Pub Date : 2020-12-06DOI: 10.1080/26375451.2020.1847505
M. Diniz, D. Bellhouse
The first English translation of Huygens' (1657) De Ratiociniis in Ludo Aleae was anonymously published in 1692; since the early eighteenth century it has been assigned to the Scottish physician John Arbuthnot (1667–1735). We have found evidence showing that Arbuthnot's work on probability was influenced by Archibald Pitcairne (1652–1713) and, most significantly, by David Gregory (1659–1708). Manuscripts found in Gregory's collection at the Edinburgh University Library suggest that Gregory had a key role in the translation. The circumstantial evidence presented in this article reveals that the circle of individuals led by Gregory, Arbuthnot and Pitcairne probably originated earlier than previously established and that the role of Arbuthnot was more important than originally thought. We have also shown that the first developments of probability theory in Great Britain took place in Scotland thanks to David Gregory.
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Pub Date : 2020-11-25DOI: 10.1080/26375451.2020.1851120
J. Bair, Piotr Błaszczyk, R. Ely, M. Katz, Karl Kuhlemann
Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g. Ishiguro, Levey) opt for a default Weierstrassian framework, Arthur compares LC to a non-Archimedean framework SIA (Smooth Infinitesimal Analysis) of Lawvere–Kock–Bell. We analyze Arthur's comparison and find it rife with equivocations and misunderstandings on issues including the non-punctiform nature of the continuum, infinite-sided polygons, and the fictionality of infinitesimals. Rabouin and Arthur claim that Leibniz considers infinities as contradictory, and that Leibniz' definition of incomparables should be understood as nominal rather than as semantic. However, such claims hinge upon a conflation of Leibnizian notions of bounded infinity and unbounded infinity, a distinction emphasized by early Knobloch. The most faithful account of LC is arguably provided by Robinson's framework for infinitesimal analysis. We exploit an axiomatic framework for infinitesimal analysis SPOT to formalize LC.
{"title":"Procedures of Leibnizian infinitesimal calculus: an account in three modern frameworks","authors":"J. Bair, Piotr Błaszczyk, R. Ely, M. Katz, Karl Kuhlemann","doi":"10.1080/26375451.2020.1851120","DOIUrl":"https://doi.org/10.1080/26375451.2020.1851120","url":null,"abstract":"Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g. Ishiguro, Levey) opt for a default Weierstrassian framework, Arthur compares LC to a non-Archimedean framework SIA (Smooth Infinitesimal Analysis) of Lawvere–Kock–Bell. We analyze Arthur's comparison and find it rife with equivocations and misunderstandings on issues including the non-punctiform nature of the continuum, infinite-sided polygons, and the fictionality of infinitesimals. Rabouin and Arthur claim that Leibniz considers infinities as contradictory, and that Leibniz' definition of incomparables should be understood as nominal rather than as semantic. However, such claims hinge upon a conflation of Leibnizian notions of bounded infinity and unbounded infinity, a distinction emphasized by early Knobloch. The most faithful account of LC is arguably provided by Robinson's framework for infinitesimal analysis. We exploit an axiomatic framework for infinitesimal analysis SPOT to formalize LC.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"170 - 209"},"PeriodicalIF":0.4,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1851120","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42091594","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}
Pub Date : 2020-11-18DOI: 10.1080/26375451.2020.1841477
Paul Ranford
I must make it clear from the outset that I enjoyed this book, not as a historian (for the history is open to sharp criticism) but for the vicarious pleasure of watching a mathematical physicist an...
{"title":"Hot molecules, cold electrons","authors":"Paul Ranford","doi":"10.1080/26375451.2020.1841477","DOIUrl":"https://doi.org/10.1080/26375451.2020.1841477","url":null,"abstract":"I must make it clear from the outset that I enjoyed this book, not as a historian (for the history is open to sharp criticism) but for the vicarious pleasure of watching a mathematical physicist an...","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"53 - 55"},"PeriodicalIF":0.4,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1841477","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48588871","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}
Pub Date : 2020-11-17DOI: 10.1080/26375451.2020.1819739
C. Mac an Bhaird
{"title":"Thomas Harriot: a life in science","authors":"C. Mac an Bhaird","doi":"10.1080/26375451.2020.1819739","DOIUrl":"https://doi.org/10.1080/26375451.2020.1819739","url":null,"abstract":"","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"43 2","pages":"50 - 51"},"PeriodicalIF":0.4,"publicationDate":"2020-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1819739","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41275287","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}
Pub Date : 2020-10-27DOI: 10.1080/26375451.2020.1823606
G. Schubring
{"title":"Dirichlet. A mathematical biography","authors":"G. Schubring","doi":"10.1080/26375451.2020.1823606","DOIUrl":"https://doi.org/10.1080/26375451.2020.1823606","url":null,"abstract":"","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"55 - 58"},"PeriodicalIF":0.4,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1823606","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48605622","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}
Pub Date : 2020-10-11DOI: 10.1080/26375451.2020.1819740
Gavin Hitchcock
{"title":"New light on George Boole","authors":"Gavin Hitchcock","doi":"10.1080/26375451.2020.1819740","DOIUrl":"https://doi.org/10.1080/26375451.2020.1819740","url":null,"abstract":"","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"36 1","pages":"51 - 53"},"PeriodicalIF":0.4,"publicationDate":"2020-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1819740","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43977616","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}
Pub Date : 2020-09-01DOI: 10.1080/26375451.2020.1811579
{"title":"BSHM Meeting News","authors":"","doi":"10.1080/26375451.2020.1811579","DOIUrl":"https://doi.org/10.1080/26375451.2020.1811579","url":null,"abstract":"","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"35 1","pages":"256 - 262"},"PeriodicalIF":0.4,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1811579","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45446360","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}
Pub Date : 2020-09-01DOI: 10.1080/26375451.2020.1797342
A. McQuoid
One would assume that to the twenty-first-century educator, and undoubtedly pupil, an eighteenth-century textbook would appear to be a far cry from the pedagogical standards of today. However, this...
{"title":"Leonhard Euler’s Letters to a German Princess: A milestone in the history of physics textbooks and more","authors":"A. McQuoid","doi":"10.1080/26375451.2020.1797342","DOIUrl":"https://doi.org/10.1080/26375451.2020.1797342","url":null,"abstract":"One would assume that to the twenty-first-century educator, and undoubtedly pupil, an eighteenth-century textbook would appear to be a far cry from the pedagogical standards of today. However, this...","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"35 1","pages":"251 - 253"},"PeriodicalIF":0.4,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1797342","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48512578","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}
Pub Date : 2020-09-01DOI: 10.1080/26375451.2020.1777781
Deepak Basyal
The Rana regime (1846–1951) in Nepal is widely known for its lack of support for public education and its notorious opposition to women's rights. Near the end of that regime, a mathematical textbook composed in the form of poetic verses was published in the Nepali language, purportedly written by a female author. This article explores the provenance, presentation style, authorship mystery, and unique mathematical content of this book. Furthermore, we explore how mathematical problems may reveal socio-cultural aspects of a country, and how original historical sources such as the one examined in this paper can be useful in the teaching and learning of mathematics today.
{"title":"A mathematical poetry book from Nepal","authors":"Deepak Basyal","doi":"10.1080/26375451.2020.1777781","DOIUrl":"https://doi.org/10.1080/26375451.2020.1777781","url":null,"abstract":"The Rana regime (1846–1951) in Nepal is widely known for its lack of support for public education and its notorious opposition to women's rights. Near the end of that regime, a mathematical textbook composed in the form of poetic verses was published in the Nepali language, purportedly written by a female author. This article explores the provenance, presentation style, authorship mystery, and unique mathematical content of this book. Furthermore, we explore how mathematical problems may reveal socio-cultural aspects of a country, and how original historical sources such as the one examined in this paper can be useful in the teaching and learning of mathematics today.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"35 1","pages":"189 - 206"},"PeriodicalIF":0.4,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1777781","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42643806","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}
Pub Date : 2020-08-19DOI: 10.1080/26375451.2020.1805934
Ellen Abrams
In the early twentieth century, researchers in the United States engaged with foundational studies in mathematics by building and evaluating postulate systems. At the same time, their contemporaries were evaluating the meaning and politics of knowledge more broadly. This article argues that the study of postulates in the United States was tied to important Progressive Era questions about the nature of knowledge, the status of the knower, and the development of American Pragmatism. While most investigations of postulate studies have considered their implications within mathematical research and education, this article looks instead to the role of postulate studies in the professionalization of mathematics in the United States and to its cultural status more broadly.
{"title":"‘An inalienable prerogative of a liberated spirit’: postulating American mathematics","authors":"Ellen Abrams","doi":"10.1080/26375451.2020.1805934","DOIUrl":"https://doi.org/10.1080/26375451.2020.1805934","url":null,"abstract":"In the early twentieth century, researchers in the United States engaged with foundational studies in mathematics by building and evaluating postulate systems. At the same time, their contemporaries were evaluating the meaning and politics of knowledge more broadly. This article argues that the study of postulates in the United States was tied to important Progressive Era questions about the nature of knowledge, the status of the knower, and the development of American Pragmatism. While most investigations of postulate studies have considered their implications within mathematical research and education, this article looks instead to the role of postulate studies in the professionalization of mathematics in the United States and to its cultural status more broadly.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"35 1","pages":"225 - 245"},"PeriodicalIF":0.4,"publicationDate":"2020-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/26375451.2020.1805934","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45037031","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}
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