Studying at Wesleyan is an opportunity for you to radically expand and enhance your view of the world and to begin to master some of the disciplines that describe it. The course is intended to introduce you to this (hopefully lifelong) project and to prepare you to get the most out of Wesleyan. To do this we will study some of the most audacious and profound intellectual leaps ever made, looking at how mathematical techniques entered ancient cultures and were developed so that rationality could replace (or at least compete with) dogmatism and appeal to authority.
The course is an opportunity for you to learn some mathematics and to form a "big picture" of how various intellectual disciplines are related, which you can keep in mind as you begin to specialize in, say, STEM, philosophy, history, classics, or psychology. We will examine the relationship between mathematics and the humanities, especially philosophy and history. To do this we will take as our overarching question: How did we come to know mathematical truths? What will be distinctive about our approach is that we will try to answer this philosophical question from a culturally and historically informed perspective. This "humanizes" mathematical thought by finding it in specific cultural contexts and practices, and in the historical expression and transmission of ideas. We will consider what is the best method for studying the history of mathematics. Should we emphasize what seems important now, in retrospect, or what we think seemed important at the time? We will reflect on examples of proto-mathematical practices (counting, measurement, record keeping, calculation), on the cognitive limitations that we overcome mathematics, as well as on examples of mathematics proper (arithmetic, geometry, algebra, computation). We will identify the distinctive features of various mathematical practices -- ancient and modern -- and ask why they take the forms they do and what general morals about mathematical knowledge can be drawn from them.
Mathematical knowledge is a crucial part of human knowledge, a pinnacle of human achievement, and the subject of many great works in philosophy (by Plato, Aristotle, Descartes, Kant, Mill, Frege, and Russell). This course will help prepare you to take other courses in philosophy of mathematics, taught by professors Sanford Shieh and Daniel Smyth. It will also enrich your understanding of STEM disciplines.
Meetings will be a mixture of lectures, discussion, and review. Assignments will include writing assignments, mathematical problem sets, and "explainer" presentations. Hints and pointers about the reading will be provided. Never fear; no calculus will be presupposed or taught! |