Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to the Mathematics of Today

Johanna Pejlare () and Kajsa Bråting ()
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Johanna Pejlare: Chalmers University of Technology and the University of Gothenburg, Department of Mathematical Sciences
Kajsa Bråting: Uppsala University, Department of Education

Chapter 90 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 2395-2420 from Springer

Abstract: Abstract In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past, as well as the distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from the seventeenth century. Two complementary but different ways of analyzing the mathematics of the past are the synchronic and diachronic perspectives, which may be useful, for instance, regarding the history of school mathematics. Furthermore, recapitulation, or the belief that students’ conceptual development in mathematics is paralleled to the historical epistemology of mathematics, is problematized emphasizing the important role of culture.

Keywords: History of mathematics; Epistemology of mathematics; Interpretations; History and heritage; Synchronic and diachronic perspectives; Recapitulation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/978-3-319-57072-3_63

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