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

Andrei Rodin
{"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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Roger Godement et les fonctions de type positif Winning Lights Out with Fibonacci A Mathematical Model of The Effects of Strike On Nigerian Universities Generalized Carlos Scales Samgamagrāma Mādhava: An Updated Biography
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1