Computers, algorithms, and artificial intelligence have touched every aspect of our society, from science, to communication, to the justice system. But despite their enormous power, computers have fundamental limits – problems that no program can solve, and thorny issues in fairness and human rights. During the 26th year of the popular Ulam Lecture Series, SFI Professor Cristopher Moore looks at two sides of computation – the mathematical structures that make problems easy or hard, and the growing debate about fairness in algorithmic predictions. These two lectures are self-contained, and can be enjoyed together or separately. Lecture 1: Easy, Hard, and Impossible Problems: The Limits of Computation Monday, September 24, 7:30 pm Every day we ask computers to solve problems for us – to find the fastest route across town, the shape a protein folds into, or a proof for an unsolved mathematical question. For all these problems, the space of possible solutions is vast. Why is it that for some problems, we can quickly zoom in on the solution, while for others it's like looking for a needle in a haystack? What is it about the structure of a problem that makes it easy, or hard, or even impossible to solve? Moore draws analogies between computation and evolution, and takes us from the simple puzzles to the heights of universal computation, Turing's halting problem, and the nature of mathematical truth and creativity.