This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools and Mathematics and Natural Sciences.

Although the concept of randomness is ubiquitous, it turns out to be difficult to generate a truly random sequence of events. The need for “pseudorandomness” in various parts of modern science, ranging from numerical simulation to cryptography, has challenged our limited understanding of this issue and our mathematical resources. In this talk, Professor Jean Bourgain explores some of the problems of pseudorandomness and tools to address them.