Constructive Mathematics and Standards of Proof: Historical and Philosophical Perspectives

Congratulations to Koray Akcaguner for successfully defending his PhD thesis, "Constructive Mathematics and Standards of Proof: Historical and Philosophical Perspectives" on April 21, 2026. The thesis was supervised by Richard Zach. It was examined by Richard Zach, Nicole Wyatt, Mark Migotti, Gillman Payette. Nicolas Fillion (Simon Fraser University) served as external examiner.

We asked Koray to provide us with some insight into his thesis and his graduate studies experience in the Department of Philosophy at the University of Calgary. 

What was your thesis about?

My thesis is about constructive mathematics, a mathematical practice that emerged in the early 20th century with strong philosophical motivations. Some mathematicians rejected certain “non-constructive” principles and techniques, arguing that they render mathematics meaningless. In my work, I trace how this tradition evolved, both historically and philosophically, into more computational approaches to mathematics. I also explore the question of what counts as a mathematical proof and argue that this is partly a non-mathematical issue, since it inevitably involves value judgments.

What was the most valuable outcome of the graduate program for you?

The most valuable outcome of the graduate program for me has been intellectual maturation. Looking back to when I began, my understanding of both my own field and philosophy more broadly has deepened and expanded. I had the opportunity to attend lectures by distinguished scholars, present my work at conferences, receive feedback from leading figures in my field, and connect with fellow graduate students. By the end of the program, I felt that I had become part of an intellectual tradition.

In the final two years of the program, I was also involved in the department’s Philosophy for Everyone (P4E) project, where we visited K-12 schools and ran philosophy sessions with children. I found this work both deeply enjoyable and meaningful. The department’s public philosophy initiatives, including P4E and the weekly colloquia, have played an important role in broadening my intellectual perspective.

What are the next steps/plans for you?

As a next step, I plan to pursue sessional instructor positions in my field while also applying for tenure-track opportunities. At the same time, I want to remain actively engaged in public philosophy, particularly in Philosophy for Children (P4C) initiatives. While philosophy of mathematics and science remains my primary passion, these recent experiences have also sparked an interest in philosophy of education and public philosophy.