Any system in which politicians represent geographical districts with boundaries chosen by the politicians themselves is vulnerable to gerrymandering: carving up districts to increase the amount of seats that a given party is expected to win. But even fairly-drawn boundaries can end up quite complex, so how do we know that a given map is unfairly skewed? Math comes to the rescue. We can ask whether the likely outcome of a given map is very unusual within the set of all possible reasonable maps. That’s a hard math problem, however — the set of all possible maps is pretty big — so we have to be clever to solve it. I talk with geometer Jordan Ellenberg about how ideas like random walks and Markov chains help us judge the fairness of political boundaries.Support Mindscape on&nbsp;<a href="https://www.patreon.com/seanmcarroll" rel="noopener noreferrer" target="_blank">Patreon</a>.Jordan Ellenberg received his Ph.D. in mathematics from Harvard University in 1998. He is currently the John D. MacArthur professor of mathematics at the University of Wisconsin. He competed in the International Mathematical Olympiad three times, winning a gold medal twice. Among his awards are the MAA Euler Book Prize and a Guggenheim Fellowship. He is the author of&nbsp;<a href="https://www.jordanellenberg.com/book/how-not-to-be-wrong/" rel="noopener noreferrer" target="_blank">How Not to Be Wrong</a>&nbsp;and the novel&nbsp;<a href="https://www.jordanellenberg.com/book/the-grasshopper-king/" rel="noopener noreferrer" target="_blank">The Grasshopper King</a>. His new book is&nbsp;<a href="https://www.jordanellenberg.com/book/shape/" rel="noopener noreferrer" target="_blank">Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else</a>.<ul><li><a href="https://www.jordanellenberg.com/" rel="noopener noreferrer" target="_blank">Web site</a></li><li><a href="https://people.math.wisc.edu/~ellenber/" rel="noopener noreferrer" target="_blank">Wisconsin web page</a></li><li><a href="https://scholar.google.com/citations?user=b7P6YbkAAAAJ&amp;hl=en" rel="noopener noreferrer" target="_blank">Google Scholar publications</a></li><li><a href="https://www.amazon.com/Jordan-Ellenberg/e/B001K8IUCG" rel="noopener noreferrer" target="_blank">Amazon author page</a></li><li><a href="https://en.wikipedia.org/wiki/Jordan_Ellenberg" rel="noopener noreferrer" target="_blank">Wikipedia</a></li><li><a href="https://twitter.com/JSEllenberg" rel="noopener noreferrer" target="_blank">Twitter</a></li></ul>

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151 | Jordan Ellenberg on the Mathematics of Political Boundaries

Sean Carroll | Wondery