Explore a thought-provoking lecture on the evolving mathematical concepts of equality and sameness. Delve into the "higher dimensional" perspective in mathematics, examining how traditional notions of equality have been categorified to isomorphism and equivalence. Investigate the challenges posed by Leibniz's identity of indiscernibles in set theoretical foundations and discover how a new proposed foundation system addresses these issues. Learn about Voevodsky's univalence axiom and its implications for mathematical practice. Gain insights from Emily Riehl of John Hopkins University as she discusses the art of naming different things in mathematics and its significance in modern mathematical thinking.