This is the eleventh talk of 2022 in the Western Hemisphere Colloquium on Geometry and Physics. See web.math.ucsb.edu/~drm/WHCGP/ for more information on this series and to sign up to receive Zoom links for future talks.
Abstract: We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories, semantic search and intelligent textbooks. After a short review of the state of the art, we survey directions where we expect progress, such as mathematical search and formal abstracts, developments in computational mathematics, integration of computation into textbooks, and organizing and verifying large calculations and proofs. For each we try to identify the barriers and potential solutions.