Explore the interplay between linear algebra, machine learning, and high-performance computing in this keynote address from JuliaCon 2021. Delve into the use of hierarchical matrix algebra for constructing low-complexity linear solvers and preconditioners, and learn how these fast solvers can accelerate large-scale PDE-based simulations and AI algorithms. Discover how statistical and machine learning methods can optimize solver selection and configuration. Examine recent developments in fast algebraic and geometric algorithms, including sketching and approximate nearest neighbor techniques. Gain insights into the STRUMPACK library and its applications. Investigate the use of Bayesian optimization in improving linear algebra computations. Engage with a Q&A session covering topics such as linear algebra code development, performance optimization using machine learning, and the potential of Julia in high-performance computing.