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

  • Johanna PejlareEmail author
  • Kajsa Bråting
Living reference work entry


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.


History of mathematics Epistemology of mathematics Interpretations History and heritage Synchronic and diachronic perspectives Recapitulation 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of Technology and the University of GothenburgGöteborgSweden
  2. 2.Department of EducationUppsala UniversityUppsalaSweden

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

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