The game of Set is a simple but addictive card game played with a special 81-card deck. A standard “folklore question” among players of this game is: what is the largest number of cards that can be on the table which do not allow a legal play? I’ll explain how this question, which seems to be about cards, is actually a very deep one about geometry over a finite field, and what it has to do with many other popular questions in number theory, and some less popular ones I’m trying to popularize. I will also try to give a sense of why this problem was so hard (until it wasn’t) and how mathematicians approach hard problems.

The Kieval Lecture Series is funded through a bequest of the late Dr. Harry S. Kieval ’36, a longtime professor of mathematics at Humboldt State University in Arcata, California, who died in 1994. In addition to this lecture series, his estate provides funding to Cornell University for a similar lecture in physics, as well as annual prizes awarded to outstanding seniors in both mathematics and physics.

Jordan Ellenberg is the John D. MacArthur Professor of Mathematics and Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin at Madison. Ellenberg is both a world-class scholar of mathematics and a world-class communicator. His mathematical expertise focuses primarily on arithmetic algebraic geometry and number theory. He is the author of Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else (2021), about the ubiquity of geometry in modern life, and How Not to Be Wrong: The Power of Mathematical Thinking (2014), a New York Times hardcover bestseller. His debut novel, The Grasshopper King (2003), has been described as “a profoundly absurd campus satire about immortality, obsession, obscurity and true love.”

This event is part of an A.D. White Professors-at-Large (ADW-PAL) visit and is co-sponsored by the Cornell Dept. of Mathematics. Ellenberg visits the Cornell campus in Ithaca as an ADW-PAL March 13-17. Ellenberg was elected as an ADW-PAL in 2019. His appointment runs through 2025.