YANSS 216 – How the answer to whether a straw has one hole or two reveals the hidden geometry that shapes everything from pandemics to democracy

In this episode we sit down with Jordan Ellenberg, the John D. MacArthur Professor of Mathematics at the University of Wisconsin-Madison.

His writing has appeared in Slate, the Wall Street Journal, the New York Times, the Washington Post, and the Boston Globe, and he is the New York Times bestselling author of How Not to Be Wrong – but in this episode we will discuss his new book, Shape: The hidden geometry of information, biology, strategy, democracy and everything else.

The official description of Shape:

From the New York Times-bestselling author of How Not to Be Wrong, himself a world-class geometer, a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything

How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play chess, and why is learning chess so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry.

For real. If you’re like most people, geometry is a sterile and dimly-remembered exercise you gladly left behind in the dust of 9th grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it’s plodding through a series of miniscule steps, only to prove some fact about triangles that was obvious to you in the first place. That’s not geometry. OK, it is geometry, but only a tiny part, a border section that has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.

Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word “geometry,” from the Greek, has the rather grand meaning of “measuring the world.” If anything, that’s an undersell. Geometry doesn’t just measure the world – it explains it. Shape shows us how.

From his official bio:

Jordan Ellenberg grew up in Potomac, MD, the child of two statisticians. He excelled in mathematics from a young age, and competed for the U.S. in the International Mathematical Olympiad three times, winning two gold medals and a silver. He went to college at Harvard, got a master’s degree in fiction writing from Johns Hopkins, and then returned to Harvard for his Ph.D. in math. After graduate school, he was a postdoc at Princeton. In 2004, he joined the faculty of the University of Wisconsin at Madison, where he is now the John D. MacArthur Professor of Mathematics. (Professional page). Ellenberg’s research centers on the fields of number theory and algebraic geometry, the parts of mathematics which address fundamental questions about algebraic equations and their solutions in whole numbers. Ellenberg’s research has uncovered new and unexpected connections between these subjects and algebraic topology, the study of abstract high-dimensional shapes and the relations between them. Ellenberg was a plenary speaker at the 2013 Joint Mathematics Meetings, the largest mathematics conference in the world, and he has lectured about his research around the United States and in ten other countries. He has held an NSF-CAREER grant and an Alfred P. Sloan Fellowship, in 2013 he was named one of the inaugural class of Fellows of the American Mathematical Society, in 2015 he was named a Guggenheim Fellow, and in 2018 a Simons Fellow.

Ellenberg has been writing for a general audience about math for more than fifteen years; his work has appeared in the New York Times, the Wall Street Journal, the Washington Post, Wired, The Believer, and the Boston Globe, and he is the author of the “Do the Math” column in Slate. His Wired feature story on compressed sensing appeared in the Best Writing on Mathematics 2011 anthology. His novel, The Grasshopper King, was a finalist for the 2004 New York Public Library Young Lions Fiction Award. His 2014 book How Not To Be Wrong was a New York Times and Sunday Times (London)bestseller and was one of Bill Gates’ top five summer books; it has been published in sixteen countries.