I will present Joel Moreira's recent solution to an old problem in Ramsey theory: if the natural numbers are colored with finitely many colors, then there must be integers \(x\) and \(y\) such that \(x\), \(x+y\), and \(x \cdot y\) all get the same color. I will describe in some detail a combinatorial, mostly elementary proof, and then I will outline Moreira's dynamical argument, which establishes the partition-regularity of a broad class of polynomial equations.