Current research project
- Empiricism in mathematics.
Funded by FQRSC, Programme Établissement de
nouveaux professeurs-chercheurs (2010—2013).
Current editorial projects
- Paul Bernays:
Editor and translator of papers on philosophy of mathematics by Paul
Bernays (Bernays Project).
- Rudolf Carnap:
Editor (with Warren Goldfarb) of volumes 3 and 5 of
Collected Works of Rudolf Carnap.
- David Hilbert:
Collaborator, David Hilbert's Lectures on the Foundations
of Mathematics and Physics, 1891 to 1933. Volume 3: David Hilbert's
Lectures on the Foundations of Arithmetic and Logic, 1917-1933.
Edited by William Ewald, Michael Hallett, Wilfried Sieg, and Ulrich Majer.
Editor, David Hilbert's Lectures on the Foundations
of Mathematics and Physics, 1891 to 1933. Volume 2: David Hilbert's
Lectures on the Foundations of Arithmetic and Logic.
Edited by William Ewald, Michael Hallett, Wilfried Sieg, and Ulrich
- Moritz Pasch:
Weierstrass' lectures on analytic functions (1865/66). With
Lectures on Modern Geometry (1882/1926) (translation).
On the educational value of mathematics (1894) (translation).
Work in progress
- Aspects of theory construction: Clark L. Hull's philosophy of
- Automated discovery and analogies. With Alison Pease.
- Dedekind's analysis of number (Part II). With
Wilfried Sieg (paper).
- Metaphors for the foundations of mathematics (paper).
- Klein and Pasch on intuition and proofs (paper).
- Pasch's ideal of proof (paper).
- Zahlendreher. With Benedikt Löwe and Samar Zebian.
- My Erdös number (Collaboration Distance to Paul Erdös) is at most 4 (August 2011).
- Co-founder of the Montreal Inter-University Workshop on History and Philosophy of Mathematics.
Analogical reasoning, axiomatics, Bernays, Carnap, Dedekind, discovery, Hilbert, history of algebra, history of geometry, neural networks, mathematical
practice, model-based reasoning, numeral systems, Pasch, Roman numerals.