MATH1702 · Complex Problems and Enduring Questions

The Making of the Moral Mind: Mathematics

Morrissey College of Arts & Sciences

This is an Enduring Questions course and is open to FRESHMEN only. You must take POLI1034 with this course.This course is devoted to an exploration of how Western mathematics developed out of the new science of algebra in the 17 th century and the implications of this development in the formation of modernity. It is a hybrid of two kinds of courses: 1) A basic math course without prerequisites (except for high school algebra and geometry) that gives attention to the history of mathematics. 2) A philosophy course that contemplates the scientific and humanistic implications of the mathematical ideas we study, especially to the formation of morals. The course will concentrate on algebra and number theory, with a digression concerning calculus, as found in the work of the French mathematicians Vite (late 16th century), Descartes, Fermat and Pascal in the 17th century, and the German mathematician Leibniz. We will explore how symbol-creating abstraction worked in the development of algebra and algebraic geometry, and how it led to an ever-growing distance between the mathematical description of the universe and the world of everyday sense perception. We will bring these ideas into our contemporary world by looking at some topics in modern Abstract Algebra and their applications to Number Theory and Public Key Cryptography. Descartes, Pascal and Leibniz were also great philosophers and religious thinkers. Some of their work in those realms will be discussed in the parallel course taught by Ryan Hanley. In our course we will try to understand some of the influences of their mathematical thinking on their philosophical thinking. There are two obvious ways mathematics influences morals: 1) through the development of science and technology and 2) as a paradigm of method and thesearch for truth. We will discuss these two ways while staying alert for other, more subtle,connections between the mathematical domain and the world of morality. We will continuallythink about ways in which these seventeenth-century ideas shaped later European thought andcontinue to shape our thinking today.