Capturing Mathematical Equality - Constructivism and Canonical Isomorphisms

Explore the implications of mainstream mathematics' rejection of constructivism in this 35-minute lecture by Kevin Buzzard at the Hausdorff Center for Mathematics. Examine how this decision has led to confusion between theorems and definitions, resulting in the overuse of the term "canonical isomorphism" in mathematical literature, particularly in number theory. Discover how this trend complicates the work of formalizers and consider the potential benefits of reintroducing constructivist principles to undergraduate mathematics education.