Revue d histoire des mathé matiques最新文献

L'algèbre sans les fictions des racines : Kronecker et la théorie des caractéristiques dans les "Vorlesungen über die algebraischen Gleichungen" L 'algèbre sans的les fictions爱德蒙拜托:Kronecker与la thé奥里的caractéristiques dan的les”讲座,关于algebraischen方程"

Revue d histoire des math&#233 matiques Pub Date : 1900-01-01 DOI: 10.24033/rhm.223

Cédric VERGNERIE

{"title":"L'algèbre sans les fictions des racines : Kronecker et la théorie des caractéristiques dans les \"Vorlesungen über die algebraischen Gleichungen\"","authors":"Cédric VERGNERIE","doi":"10.24033/rhm.223","DOIUrl":"https://doi.org/10.24033/rhm.223","url":null,"abstract":"Algebra without “all the fictions about the roots of equations”: the theory of characteristics in Kronecker’s Vorlesungen über die algebraischen Gleichungen) For the better part of the second half of the nineteenth century, Leopold Kronecker gave a course on the theory of algebraic equations, which represents his Algebra lectures. In this Vorlesungen über die Theorie der algebraischen Gleichungen, he asked Algebra to be “as far as possible independent from all the fictions about the roots of equations”. We will show how Kronecker, in the context of the theory of characteristics—a generalization of Sturm’s theorem—, dealt with the concept of continuity and how, in his practice, the very notion of root is questioned. Texte reçu le 2 juillet 2018, accepté le 3 novembre 2018, révisé le 26 décembre 2018. C. Vergnerie, Université Paris Diderot – CNRS, Laboratoire SPHERE, UMR 7219, bâtiment Condorcet, case 7093, 5 rue Thomas Mann, 75205 Paris cedex 13, France. Courrier électronique : cedric.vergnerie@gmail.com Classification mathématique par sujets (2000) : 01A55. Mots clefs : Kronecker, Sturm, Gauss, Équation, Théorème fondamental de l’algèbre, histoire de l’algèbre, théorie des caractéristiques, continuité, racines.","PeriodicalId":183845,"journal":{"name":"Revue d histoire des math&#233 matiques","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122084781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Une analyse génétique de l'"Introduction à l'analyse des lignes courbes algébriques" de Gabriel Cramer (1750) 加布里埃尔·克莱默(Gabriel Cramer, 1750)的《代数曲线分析导论》的遗传分析

Revue d histoire des math&#233 matiques Pub Date : 1900-01-01 DOI: 10.24033/rhm.226

Thierry JOFFREDO

引用次数: 0

A plurality of (non)visualizations: Branch points and branch curves at the turn of the 19th century 多个(非)可视化:19世纪初的分支点和分支曲线

Revue d histoire des math&#233 matiques Pub Date : 1900-01-01 DOI: 10.24033/rhm.224

M. Friedman

{"title":"A plurality of (non)visualizations: Branch points and branch curves at the turn of the 19th century","authors":"M. Friedman","doi":"10.24033/rhm.224","DOIUrl":"https://doi.org/10.24033/rhm.224","url":null,"abstract":"— This article deals with the different ways branch points and branch curves were visualized at the turn of the 19th century. On the one hand, for branch points of complex curves one finds an abundance of visualization techniques employed. German mathematicians such as Felix Klein or Walther von Dyck were the main promoters of these numerous forms of visualization, which appeared either as two-dimensional illustrations or three-dimensional material models. This plurality of visualization techniques, however, also resulted in inadequate images that aimed to show the varied ways branch points could possibly be represented. For branch (and ramification) curves of complex surfaces, on the other hand, there were hardly any representations. When the Italian school of algebraic geometry studied branch curves systematically only partial illustrations can be seen, and branch curves were generally made “invisible”. The plurality of visualizations shifted into various forms of non-visualization. This can be seen in the different ways visualization techniques disappeared. Texte reçu le 9 novembre 2017, accepté le 16 juillet 2018, révisé le 15 août 2018. M. Friedman, Humboldt University, Cluster of Excellence Matters of Activity. Image Space Material, Sophienstr. 22a, Berlin 10178, Germany. Courrier électronique : michael.friedman@hu-berlin.de 2000 Mathematics Subject Classification : 01A55, 01A60, 14–03, 14H30, 14J99.","PeriodicalId":183845,"journal":{"name":"Revue d histoire des math&#233 matiques","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128108430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

A connected effort? American Editors Pursue Mathematical Journal Publication, 1804-1878 一个相互关联的努力?美国编辑追求数学期刊出版，1804-1878

Revue d histoire des math&#233 matiques Pub Date : 1900-01-01 DOI: 10.24033/rhm.225

Deborah KENT

引用次数: 0

Revue d histoire des math&#233 matiques最新文献