{"title":"弗拉基米尔-沃耶沃茨基在与安德烈-罗丹的书信往来中谈及数学结构的概念","authors":"Andrei Rodin","doi":"arxiv-2409.02935","DOIUrl":null,"url":null,"abstract":"In 2016 Vladimir Voevodsky sent the author an email message where he\nexplained his conception of mathematical structure using a historical example\nborrowed from the \\emph{Commentary to the First Book of Euclid's Elements} by\nProclus; this message was followed by a short exchange where Vladimir clarified\nhis conception of structure. In this Chapter Voevodsky's historical example is\nexplained in detail, and the relevance of Voevodsky's conception of\nmathematical structure in Homotopy Type theory is shown. The Chapter also\ndiscusses some related historical and philosophical issues risen by Vladimir\nVoevodsky in the same email exchange. This includes a comparison of Voevodsky's\nconception of mathematical structure and other conceptions of structure found\nin the current literature. The concluding part of this Chapter includes\nrelevant fragments of the email exchange between Vladimir Voevodsky and the\nauthor.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"73 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Vladimir Voevodsky on the concept of mathematical structure in his letter exchange with Andrei Rodin\",\"authors\":\"Andrei Rodin\",\"doi\":\"arxiv-2409.02935\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 2016 Vladimir Voevodsky sent the author an email message where he\\nexplained his conception of mathematical structure using a historical example\\nborrowed from the \\\\emph{Commentary to the First Book of Euclid's Elements} by\\nProclus; this message was followed by a short exchange where Vladimir clarified\\nhis conception of structure. In this Chapter Voevodsky's historical example is\\nexplained in detail, and the relevance of Voevodsky's conception of\\nmathematical structure in Homotopy Type theory is shown. The Chapter also\\ndiscusses some related historical and philosophical issues risen by Vladimir\\nVoevodsky in the same email exchange. This includes a comparison of Voevodsky's\\nconception of mathematical structure and other conceptions of structure found\\nin the current literature. The concluding part of this Chapter includes\\nrelevant fragments of the email exchange between Vladimir Voevodsky and the\\nauthor.\",\"PeriodicalId\":501462,\"journal\":{\"name\":\"arXiv - MATH - History and Overview\",\"volume\":\"73 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - History and Overview\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.02935\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02935","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
2016年,弗拉基米尔-沃韦沃德斯基给笔者发来一封电子邮件,他用一个历史性的例子解释了他的数学结构概念,这个例子借用了普罗克洛斯(Proclus)的《欧几里得圆方程第一册注释》(emph{Commentary to the First Book of Euclid's Elements});随后,弗拉基米尔在简短的交流中澄清了他的结构概念。本章详细解释了沃耶沃茨基的历史例子,并说明了沃耶沃茨基的数学结构概念与同调类型理论的相关性。本章还讨论了弗拉基米尔-沃韦沃德斯基在同一封电子邮件中提出的一些相关的历史和哲学问题。本章还讨论了弗拉基米尔-沃耶沃德斯基在同一封电子邮件中提出的一些相关的历史和哲学问题,包括比较沃耶沃德斯基的数学结构概念和当前文献中的其他结构概念。本章的结论部分包括弗拉基米尔-沃耶沃德斯基与作者之间电子邮件交流的相关片段。
Vladimir Voevodsky on the concept of mathematical structure in his letter exchange with Andrei Rodin
In 2016 Vladimir Voevodsky sent the author an email message where he
explained his conception of mathematical structure using a historical example
borrowed from the \emph{Commentary to the First Book of Euclid's Elements} by
Proclus; this message was followed by a short exchange where Vladimir clarified
his conception of structure. In this Chapter Voevodsky's historical example is
explained in detail, and the relevance of Voevodsky's conception of
mathematical structure in Homotopy Type theory is shown. The Chapter also
discusses some related historical and philosophical issues risen by Vladimir
Voevodsky in the same email exchange. This includes a comparison of Voevodsky's
conception of mathematical structure and other conceptions of structure found
in the current literature. The concluding part of this Chapter includes
relevant fragments of the email exchange between Vladimir Voevodsky and the
author.