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 investigating the development of Hamilton-Jacobi methods in celestial mechanics in the nineteenth century, looking in particular at the creation of a theory of transformations. Another area of research concerns 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. Finally, I am producing a study on the historiography of mathematics, focusing on the work of Euler on divergent series.
- “The Culture of Research Mathematics in 1860s Prussia: Adolph Mayer and the Theory of the Second Variation in the Calculus of Variations,” in press in Research in History and Philosophy of Mathematics: The CSHPM 2017 Annual Meeting in Toronto. Birkhäuser, Basel.
- “Mathematics in Library Subject Classification Systems,” Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta, pp. 181-197. 2017. Birkhäuser, Basel.
- “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 Mathematica36 (2009), 420-427.
- The Cosmos: A Historical Perspective. Greenwood Publishers, 2006.
- Calculus and Analytical Mechanics in the Age of Enlightenment. Aldershot, Hampshire: Ashgate, 1997.
Toby Reid, “From Mathematizing to Physicalizing “The Universe”: A History of the Emergence and Maturation of a Community of American Relativistic Cosmologists, 1925-1950,” PhD in progress
Andrew Oakes, “On the Founding of Canadian Professional Astronomy – Clarence Chant at the University of Toronto,” PhD in progress
Mariya Boyko, Soviet Mathematics Curriculum Reforms (1960-1980): Redefining the Purpose of Mathematics Education,” PhD in progress
Bruce Petrie, “The Roots of Transcendental Numbers: 1700-1900,” PhD in progress.
Sylvia Nickerson, “Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930,” PhD conferred June 2014.
Allan Olley, “Computer Methods in Celestial Mechanics: The Case of Wallace Eckert,” PhD conferred June 2011.
Daniela Monaldi, “The Fate of the Mesotron: The Rome Experiment on the Nuclear Absorption of Hard Cosmic Rays,” PhD conferred March 2005.
Katherine L Hill, “The Evolution of Concepts of the Continuum in Seventeenth Century Mathematics,” PhD conferred 1996.