Pub Date : 2025-09-01DOI: 10.1016/j.hm.2025.08.001
Tony Crilly , Peter Elliott
Using hitherto unpublished material we chart the creation of Sir Thomas Muir’s magnum opus on determinants, a landmark in the history of mathematics.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.
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.
在这里，你可以找到托马斯·缪尔爵士（Sir Thomas Muir）关于决定因素的巨著的创作，这是数学史上的一个里程碑。1906年至1930年间，缪尔出版了五卷关于行为人历史的书，这是他最广为人知的纪念碑。通过参考以前未发表的文献，我们为托马斯·缪尔爵士关于决定因素史的巨著的出版铺平了道路，这是数学史上的一个里程碑。从1906年到1930年，缪尔出版了五卷关于决定因素的历史，这是一座纪念碑。我们今天还记得。
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Pub Date : 2025-09-01DOI: 10.1016/j.hm.2025.08.002
Horst Struve , Rolf Struve
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 (Lützen, 2021) - 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 Lützen (2021).
Johannes Hjelmslev（1873 - 1950）是一位著名的丹麦数学家，也是他那个时代最杰出的数学家之一。他的一个特点是活跃于数学（几何基础）和数学教学法（几何教学法）两个领域。他不仅在这两个领域贡献了原创性和富有成果的思想，而且对数学和学校数学的概念产生了重大影响，直到今天。虽然对他的研究工作的个别主题已经发表了历史评价-例如他所谓的现实几何(l tzen, 2021) -在历史背景下对他在这两个领域的工作的总结和评价仍然缺乏。这是本文的目的，顺便说一句，这是对岑（2021）对海姆斯列夫的成就和他的现实几何的不太赞赏的评价的回应。
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Pub Date : 2025-09-01DOI: 10.1016/j.hm.2025.07.003
Cédric Vergnerie
The 19th 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 Lehrbuch der Algebra and Kronecker's Vorlesungen über die Theorie der algebraischen Gleichungen. I will then attempt to show how this study allows us to gain insight into their respective conceptions of mathematics.
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Pub Date : 2025-09-01DOI: 10.1016/j.hm.2025.07.005
Hourya Benis-Sinaceur
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 Wissenschaftslehre, this position is already at work in the early mathematical writings, e.g. in the Rein analytischer Beweis. 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.
Résumé
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 XIXe siècle. Étudiée le plus souvent à partir de la Wissenschaftslehre, cette position est déjà à l’œuvre dans les premiers écrits mathématiques, par exemple dans le Rein analytischer Beweis. 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.
本文旨在阐明博尔扎诺作为19世纪德国流行的“语言哲学”的一部分对语言和意义的立场。这一立场在早期的数学著作中已经开始发挥作用，例如在《雷小山分析者》中。博尔扎诺指出需要发展客观语义学作为证明的演绎严谨性的先决条件。我们必须首先确定表示概念的词语的意义，仔细地表述命题，以便明确它们的数学内容，并把它与相应的学科联系起来。分析的自主性就是这样建立起来的，不仅与几何有关，而且与代数有关。rsamsamuest第3条规定：“在Bolzano的位置上，语言和意义上的位置”，即“Sprachphilosophie”和“l’allemagne du xixsi”。Étudiée le + souvent partipartir de la Wissenschaftslehre, ceteposition est danci.com.com œuvre danci.com.com, danci.com.com, danci.com.com，例如danci.com.com分析师Beweis。Bolzano y montre la nsametessitored ' samtablir une sammantique objective comme pracalable com la rigueur dsamtive des preuves。我认为开始者和固定者都有不同的概念，提出者都有不同的命题，开始者都有不同的概念，开始者都有不同的概念，开始者都有不同的概念，开始者都有不同的概念，开始者都有不同的概念。L 'autonomie de L 'Analyse ' est ainsi samtabi not sesusuplisparetport, la samacometport, maussi paretport, L ' algubre。
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Pub Date : 2025-06-01DOI: 10.1016/j.hm.2025.04.002
Gregg De Young
I introduce a recently discovered Arabic manuscript containing a version of Euclid's Elements: 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 Brentjes (2006, 2018).
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.
{"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}
Pub Date : 2025-06-01DOI: 10.1016/j.hm.2025.03.001
Christián C. Carman , Diego Pelegrin
This paper investigates the transmission of diagrams in Copernicus' De Revolutionibus, focusing on the phenomena of overspecification and indifference to visual accuracy. Unlike previous studies that assumed the original diagrams, this research uses source diagrams to analyze how these features emerge and persist through various editions and manuscripts. The study demonstrates the gradual and independent development of overspecification and visual inaccuracies during transmission, highlighting their stability over multiple copies. Additionally, it explores errors in labeling and the introduction of spurious elements in diagrams, reinforcing the belief that these characteristics arise during the transmission process. The findings challenge the notion that these diagrammatic features were common practices confined to ancient and medieval times, showing that they persist into the 21st century.
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