May 27, 2024


Special Lecturer:
Rafael Núñez (UC San Diego)

Friday October 14, 2011
10:00 am
Stewart Library, Fields Institute

What is Mathematics? And why is it now time to address this question scientifically? A view from Cognitive Science

What is mathematics and what are its foundations? The question of the nature of mathematics has been addressed primarily within the confines of the philosophy of mathematics (e.g., formal logical) and mathematics proper (e.g., metamathematics), with little, or no input from other scientific disciplines. Given current scientific developments --- especially concerning new findings about how human abstraction and imagination work --- this is arguably an unnecessarily narrow approach to the investigation of such deep and important question. In this presentation I'll discuss results in cognitive science --- the interdisciplinary scientific investigation of the mind, which gathering advances in neuroscience, psychology, linguistics, and anthropology, among others, has empirically investigated mathematics as a human conceptual system --- one that is abstract, precise, objective, effective, and formalizable, but that is human nonetheless. Discussing cognitive studies in infinitesimal calculus and set theory, I'll argue that the time has come to approach the study of the nature of Mathematics with empirical observations and testable explanations, and not just with old philosophical beliefs and dogmas. The portrait of mathematics has a human face, and it is up to us to get to know it!