This course will focus on two central questions. First, to what degree are mathematical theorems justified by rational insight, sensory experience, and/or purely symbolic computations? We will trace answers to this question from Ancient Greece until the beginning of the nineteenth century, and we will pay close attention to how answers to this question are related to mathematical developments concerning the relationship between arithmetic and geometry. Second, what is the infinite, and how one can reason about infinite sets, spaces, and numbers without becoming entangled in contradictions? The course presupposes no mathematical background, except familiarity with high-school algebra and geometry.
TEXT: No Textbook Required. Course materials on CANVAS.