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An early example of a nondecimal positional number system 一个非十进制位置数字系统的早期例子
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.07.001
Libor Koudela
{"title":"An early example of a nondecimal positional number system","authors":"Libor Koudela","doi":"10.1016/j.hm.2025.07.001","DOIUrl":"10.1016/j.hm.2025.07.001","url":null,"abstract":"<div><div>The idea of nondecimal number systems was developed during the 17th century by several mathematicians, especially by Thomas Harriot, Gottfried Wilhelm Leibniz, Juan Caramuel y Lobkowitz and Erhard Weigel. Already at the end of the 16th century, a German mathematician Anton Schultze described the base-24 positional number system and showed the basic arithmetic operations in this system. Schultze did so in an example that he included in his textbook of commercial arithmetic published in 1584 and – in a slightly modified form – in an extended version of the textbook that appeared in 1600.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 2-7"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The edition of Leibniz’s mathematical writings: past, present and future 莱布尼茨的数学著作的版本：过去，现在和未来
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.07.004
Siegmund Probst
{"title":"The edition of Leibniz’s mathematical writings: past, present and future","authors":"Siegmund Probst","doi":"10.1016/j.hm.2025.07.004","DOIUrl":"10.1016/j.hm.2025.07.004","url":null,"abstract":"<div><div>The edition of Leibniz's mathematical writings is a monumental task: 10,000 manuscript pages will fill 30 volumes (out of 130 planned for his complete works). At his death (1716), only 1 book and ∼100 journal articles were published. 19th century editions by Gerhardt (1849-1863) greatly increased availability. In the 20th century, Eberhard Knobloch spearheaded the Academy Edition (Series VII), publishing 4 volumes (1990-2008) with 90% unpublished texts. Volumes 1-7 cover Leibniz's Paris years (1672-1676). Future plans: 22 more volumes in 30 years, requiring 2 to 8 editors. Collaborations (ERC Philiumm) already yield online pre-editions and translations, boosting worldwide Leibniz research.<span><span><sup>1</sup></span></span></div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 39-45"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sir Thomas Muir’s History of Determinants (1890-1930): the making of a mathematical monument 托马斯·缪尔爵士的《行列式的历史》（1890-1930）：一座数学丰碑的建立
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.08.001
Tony Crilly , Peter Elliott
{"title":"Sir Thomas Muir’s History of Determinants (1890-1930): the making of a mathematical monument","authors":"Tony Crilly ,&nbsp;Peter Elliott","doi":"10.1016/j.hm.2025.08.001","DOIUrl":"10.1016/j.hm.2025.08.001","url":null,"abstract":"<div><div>Using hitherto unpublished material we chart the creation of Sir Thomas Muir’s magnum opus on determinants, a landmark in the history of mathematics. Between 1906–1930 Muir published 5 vol on the history of determinants, a monument for which he is best remembered.</div><div>En nous référant à des documents jusqu'ici inédits, nous traçons la voie vers la publication du magnum opus de Sir Thomas Muir sur l'histoire des déterminants, un jalon dans l'histoire des mathématiques. Entre 1906 et 1930, Muir a publié 5 vol sur l'histoire des déterminants, un monument; dont on se souvient aujourd'hui.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 61-72"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.04.005
Glen Van Brummelen
{"title":"","authors":"Glen Van Brummelen","doi":"10.1016/j.hm.2025.04.005","DOIUrl":"10.1016/j.hm.2025.04.005","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 92-93"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Johannes Hjelmslev – mathematician and mathematics educator 约翰内斯·海姆斯列夫-数学家和数学教育家
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.08.002
Horst Struve , Rolf Struve
{"title":"Johannes Hjelmslev – mathematician and mathematics educator","authors":"Horst Struve ,&nbsp;Rolf Struve","doi":"10.1016/j.hm.2025.08.002","DOIUrl":"10.1016/j.hm.2025.08.002","url":null,"abstract":"<div><div>Johannes Hjelmslev (1873 - 1950) was a renowned Danish mathematician and one of the most remarkable mathematicians of his time. A special feature is that he was active in two fields, mathematics (the foundations of geometry) and the didactics of mathematics (the didactics of geometry). He not only contributed original and fruitful ideas to both areas, but also had a significant impact on the concept of mathematics and school mathematics until the present day. While historical appraisals have already been published on individual topics of his research work - for example on his so-called geometry of reality (<span><span>Lützen, 2021</span></span>) - a summarizing presentation and appraisal of his work in both fields in a historical context is still lacking. This is the aim of this article, which, incidentally, is a response on the less appreciative assessment of Hjelmslev's achievements and his geometry of reality by <span><span>Lützen (2021)</span></span>.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 73-91"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.05.001
Reinhard Siegmund-Schultze
{"title":"","authors":"Reinhard Siegmund-Schultze","doi":"10.1016/j.hm.2025.05.001","DOIUrl":"10.1016/j.hm.2025.05.001","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 94-95"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weber's Lehrbuch der Algebra and Kronecker's Vorlesungen: Similarities and differences 韦伯的《代数》与克罗内克的《Vorlesungen》：异同
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.07.003
Cédric Vergnerie
{"title":"Weber's Lehrbuch der Algebra and Kronecker's Vorlesungen: Similarities and differences","authors":"Cédric Vergnerie","doi":"10.1016/j.hm.2025.07.003","DOIUrl":"10.1016/j.hm.2025.07.003","url":null,"abstract":"<div><div>The 19<sup>th</sup> century witnessed significant developments in the field of algebra, particularly in the theory of equations, which will be the focus of this examination. The contributions of Heinrich Weber and Leopold Kronecker to this area are especially noteworthy. To explore this, the article undertakes a comparative analysis of both the structure and content of Weber's <em>Lehrbuch der Algebra</em> and Kronecker's <em>Vorlesungen über die Theorie der algebraischen Gleichungen</em>. I will then attempt to show how this study allows us to gain insight into their respective conceptions of mathematics.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 8-38"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semantic outlook and deductive structure in Bolzano’s Rein analytischer Beweis 博尔扎诺的《雷恩分析》中的语义观与演绎结构
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.07.005
Hourya Benis-Sinaceur
{"title":"Semantic outlook and deductive structure in Bolzano’s Rein analytischer Beweis","authors":"Hourya Benis-Sinaceur","doi":"10.1016/j.hm.2025.07.005","DOIUrl":"10.1016/j.hm.2025.07.005","url":null,"abstract":"<div><div>This paper aims to shed light on Bolzano’s position on language and meaning as part of the “Sprachphilosophie” current in 19th century Germany. Studied most often from the <em>Wissenschaftslehre</em>, this position is already at work in the early mathematical writings, e.g. in the <em>Rein analytischer Beweis</em>. Bolzano shows the need to develop objective semantics as a prerequisite for the deductive rigor of proofs. We must first fix the meaning of words denoting concepts, and carefully formulate propositions in order to specify their mathematical content and refer it to the corresponding discipline. This is how the autonomy of Analysis is established not only in relation to Geometry but also in relation to Algebra.</div></div><div><h3>Résumé</h3><div>Cet article vise à mettre en lumière la position de Bolzano sur le langage et la signification, qui s’inscrit dans le courant de « Sprachphilosophie » dans l’Allemagne du XIX<sup>e</sup> siècle. Étudiée le plus souvent à partir de la <em>Wissenschaftslehre</em>, cette position est déjà à l’œuvre dans les premiers écrits mathématiques, par exemple dans le <em>Rein analytischer Beweis</em>. Bolzano y montre la nécessité d’établir une sémantique objective comme préalable à la rigueur déductive des preuves. Il faut commencer par fixer le sens des mots désignant les concepts, formuler avec soin les propositions, spécifier leur contenu mathématique et le référer à la discipline correspondante. L’autonomie de l’Analyse est ainsi établie non seulement par rapport à la Géométrie, mais aussi par rapport à l’Algèbre.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 46-60"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IF 0.4 3区 哲学
Historia Mathematica Pub Date : 2025-09-01 DOI: 10.1016/j.hm.2025.07.002
Stephen Chrisomalis
{"title":"","authors":"Stephen Chrisomalis","doi":"10.1016/j.hm.2025.07.002","DOIUrl":"10.1016/j.hm.2025.07.002","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 96-97"},"PeriodicalIF":0.4,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Paris, BULAC Ara 606 and its relation to the Arabic Euclidean transmission attributed to al-Ḥajjāj 巴黎，BULAC Ara 606及其与阿拉伯欧几里得传播归因于al-Ḥajjāj的关系
IF 0.5 3区 哲学
Historia Mathematica Pub Date : 2025-06-01 DOI: 10.1016/j.hm.2025.04.002
Gregg De Young
{"title":"Paris, BULAC Ara 606 and its relation to the Arabic Euclidean transmission attributed to al-Ḥajjāj","authors":"Gregg De Young","doi":"10.1016/j.hm.2025.04.002","DOIUrl":"10.1016/j.hm.2025.04.002","url":null,"abstract":"<div><div>I introduce a recently discovered Arabic manuscript containing a version of Euclid's <em>Elements</em>: Paris, BULAC, Ara 606. In an attempt to situate Ara 606 within the Arabic Euclidean tradition, I survey the manuscript evidence currently known to me reporting characteristics of the tradition ascribed by medieval authors to al-Ḥajjāj and show that Ara 606 includes all the formulations explicitly attributed to al-Ḥajjāj. These features suggest that Ara 606 belongs to the Ḥajjāj tradition, along with Mumbai, Mullā Fīrūz, R.I.6 studied by <span><span>Brentjes</span></span> (<span><span>2006</span></span>, <span><span>2018</span></span>).</div><div>Another surprising result is that St. Petersburg, Akad. Nauk, S-2145 appears to be a hybrid manuscript, containing a traditional Isḥāq-Thābit version in books I–VI but containing a version very similar to Ara 606 in books VII–XIII. These two manuscripts thus provide an important complement to the Mumbai manuscript because they contain a Ḥajjāj-related version similar to that found in Mumbai but extending beyond book IX, where the Mumbai manuscript breaks off.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"71 ","pages":"Pages 87-126"},"PeriodicalIF":0.5,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144264110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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