Methods and data structures that whole software ecosystems depend on, and the limits of what they can do.
Conflict-driven clause-learning solvers decide Boolean satisfiability on formulas with millions of variables, powering hardware and software verification, planning and computer-assisted mathematics.
Algorithms for quantum computers, from Shor's factoring and Grover's search to quantum simulation, and the evidence about which speedups are real, provable or only heuristic.