The confluence of big data sets, technologies of Artificial Intelligence, and proof assistants are revolutionizing modern mathematical practice. While these modern tools are reshaping current mathematical research, many underlying technologies emerged in prior centuries. Through both historical investigation and contemporary interviews, the project will establish how such developments represent both continuity with and rupture from earlier attempts to mechanize mathematical reasoning. The scientists intend to show that various historical examples share with large data sets, proof assistants and AI a common ambition and related result: they automate mathematical operations and drive transformations of mathematical intuition. By examining this trajectory, the researchers aim to contextualize current developments within the longer arc of debates about the relationship between human cognition and computational aids in mathematical discovery. Alongside historical research, the project will engage with mathematical communities currently navigating these technological changes. It will contribute to current debates about the nature of scientific reasoning in the age of AI; the project’s significance further extends to broader questions about human-machine collaboration in knowledge production.
The Collaborative Research Grants program of the University of St Andrews fosters international research broadly. Applicants from all schools and disciplines are encouraged to submit funding applications for innovative and sustainable projects built around collaborative research linking staff at the University of St Andrews and the University of Bonn. The research may take place in any country or regions as long as it is done collaboratively. The expectation is that these initial projects will lead to longer-term collaborations, institutional and research relations, and when applicable, generate publications, exhibitions, or external funding.
Michael Friedman is a member of the Hausdorff School for Mathematics and an associate member of the Hausdorff Center for Mathematics. He is a historian of mathematics whose research focuses on the history of algebraic geometry, conceptions material mathematical practices between the 17th and the 21st century, as well as the history of uses of AI in mathematics. Before coming to Bonn, he held positions at the at the Cohn Institute For History And Philosophy of Science And Ideas at Tel Aviv University, at the Humboldt University, Berlin, at the Fourier Institute at Grenoble and at the Max Planck Institute for Mathematics in Bonn.