A large discourse concerning algebra: John Wallis's 1685 <i>Treatise of algebra</i>

A treatise of algebra historical and practical (London 1685) by John Wallis (1616-1703) was the first full length history of algebra. In four hundred pages Wallis explored the development of algebra from its appearances in Classical, Islamic and medieval cultures to the modern forms that had evolved by the end of the seventeenth century. Wallis dwelt especially on the work of his countrymen and contemporaries, Oughtred, Harriot, Pell, Brouncker and Newton, and on his own contribution to the emergence of algebra as the common language of mathematics. This thesis explores why and how A treatise of algebra was written, and the sources Wallis used. It begins by analysing Wallis's account of mathematical learning in medieval England, never previously investigated. In his researches on the origins and spread of the numeral system Wallis was at his best as a historian, and initiated many modern historiographical techniques. His summary of algebra in Renaissance Europe was less detailed, but for Wallis this part of the story set the scene for the English flowering that was to be his main theme. The influence of Oughtred's Clavis on Wallis and his contemporaries, and Wallis's efforts to promote the book, are explored in detail. Wallis's controversial account of Harriot's algebra is also examined and it is argued that it was better founded than has sometimes been supposed and that Wallis had direct access to Harriot's algebra through Pell. Many other chapters of A treatise of algebra contain mathematics that can be linked or traced to Pell, a hitherto unsuspected secret of the book. The later chapters of the thesis, like the final part of A treatise of algebra, explore Wallis's Arithmetica infinitorum and the work which arose from it up to Newton's foundation of modern analysis, and include a discussion of Brouncker's treatment of the number challenges set by Fermat. The thesis ends with a summary of contemporary and later reactions to A treatise of algebra and an assessment of Wallis's view of algebra and its history

Enacting Inquiry Learning in Mathematics through History

International audienceWe explain how history of mathematics can function as a means for enacting inquiry learning activities in mathematics as a scientific subject. It will be discussed how students develop informed conception about i) the epistemology of mathematics, ii) of how mathematicians produce mathematical knowledge, and iii) what kind of questions that drive mathematical research. We give examples from the mathematics education at Roskilde University and we show how (teacher) students from this program are themselves capable of using history to establish inquiry learning environments in mathematics in high school. The realization is argued for in the context of an explicit-reflective framework in the sense of Abd-El-Khalick (2013) and his work in science education

Original Sources in the Mathematical Classroom

International audienceThis discussion group seeks to bring together individuals who are interested in the use of original sources in the mathematics classroom, from the perspective of a classroom teacher or a mathematics education researcher, for a discussion of issues and concerns related to their educational potential and effects. Each of the two sessions will focus on a different theme related to the use of original sources in the mathematics classroom. The two sessions will structured around a common framework but sufficiently independent of each other to allow interested individuals to participate in the second session, even if they did not participate in the first session. Both novice and more experienced users of original sources are strongly encouraged to participate in both sessions

History of Mathematics in Mathematics Education: Recent devlopments

International audience<p>This is a concise survey on the recent developments (since 2000) concerning research on the relations between History and Pedagogy of Mathematics (the <i>HPM domain</i>). Section 1 explains the rationale of the study and formulates the key issues. Section 2 gives a brief historical account of the development of the <i>HPM domain</i> with focus on the main activities in its context and their outcomes. Section 3 provides a sufficiently comprehensive bibliographical survey of the work done in this area since 2000. Finally, section 4 summarizes the main points of this study.</p

Self-Translation of Mathematical Texts in Seventeenth-Century France: The Cases of Pascal, Mersenne and Hérigone

This study investigates self-translation – the process of producing a second version of a text in another language – as it relates to three pairs of mathematical works created in Latin and French in mid-seventeenth-century France: Pierre Hérigone’s Cursus mathematicus and Cours mathématique, Marin Mersenne’s Harmonicorum libri and Harmonie universelle, and Blaise Pascal’s treatises on the Arithmetic Triangle. The investigation uses case-study methodology and self-translation research as a framework to examine why and how the three scholars produced bilingual versions of their texts, and does so against the background of the most significant contemporary social and historical factors. As research into pre-twentieth-century non-literary self-translation, it examines material and practices that have largely fallen outside the most frequently investigated areas of self-translation research. The study shows that the most common reasons for writing bilingual works in France during the period in question were related to the emergence of new and changing audiences. This was particularly attributable to the changing relationship between Latin and French: the early seventeenth century was a time of flux, where French was gradually taking over from Latin in French scholarly writing and was the language of the scientific cabinets, attended by an increasingly educated populace, while, at the same time, Latin was consolidating its position as the language of the pan-European Republic of Letters. Many French scholars who wished to maximise their audiences, both within France and across Europe, chose to write their works in Latin, slightly more opted for French, while others, including the case-study scholars, chose to compose their books in both languages. Other, more individual factors were involved in the case-study authors’ decision to self-translate, including the desire to develop ideas, teach mathematics and compose a significant musical work for as large an audience as possible. The different types of text composed by the three mathematicians and their differing motivations led to a range of approaches to self-translation and a variety of outcomes. Some features of the bilingual works are common to all three case studies, including the use of French mathematical terminology derived from its Latin equivalents, a desire to accommodate different audiences for the texts in the two languages, and the use of rhetoric, including ‘mathematical rhetoric’, in both Latin and French

The art and architecture of mathematics education: a study in metaphors

This chapter presents the summary of a talk given at the Eighth European Summer University, held in Oslo in 2018. It attempts to show how art, literature, and history, can paint images of mathematics that are not only useful but relevant to learners as they can support their personal development as well as their appreciation of mathematics as a discipline. To achieve this goal, several metaphors about and of mathematics are explored

Putting Chinese natural knowledge to work in an eighteenth-century Swiss canton: the case of Dr Laurent Garcin

Symposium: S048 - Putting Chinese natural knowledge to work in the long eighteenth centuryThis paper takes as a case study the experience of the eighteenth-century Swiss physician, Laurent Garcin (1683-1752), with Chinese medical and pharmacological knowledge. A Neuchâtel bourgeois of Huguenot origin, who studied in Leiden with Hermann Boerhaave, Garcin spent nine years (1720-1729) in South and Southeast Asia as a surgeon in the service of the Dutch East India Company. Upon his return to Neuchâtel in 1739 he became primus inter pares in the small local community of physician-botanists, introducing them to the artificial sexual system of classification. He practiced medicine, incorporating treatments acquired during his travels. taught botany, collected rare plants for major botanical gardens, and contributed to the Journal Helvetique on a range of topics; he was elected a Fellow of the Royal Society of London, where two of his papers were read in translation and published in the Philosophical Transactions; one of these concerned the mangosteen (Garcinia mangostana), leading Linnaeus to name the genus Garcinia after Garcin. He was likewise consulted as an expert on the East Indies, exotic flora, and medicines, and contributed to important publications on these topics. During his time with the Dutch East India Company Garcin encountered Chinese medical practitioners whose work he evaluated favourably as being on a par with that of the Brahmin physicians, whom he particularly esteemed. Yet Garcin never went to China, basing his entire experience of Chinese medical practice on what he witnessed in the Chinese diaspora in Southeast Asia (the ‘East Indies’). This case demonstrates that there were myriad routes to Europeans developing an understanding of Chinese natural knowledge; the Chinese diaspora also afforded a valuable opportunity for comparisons of its knowledge and practice with other non-European bodies of medical and natural (e.g. pharmacological) knowledge.postprin