This is an introductory course in the history of mathematics, in which we will pursue a multi-disciplinary approach: we will do some history, some philosophy, and (of course) some math.
Historically, we will be concerned with culturally specific practices of mathematics, how those practices interact with related cultural activities (astronomy, the arts, commerce, taxation, etc.), how they have been disseminated across space and time, and how their reception (in different places and in different ages) has led to transformations in the practices themselves. We will make use of Special Collections to consider the varied ways mathematics has been preserved in writing and pay some attention to the material transmission of mathematical texts: i.e., how demonstrations worked out in 250 BC in Syracuse, Sicily eventually make their way into our 21st century textbooks in Connecticut.
Mathematically, we focus on developments in geometry and in algebra from the ancient world and culminating in the development of calculus at the end of the seventeenth century. No prior knowledge of these fields will be presupposed but significant effort will be required of everyone, regardless of mathematical background, to internalize the intellectual styles of different mathematical paradigms and to appreciate their distinctive methods and results. Some of these results (such as the Pythagorean theorem) will be familiar, but our approach to them likely will not be. There will be problem sets and tutorial sessions to help us appreciate the mathematical content.
Philosophically, we will interrogate the notion of mathematical proof by considering different methods of demonstration (reduction, construction, induction, analysis) and identifying the principles of adequacy to which they appeal. We will also reflect on the forms in which mathematical knowledge is presented (axiomatic systems, treatises, problems, theorems, methods) and ask what makes a result significant or generative in a specific tradition or paradigm. |