#### Easy, Hard, Impossible Problems: An Ulam Lecture with Cris Moore

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 this 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.

This is the** first of two** lectures presented as part of SFI's Annual Stanislaw Ulam Memorial Lecture Series. These two lectures are self-contained, and can be enjoyed together or separately.

The title of the lecture presented on Monday, September 24th is "**Easy, Hard, and Impossible Problems: The Limits of Computation"**

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 simple puzzles to the heights of universal computation, Turing’s halting problem, and the nature of mathematical truth and creativity.

Cristopher Moore is a Professor at the Santa Fe Institute where he works on problems at the interface of mathematics, computer science, and physics. The co-author of *The Nature of Computation* (Oxford University Press), a classic textbook in modern mathematics, Moore has also written more than 150 scientific papers on topics ranging from quantum computing to the theory of social networks.

Moore is an elected fellow of the American Association for the Advancement of Science, the American Physical Society, and the American Mathematical Society. He served on the Santa Fe City Council from 1994-2002.

SFI's Community Lecture series is underwritten by Thornburg Investment Management, with generous support from the Lensic Performing Arts Center, and Enterprise Holdings Foundation.