Mathematical Theory Development in America

Cornell University, Ithaca NY

Investigators

Abstract

This award supports a doctoral dissertation research project in the history of mathematics. It uses postulate theory, an approach to the foundations of mathematics that searches for and establishes the basic postulates (or principles) that govern a particular mathematical field, as a window into the relationship between mathematics and American society during the first half of the 20th Century. The goal is to show how the relationship between mathematics and society in the early twentieth century helped erect barriers to participation in the mathematics community today. Closely tied to culture and diversity issues are ongoing debates about math education and the challenge of public engagement. This study's analysis of math education debates in the early twentieth century will highlight the many factors that are at stake in such debates, which are important to consider when drafting and deliberating current policy. The project addresses three primary research questions: How did the exploration of the foundations of mathematics inform the meaning and value of American mathematics in the early 1900s? How were the boundaries of professional mathematics redefined in the US during that time? How did the cultural identity and public image of American mathematicians change alongside Progressive Era conceptions of hierarchy and difference? These questions will be answered through the analysis of institutional and public media archives as well as the work of individual mathematicians engaged in the study of postulates. The overall purpose is to further understand the development of American mathematics by situating its early-twentieth-century growth within the context of American society. By exploring the image and status of professional mathematicians in the Progressive Era United States alongside historical perceptions of who was thought capable of contributing to mathematical knowledge, this study will shed light on the dynamics of inclusivity and cultural identity in American science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.