Toy puzzles that involve randomness often have surprising and counterintuitive answers. For example, in fair coin flipping, the expected time to see heads, followed immediately by tails, is four coin flips, but the time to see heads followed by heads is six coin flips. In a classroom with twenty-three or more students, there is a good chance at least two students will have the same birthday. We will introduce a few puzzles in this spirit and then discuss how the lessons gained from studying them can be transferred to a new way to look at real-world news stories through a more skeptical and thoughtful lens.
Ivan Corwin is a professor of mathematics at Columbia University. He was the 2021 recipient of the Loeve Prize in Probability Theory and has held fellowships from the Clay Mathematics Institute, Packard Foundation, Simons Foundation, and Keck Foundation, and visiting professorships in Paris and Berkeley. Corwin is a proponent of using probabilistic thinking across science, with affiliations at Columbia in the Data Science Institute, Program for Mathematical Genomics, Irving Institute for Cancer Dynamics, and Quantum Initiative. Recently, he has been working to create a National Institute for Mathematical Theory in Biology at Columbia.