This is the home page for a seminar that was run by Jeremy Avigad (avigad@cmu.edu) and Ken Manders (mandersk+@pitt.edu) in the Fall of 2005. The seminar was offered jointly by Carnegie Mellon University (80-513/813) and the University of Pittsburgh (Philosophy/HPS), and met on Mondays, 9:30-11:50, in Porter Hall A19A.

Assignments: html

Outline of topics covered: html

Bibliography: html

Description

The power of modern mathematics is often attributed, in part, to the use of algebraic methods that were introduced in the nineteenth and early twentieth centuries. The goal of this seminar is to understand these methods, as well as how, and in what sense, they are useful.

To do so, we will combine historical and philosophical approaches. On the historical side, we will consider the development of Galois theory from the original work of Galois and Abel to the increasingly modern approaches of Dedekind, Weber, and/or Artin.

Informal discussions of the importance of these developments often make reference to mathematical "thought," "understanding," "practice," "concepts," and "representations." We will try to develop a better philosophical understanding of these terms, drawing inspiration from Kant, Husserl, and Wittgenstein.

The course can be taken for either undergraduate or graduate credit, in which case a final grade will be determined based on participation and a written work. Auditors and visitors are welcome.