Cultural Perspectives on Mathematics

Catalog description

This course will investigate the development of mathematical thought in multiple Afro-Eurasian cultures from the Bronze Age through the early medieval period, including Mesopotamia, Egypt, Greece, India, China, and the Islamic world. Math will be examined as a cultural product, with specific developments contextualized in the generating civilization's history, socio-political structures, economic systems, artistic and literary movements, and prevailing religious and philosophical ideas. Students will investigate the ways in which specific aspects of a culture influenced the development of specific ideas about, approaches to, and techniques regarding number and mathematical processes. Key themes in this respect will be what social forces encourage the development of practical or theoretical mathematics; how a society determines what is truth; the conception of abstract ideas such as zero and negative, infinite, and irrational numbers; the social status of mathematicians and their relationship with political and social authorities; and what social forces hinder the development of practical and/or theoretical mathematics. Students will also consider how the availability of certain mathematical knowledge enabled the development of particular social systems, architectural achievements, and more. Key themes in this respect will be the mathematical needs of specific political systems (such as the accounting involved in imperial administration), legal systems (such as fair division of goods), and religious systems (such as the calculation of accurate systems of time). At the same time, students will draw connections across time periods and cultures by examining the interactions between civilizations and how those interactions influenced the development of mathematics as a human endeavor. Key themes in this respect will be understanding what political, economic, and other forces cause cultures to come into contact or seek out contact; and how the exchange of knowledge shapes both the receiving culture and the study of mathematics as a whole. As part of this course, students will study both specific mathematical ideas (e.g., number systems, deductive reasoning, geometric algebra, and the motivating problems that spurred development) and the specific ancient and medieval cultures named above.