Explore the mathematics of computation through the lens of linear equations and lattices in this 45-minute lecture by Muli Safra. Delve into topics such as error-correcting codes, the Closest Vector Problem, and unique games. Examine lattices as discrete subgroups and their role in computational problems. Investigate the relationship between worst-case and average-case scenarios, and learn about Minkowski's theorem and its reverse. Discover open questions related to classical problems and the hardness of approximating SVP/CVP. Gain insights into the potential future of computing while exploring the intricate connections between linear algebra, geometry, and computational complexity.