}.
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