Explore the mathematical origins and applications of supersymmetry in this Stony Brook Mathematics Colloquium talk. Delve into the concept's relation to bosons and fermions, and its significance in mathematics despite lacking experimental confirmation in physics. Learn about the derivation of the Atiyah-Singer formula for the index of the Dirac operator using supersymmetry principles. Discover new applications leading to classical trace formulas of Jacobi-Poisson and Selberg. Gain insights from the speaker's joint work with Changha Choi, as presented in their recent arXiv publications.