Pub Date : 2025-12-01DOI: 10.1016/j.hm.2025.06.001
Viktor Blåsjö
Gil-Férez et al. (2025) claim to prove Euclid's fourth postulate by strictly Euclidean means. In fact, however, they assume a principle that is neither stated nor used by Euclid. This is all the more impermissible since this inserted assumption precludes established interpretations of the fourth postulate in terms of cone points, homogeneity of space, and line-extension uniqueness.
gil - fsamurez等人（2025）声称用严格的欧几里得方法证明了欧几里得的第四个公设。然而事实上，它们假设的原理既没有被欧几里得陈述过，也没有被欧几里得使用过。这是更不允许的，因为这个插入的假设排除了第四个假设在锥点、空间同质性和线延伸唯一性方面的既定解释。
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Pub Date : 2025-12-01DOI: 10.1016/j.hm.2025.09.004
Norbert Schappacher
The paper outlines the history of libraries at the Strasbourg Universities between the 1880s and post WWII, and focusses on the history of the Strasbourg mathematics library, in particular on its unlikely enrichment during the second WW. The German period of Strasbourg ended with the German defeat in 1918. The subsequent French period was disrupted by the 1939 evacuation of Strasbourg and the annexation of Alsace-Lorraine by the Nazi government in 1940. When Strasbourg was liberated in November 1944, most of the mathematical library was put up elsewhere, a large part of it at Oberwolfach.
{"title":"National pride in the interest of science? The Strasbourg mathematical library between Germany and France","authors":"Norbert Schappacher","doi":"10.1016/j.hm.2025.09.004","DOIUrl":"10.1016/j.hm.2025.09.004","url":null,"abstract":"<div><div>The paper outlines the history of libraries at the Strasbourg Universities between the 1880s and post WWII, and focusses on the history of the Strasbourg mathematics library, in particular on its unlikely enrichment during the second WW. The German period of Strasbourg ended with the German defeat in 1918. The subsequent French period was disrupted by the 1939 evacuation of Strasbourg and the annexation of Alsace-Lorraine by the Nazi government in 1940. When Strasbourg was liberated in November 1944, most of the mathematical library was put up elsewhere, a large part of it at Oberwolfach.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"73 ","pages":"Article 103185"},"PeriodicalIF":0.4,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747777","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 : 2025-12-01DOI: 10.1016/j.hm.2025.07.006
Thomas Preveraud
Nathaniel Bowditch (1773-1838), a leading mathematician of the young American Republic, authored numerous works in mathematical astronomy. As a reader of Pierre-Simon de Laplace, he translated and annotated with rich commentary the first four volumes of Laplace’s Mécanique céleste (1799-1825), which were published in Boston between 1829 and 1839. At a time when mathematical practice had little institutional support in the United States, Bowditch contributed to the dissemination of mathematical knowledge produced in France since the Revolution, particularly the works in analysis and mathematical physics by Laplace, Lagrange, or Legendre, which he deemed insufficiently known on his side of the Atlantic.
This article studies Bowditch’s library, which contained over 1,000 documents acquired between 1788 and 1838. The study comprises three movements that analyze the mathematical part of the library from different perspectives. Firstly, we characterize the books and periodicals held by Bowditch in terms of content, publication date and geographical origin. Doing so, we highlight the great diversity of thematic contents – from analysis to mathematical astronomy – and the central place occupied by very contemporary European (especially French) documents in the library. The second result highlights the material and intellectual dynamics that guided the constitution of the library throughout Bowditch’s life. Finally, the article demonstrates how the library’s works were used by its owner in his scholarly productions and supports the thesis of a library for practical use.
In the study of the processes of mathematical heritage, the article contributes to understanding the role of private libraries in the constitution and circulation of a body of knowledge in a territory still marked by great institutional precariousness in scientific practice.
{"title":"The library of Nathaniel Bowditch: Creating, holding, and using a mathematical books collection in the early 19th century United States","authors":"Thomas Preveraud","doi":"10.1016/j.hm.2025.07.006","DOIUrl":"10.1016/j.hm.2025.07.006","url":null,"abstract":"<div><div>Nathaniel Bowditch (1773-1838), a leading mathematician of the young American Republic, authored numerous works in mathematical astronomy. As a reader of Pierre-Simon de Laplace, he translated and annotated with rich commentary the first four volumes of Laplace’s <em>Mécanique céleste</em> (1799-1825), which were published in Boston between 1829 and 1839. At a time when mathematical practice had little institutional support in the United States, Bowditch contributed to the dissemination of mathematical knowledge produced in France since the Revolution, particularly the works in analysis and mathematical physics by Laplace, Lagrange, or Legendre, which he deemed insufficiently known on his side of the Atlantic.</div><div>This article studies Bowditch’s library, which contained over 1,000 documents acquired between 1788 and 1838. The study comprises three movements that analyze the mathematical part of the library from different perspectives. Firstly, we characterize the books and periodicals held by Bowditch in terms of content, publication date and geographical origin. Doing so, we highlight the great diversity of thematic contents – from analysis to mathematical astronomy – and the central place occupied by very contemporary European (especially French) documents in the library. The second result highlights the material and intellectual dynamics that guided the constitution of the library throughout Bowditch’s life. Finally, the article demonstrates how the library’s works were used by its owner in his scholarly productions and supports the thesis of a library for practical use.</div><div>In the study of the processes of mathematical heritage, the article contributes to understanding the role of private libraries in the constitution and circulation of a body of knowledge in a territory still marked by great institutional precariousness in scientific practice.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"73 ","pages":"Article 103177"},"PeriodicalIF":0.4,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747778","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 : 2025-11-24DOI: 10.1016/j.hm.2025.11.001
Giovanni Gaia
The article aims to explore the value assigned to pi in Roman literature. Selected passages from technical and erudite works have been analyzed to contextualize how this value was used. The results indicate that the correct value of the ratio between a circle's circumference and its diameter, as discovered by Archimedes, was widely known. However, the ways in which it was utilized vary significantly from one author to another.
L'articolo mira a esplorare il valore attribuito a π nella letteratura romana. Sono stati analizzati passaggi selezionati da opere tecniche ed erudite per contestualizzare come veniva utilizzato tale valore. I risultati indicano che il valore corretto del rapporto tra la circonferenza di un cerchio e il suo diametro, scoperto da Archimede, era ampiamente conosciuto. Tuttavia, i modi in cui veniva impiegato variano significativamente da un autore all'altro.
{"title":"The value of π in Latin erudite and technical literature","authors":"Giovanni Gaia","doi":"10.1016/j.hm.2025.11.001","DOIUrl":"10.1016/j.hm.2025.11.001","url":null,"abstract":"<div><div>The article aims to explore the value assigned to pi in Roman literature. Selected passages from technical and erudite works have been analyzed to contextualize how this value was used. The results indicate that the correct value of the ratio between a circle's circumference and its diameter, as discovered by Archimedes, was widely known. However, the ways in which it was utilized vary significantly from one author to another.</div><div>L'articolo mira a esplorare il valore attribuito a π nella letteratura romana. Sono stati analizzati passaggi selezionati da opere tecniche ed erudite per contestualizzare come veniva utilizzato tale valore. I risultati indicano che il valore corretto del rapporto tra la circonferenza di un cerchio e il suo diametro, scoperto da Archimede, era ampiamente conosciuto. Tuttavia, i modi in cui veniva impiegato variano significativamente da un autore all'altro.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"73 ","pages":"Article 103193"},"PeriodicalIF":0.4,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584293","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 : 2025-09-01DOI: 10.1016/j.hm.2025.07.001
Libor Koudela
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.
{"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}
Pub Date : 2025-09-01DOI: 10.1016/j.hm.2025.07.004
Siegmund Probst
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.1
{"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}
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