# Current research projects

- Empiricism in mathematics
- History and philosophy of geometry

— Geometric reasoning in the 19th century - Pasch's philosophy of mathematics

— Pasch and Klein on the role of intuition in proofs

— Pasch's views on logic - Mathematical cognition

— Numeral systems

— Reasoning with logical notations

# Current editorial projects

**Paul Bernays:**

Editor and translator of papers on philosophy of mathematics by Paul Bernays (Bernays Project).**Rudolf Carnap:**

— Editor (with E. Reck and G. Schiemer) of volume 3,*Pre-Syntax Logic 1927-1934*, of The Collected Works of Rudolf Carnap.

— Editor (with Warren Goldfarb) of volume 5,*Logical Syntax of Language*, of The Collected Works of Rudolf Carnap.**David Hilbert:**

— 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 Majer.**Moritz Pasch:**

—*Weierstrass' lectures on analytic functions (1865/66)*. With Rachel Rudolph.

—*Lectures on Modern Geometry*(1882/1926) (translation).

—*On the educational value of mathematics*(1894) (translation).

# Other

- 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.
**Research Keywords:**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.

# Links to related associations, societies, etc.

History and Philosophy of Mathematics:

- Association for the Philosophy of Mathematical Practice (APMP)
- Canadian Society for History and Philosophy of Mathematics (CSHPM)
- Association of Symbolic Logic (ASL)
- Philosophy of Mathematics Association (PMA)
- Practice and Cultures of Mathematics

History and Philosophy of Science:

- Canadian Society for History and Philosophy of Science (CSHPS)
- International Society for the History of Philosophy of Science (HOPOS)
- Philosophy of Science Association (PSA)

Philosophy:

Cognitive Science: