Doctoral Dissertation Research: On Negotiating the Role of Computers in Developing Mathematical Proofs

Harvard University, Cambridge MA

Investigators

Abstract

Introduction Digital computing changed mathematics at every level down to the core of mathematical practice, the search for proofs. This award supports doctoral dissertation research that traces how computers have been used in the development of proofs and how their use changed mathematical knowledge and practice in the United States. The project is motivated historically, anthropologically, and philosophically to explore the following questions. How are mathematical ideas related to the technologies with which they are discovered and explored? How is the cognitive work of mathematics altered by the introduction of computing? How is human intelligence understood through attempts to build reasoning machines? The period of interest begins in the mid-1950s with early Artificial Intelligence, and it concludes with the contemporary work of Fields medalist Vladimir Voevodksy. Intellectual Merit This project engages the ongoing interest of Science Studies in knowledge making, especially at the interface between humans and machines. It will explore mathematical knowledge and its material dimensions, which has until now been largely unexplored. Using archival materials, interviews, and technical documents including operations manuals and source code, the doctoral candidate will explore transformations in the institutional setting, material constitution, practices, and cognitive landscape of mathematical research that manifested around the digital computer. The intellectual merit of this project lies in its synthesizing and intervening in theoretical scholarship from science studies, history of mathematics, history of technology, and history of science (often pursued separately). Potential Broader Impact The significance of computer proof assistance in mathematical research is intensifying. This project can assist current researchers and funding agencies in the assessment and pursuit of new projects in light of past research and historical context. Further, an analysis of the multifarious past and present strategies for using computing in mathematics can suggest new possibilities for using computer assistance in other disciplines that may otherwise be unaware of them.