Why Is the History of Mathematics Not a Central Strand of Intellectual History?

Despite its status as queen of the sciences, one of the most allegedly pure forms of thought, and a subject of central importance in the modern world, mathematics receives a comparatively limited amount of attention. In answering this question, my talk will primarily touch on three points. First, I will insert mathematics back into two pivotal points in intellectual history to show how much is lost when we segregate out changes and debates within mathematics from other trends. This section will focus on the work and thought of the early modern polymath Rene Descartes, and the debates between Henri Poincaré and David Hilbert over the axiomatization of mathematics. Second, by focusing on the Poincare and Hilbert debate, and in general on how systematically mathematics can be formulated (or not), I will show how the popular view of mathematics itself is often unknowingly partial to one side in this debate (the formalist view) and how that has strongly shaped mainstream discussion about how math should be taught. Keeping in mind these first two points, I will finally consider some of the possible implications for our understanding of education, intellectual history, and modernity writ large if we both reconsider the history of mathematics and integrate it more thoroughly into our larger historical questions.