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Research Interests

My primary area of research is the history of analysis and mechanics in the eighteenth and nineteenth centuries. I have written an account of the original formulation by Jean d’Alembert of “d’Alembert’s principle” in dynamics. I have documented a major foundational shift in the writings on calculus of Leonhard  Euler and Joseph Louis Lagrange as the calculus was separated in the eighteenth century from geometry and made part of pure analysis. I have investigated the evolution of the calculus of variations in the nineteenth century, focusing on the work of such mathematicians as William Hamilton, Carl Jacobi, Adolph Mayer and David Hilbert. I am currently examining the history of complex analysis from its origins in the eighteenth century to its development as a major branch of analysis in the nineteenth century. A secondary field of interest is the history of astronomy and cosmology, particularly the relationship between relativistic cosmology and observational cosmology in the twentieth century.

Selected Publications

  • “Nonstandard Analysis, Infinitesimals, and the History of Calculus,” in David Rowe and Wann-Sheng Horng (Eds.), A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics A Festschrift in Honor of Joseph W. Dauben. Birkhäuser, 2015, pp. 25-49.
  • “Mechanics in the Eighteenth Century,” in Jed Buchwald and Robert Fox (Eds.),   Oxford Handbook of the History of Physics. Oxford University Press, 2013, pp. 358-405.  Co-authored with Sandro Capparini.
  • Introduction to Ernst Zermelo’s 1894 doctoral dissertation and to Zermelo’s papers on the navigation problem. In Heinz-Dieter Ebbinghaus et al. (Eds.), Ernst Zermelo – Collected Works/Gesammelte Werke: Volume II/Band II – Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung. Springer: Heidelberger Akademie der Wissenschaften, 2013.
  • “Sufficient Conditions, Fields and the Calculus of Variations,” Historia Mathematica 36 (2009), 420-427.
  • The Cosmos: A Historical Perspective. Greenwood Publishers, 2006.
  • Calculus and Analytical Mechanics in the Age of Enlightenment. Aldershot, Hampshire: Ashgate, 1997.


Bruce Petrie, (Supervisor), “The Roots of Transcendental Numbers: 1700-1900,” PhD in progress.

Sylvia Nickerson, (Supervisor), “Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930,” PhD conferred June 2014.

Allan Olley, (Supervisor), “Computer Methods in Celestial Mechanics: The Case of Wallace Eckert,” PhD conferred June 2011.

Daniela Monaldi, (Co-supervisor / S. Hong), “The Fate of the Mesotron: The Rome Experiment on the Nuclear Absorption of Hard Cosmic Rays,” PhD conferred March 2005.

Katherine L Hill, (Supervisor). “The Evolution of Concepts of the Continuum in Seventeenth Century Mathematics,” PhD conferred 1996.

Adam Richter, (Supervisory committee), “The Theology of John Wallis,” PhD in progress.

Teri Gee, (Supervisory committee), “Strategies of Defending Astrology: A Continuing Tradition,” PhD conferred November 2012.

Elizabeth Hamm (Burns), (Supervisory committee), “Ptolemy’s Planetary Theory: An English Translation of Book One, Part A of the Planetary Hypotheses with Introduction and Commentary,” PhD conferred November 2011.

Jacqueline Feke, (Supervisory committee), “Ptolemy in Philosophical Context: A Study of the Relationships Between Physics, Mathematics, and Theology,” PhD conferred June 2009.

Martha L. Harris, “The Physico-Chemical Nature of the Chemical Bond: Valence Bonding and the Path of Physico-chemical Emergence,” PhD conferred 2007.

Nathan Sidoli, “Ptolemy’s Mathematical Approach: Applied Mathematics in the Second Century,” PhD conferred 2004.


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