© 2017

Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe

  • Lesley B. Cormack
  • Steven A. Walton
  • John A. Schuster

Part of the Studies in History and Philosophy of Science book series (AUST, volume 45)

Table of contents

About this book


This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners (those who know by doing) and scholars (those who know by thinking). These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new methods, new subjects of enquiry, and new social structures of natural philosophy and science.

The case for connection between theory and practice can be most persuasively drawn in the area of mathematics, which is the focus of this book. Practical mathematics was a growing field in early modern Europe and these essays are organised into three parts which contribute to the debate about the role of mathematical practice in the Scientific Revolution. First, they demonstrate the variability of the identity of practical mathematicians, and of the practices involved in their activities in early modern Europe. Second, readers are invited to consider what practical mathematics looked like and that although practical mathematical knowledge was transmitted and circulated in a wide variety of ways, participants were able to recognize them all as practical mathematics. Third, the authors show how differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced: social, cultural, political, and economic particularities matter. Historians of science, especially those interested in the Scientific Revolution period and the history of mathematics will find this book and its ground-breaking approach of particular interest.


E.G.R. Taylor Edgar Zilsel Joseph Needham Mathematical Practitioners Mathematical instruments Scholar and craftsman thesis Scientific Revolution Theory and practice in history of science Zilsel Thesis

Editors and affiliations

  • Lesley B. Cormack
    • 1
  • Steven A. Walton
    • 2
  • John A. Schuster
    • 3
  1. 1.Department of History and ClassicsUniversity of AlbertaEdmontonCanada
  2. 2.Department of Social SciencesMichigan Technological UniversityHoughtonUSA
  3. 3.Unit for History and Philosophy of ScienceUniversity of SydneySydneyAustralia

About the editors

Lesley B. Cormack is a historian of science and now Dean of Arts at the University of Alberta.  She is the author of Charting an Empire: Geography at the English Universities 1580-1620 (Chicago, 1997), A History of Science in Society: From Philosophy to Utility with Andrew Ede (Broadview Press,2004, 3rd Edition University of Toronto Press, 2017) and editor of Making Contact:  Maps, Identity, and Travel (University of Alberta Press, 2003) and A History of Science in Society: A Reader (Broadview Press, 2007)She is now completing a book on the development and use of the Molyneux Globes in sixteenth century England.

Steven A. Walton teaches history of science and technology, European history, and military history at Michigan Technological University, where is also actively involved with the graduate program in Industrial Archaeology.  His primary scholarly writing is on the intersections between science, technology and the military, particularly in the early modern and antebellum American world. He has just published the travel diaries of Thomas Kelah Wharton, a nineteenth-century architect and artist, an article on U.S. Civil War artillery, and is working on a book on Transitions in Defense, on changed in fortification practice and rationale in sixteenth-century England.  He has edited works on Fifty Years of Medieval Technology & Social Change (Ashgate, 2017); Wind & Water in the Middle Ages: Fluid Technologies from Antiquity to the Renaissance (ACMRS, 2006); and Instrumental in War: Science, Research, and Instruments Between Knowledge and the World (Brill, 2005).

John A. Schuster is Honorary Research Fellow in the Unit for History and Philosophy of Science and Sydney Centre for the Foundations of Science, University of Sydney; and Honorary Fellow, Campion College, Sydney, the only private liberal arts college in Australia. He previously taught at Princeton, Leeds, Cambridge and the University of New South Wales. He is a Fellow of the Australian Academy of the Humanities. He has published on the historiography of the Scientific Revolution; the nature and dynamics of the field of early modern natural philosophy; Descartes' natural philosophical and mathematical career; the problem of the origin of experimental sciences in the 17th and 18th centuries; and the political and rhetorical roles of scientific method. Recent publications include Descartes-agonistes: Physico-Mathematics, Method and Corpuscular-Mechanism—1618-33 (Springer, 2013) and ‘Cartesian Physics’ in The Oxford Handbook of the History of Physics  (2013): 56-95

Bibliographic information

  • Book Title Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe
  • Editors Lesley B. Cormack
    Steven A. Walton
    John A. Schuster
  • Series Title Studies in History and Philosophy of Science
  • Series Abbreviated Title Stud. History, Philosophy (formerly: Australasian Stud....)
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages History History (R0)
  • Hardcover ISBN 978-3-319-49429-6
  • Softcover ISBN 978-3-319-84160-1
  • eBook ISBN 978-3-319-49430-2
  • Series ISSN 0929-6425
  • Series E-ISSN 2215-1958
  • Edition Number 1
  • Number of Pages XII, 203
  • Number of Illustrations 12 b/w illustrations, 1 illustrations in colour
  • Topics History of Science
    History and Philosophical Foundations of Physics
    History of Mathematical Sciences
    History of Early Modern Europe
  • Buy this book on publisher's site


“The volume reads well, and constitutes a valuable addition to our understanding of the role of mathematics at the time of the Scientific Revolution.” (Mihnea Dobre, Early Science and Medicine, Vol. 24, 2019)

“This book shows that diverse and new historiographical approaches to the study of practical mathematics should be considered. Historians of science, especially those interested in the Scientific Revolution and the history of mathematics, will find this book and its ground-breaking approach of particular interest.” (Argante Ciocci, Nuncius, Vol. 33 (3), November, 2018)

“This slim yet wide-ranging volume offers compelling perspectives for broadening the scholar/craftsman debate. It is relevant to anyone studying the history of science in early modern Europe. As a whole, the essays capture the complexities of the theoretical, practical, and material concerns of mathematical practitioners and invite further discussion.” (Catherine Abou-Nemeh, ISIS, Vol. 109 (2), June, 2018)

“Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe is a collection of nine papers from various authors from around the globe. … I do believe that this text could be a good supplement for students, and I firmly believe that this could be very useful for any professor looking for additional historical content.” (Brent Kelderman, MAA Reviews, June, 2017)