5 April: Nicolas Fillion
“Conceptual and Computational Mathematics”
Abstract: This paper examines from a philosophical angle the consequences of the computer revolution that has importantly transformed modern mathematics. By comparing its repercussions on mathematics with those of the conceptual revolution that originated in the 19th century, I will stress the epistemological importance of practices that have to some extent been neglected. I argue that the key lesson to be drawn from the two revolutions that have shaped modern mathematics is an aspect of mathematical practice that is key to the effective and successful use of mathematics in science, namely, that good mathematical practice results from integrating the computational and conceptual styles of mathematics. Finally, I show that the methodology deployed by applied mathematicians in modern scientific computing is a paradigmatic instance of this key lesson.