Explore the transition from Homotopy Type Theory (HoTT) to Higher-Order Type Theory (HOTT) in this illuminating conference talk by Michael Shulman from the University of San Diego. Delivered as part of a conference celebrating the inaugural year of Chapman University's Doctor of Science program in Mathematics, Philosophy and Physics, this hour-long presentation delves into advanced concepts in mathematical logic and foundations. Gain insights into the latest developments in type theory and its applications in mathematics and computer science. Suitable for graduate students and researchers in mathematics, computer science, and philosophy of mathematics, this talk offers a deep dive into cutting-edge research at the intersection of these fields.