A talk I gave for the Johns Hopkins University What is… Seminar 2022, in which I give an introduction to constructive mathematics and synthetic differential geometry. A recording of the talk can be found here, and the abstract can be found below.
Abstract: Constructive mathematics has been growing in popularity recently, but what is it? It is not merely the study of classical mathematics with one hand needlessly tied behind your back. On the contrary, in certain situations you can only work with constructive mathematics. But far from being a hindrance, this can open up entirely new perspectives on existing mathematical subjects, such as in the case of synthetic differential geometry.