Historiography of Mathematics in the 19th and 20th Centuries

1. Front Matter

   Pages i-x

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2. Introductory Remarks

   • Volker R. Remmert, Martina R. Schneider, Henrik Kragh Sørensen

   Pages 1-8

3. The History of Mathematics in the Progress of Mankind. Modifying the Narrative Around 1800

   • Maarten Bullynck

   Pages 9-23

4. Practicing History of Mathematics in Islamicate Societies in 19th-Century Germany and France

   • Sonja Brentjes

   Pages 25-52

5. Mesopotamian Mathematics, Seen “from the Inside” (by Assyriologists) and “from the Outside” (by Historians of Mathematics)

   • Jens Høyrup

   Pages 53-78

6. Appropriating Role Models for the Mathematical Profession: Biographies in the American Mathematical Monthly Around 1900

   • Henrik Kragh Sørensen

   Pages 79-108

7. Greek Mathematics in English: The Work of Sir Thomas L. Heath (1861–1940)

   • Benjamin Wardhaugh

   Pages 109-122

8. Otto Neugebauer’s Vision for Rewriting the History of Ancient Mathematics

   • David E. Rowe

   Pages 123-141

9. The ‘Mathematization of Nature’: The Making of a Concept, and How It Has Fared in Later Years

   • H. Floris Cohen

   Pages 143-160

10. Histories of Modern Mathematics in English in the 1940s, 50s, and 60s

    • Jeremy Gray

    Pages 161-183

11. Polycephalic Euclid? Collective Practices in Bourbaki’s History of Mathematics

    • Anne-Sandrine Paumier, David Aubin

    Pages 185-218

12. Pulling Harriot Out of Newton’s Shadow: How the Norwegian Outsider Johannes Lohne Came to Contribute to Mainstream History of Mathematics

    • Reinhard Siegmund-Schultze

    Pages 219-243

13. Contextualizing Unguru’s 1975 Attack on the Historiography of Ancient Greek Mathematics

    • Martina R. Schneider

    Pages 245-267

14. Back Matter

    Pages 269-276

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This book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written.

In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different motivations and aims. These backgrounds often shaped not only their writing on the history of mathematics, but, in some instances, were also influential in their subsequent reception.

During the period from roughly 1880-1940, mathematics modernized in important ways, with regard to its content, its conditions for cultivation, and its identity; and the writing of the history of mathematics played into the last part in particular.

Parallel to the modernization of mathematics, the history of mathematics gradually evolved into a field of research with its own journals, societies and academic positions. Reflecting both

a new professional identity and changes in its primary audience, various shifts of perspective in the way the history of mathematics was and is written can still be observed to this day. Initially concentrating on major internal, universal developments in certain sub-disciplines of mathematics, the field gradually gravitated towards a focus on contexts of knowledge production involving individuals, local practices, problems, communities, and networks.

The goal of this book is to link these disciplinary and methodological changes in the history of mathematics to the broader cultural contexts of its practitioners, namely the historians of mathematics during the period in question.

• historiography of mathematics
• cultural context
• 19th and 20th centuries
• history of mathematics
• historiography of ancient mathematics
• historiography of modern mathematics

“The editors have compiled eleven articles with the aim of showing ‘through detailed case studies how the historiography of mathematics has been influenced by the contexts and motivations of its practitioners.’ … Each article can be read independently of the rest. … Professional historians and mathematicians with a curiosity about the work of historians will find much of interest here.” (Daniel J. Curtin, MAA Reviews, maa.org, July, 2017)

• Interdisziplinäres Zentrum für Wissenschafts- und Technikforschung (IZWT), Bergische Universität Wuppertal, Wuppertal, Germany

  Volker R. Remmert

• Institut für Mathematik, AG Geschichte der Mathematik, Johannes Gutenberg-Universität Mainz, Mainz, Germany

  Martina R. Schneider

• Department of Science Education, University of Copenhagen, Copenhagen, Denmark

  Henrik Kragh Sørensen