Color Me Polynomial — Quanta Magazine

My latest column for Quanta Magazine highlights one of math’s most misunderstood objects: the polynomial. Polynomials may be the bane of an algebra student’s existence, but polynomials help us see the mathematical structure around us.

At some point in school you were probably asked to combine, factor and simplify polynomials. For example, you may remember that x² + 2xy + y² = (x + y)². That’s a neat algebra trick, but what is it actually good for? It turns out that polynomials excel at uncovering hidden structure, a fact Huh used to great effect in his proof. Here’s a simple puzzle that illustrates how.

My column explores how certain polynomials, called chormatic polynomials, can tell us about the structure of certain graphs, and vice versa. This intimate connection lies at the heart of some interesting results in graph theory, including some big theorems that were proved only recently.

To learn more, read the full article, which is freely available here.