1. What is history? Why should readers want to research and write it well?

2. How do we know about the past?

3. How do we create history based on what we know about the past?

4. What is the history of the history of mathematics?

5. How can readers articulate their own philosophies of the history of mathematics?

This talk will focus on the fifth activity as an exercise that not only encourages researchers, educators, and students to consume quality scholarship in the history of mathematics but also calls them to join the effort to produce original research in this field. I will end the presentation by asking for audience feedback on what mathematicians new to the endeavor need to know to research and write the history of mathematics.

The shape of x = the shape of y if and only if x is similar to y.

Neo-Fregean abstractionists today continue to defend this view. I will consider abstraction principles in the context of modal and tense logic, arguing that neo-Fregean abstractionism conflicts with both “serious presentism” and “serious actualism”.

I accept the first conclusion but reject the second. I argue that there is a mathematically rigorous definition of “fairness” that validates Huygens’ proofs in “The Value of All Chances.”

I conclude by defending a methodological precept. Existing scholarship on classical probability has focused on the definitions of “expectation” or “probability” offered by Huygens and Laplace, among others. By contrast, historians of geometry argue that Euclid's definitions are of little interest and that to understand Ancient Greek geometry, we must carefully study the implicit rules of inference in Euclid's work. Similarly, I argue that we must investigate the implicit rules and axioms used in the proofs in the “classical” theory of probability.

In 1740, Gabrielle Émilie Marquise Du Châtelet published "Physical Institutions" to expound the theories of Newton and Leibniz. An ardent Newtonian, she questioned the idea of forces promoted by Dortous de Mairan, a Cartesian and Secrétaire Perpétuel of the French Academy. He responded with a disparaging essay, starting a public dispute that centered on the concept of les forces vives. In 1741, Du Châtelet asked Euler for support, as neither Maupertuis nor Clairaut (her teachers) had come to her defense. Leonhard Euler, the incomparable Mathematicorum Principi, was the most eminent authority in mechanics.

The Châtelet-Mairan debate occurred during a time when philosophical disagreements, clashing personalities, and confusing terminology clouded the physical understanding of forces and motion. Did mathematical formulations settle the questions the debate had raised?

While framework and some programme highlights provided by the Association’s headquarters and Toronto committee, bulk of programming from Sections and related Societies. Sections, from A Mathematics to Q Education.

These congresses allowed Canadian mathematicians to meet colleagues and share work. Section A had short joint session with AMS and MAA. Vice-Presidential address, “A Mechanical Analogy in the Theory of Equations”, then three papers of general interest to mathematicians. A new Section V-P: George Abram Miller.

AMS programme: 32 papers, 84 members attending. Canadian presenters: J.S.C. Glashan (Isodyadic Equations), and Samuel Beatty (Algebraic Functions). Miller, two papers on Group Theory. Two women: Olive C. Hazlett (Orthogonal Functions) and Louise D. Cummings (Weddel Surface). 110 members MAA members present. Seven papers, none by women. Ten American women present, including Hazlett and Cummings; one Canadian : Jennie A. Kinnear. Afterwards, mathematicians joined physicists at joint banquet, possibly some at simultaneous Women’s Dinner.

Section B Physics, with Vice-President UofT's J. C. McLennan, a Canadian-American partnership; Section D Astronomy largely Canadian. American Physical Society at Toronto, but American Astronomical Society at Strathmore College. Section D Astronomy relied on Royal Astronomical Society of Canada for programming.

The 1921 Toronto AAAS Meeting’s success necessary for success of the International Mathematical Congress, Toronto, August 1924. Both chaired and organised by Toronto mathematician, J. C. Fields.