In this talk, we will explore some applications of mathematics. Weather forecasting is notoriously difficult, so we begin by taking a look at some of the reasons why this is the case. Next, we present a strategy to cloak an object in such a way that the object and the fact that something is being cloaked are hidden from external observers. Finally, we utilize one of the most powerful tools in mathematics - Fourier series - to examine why instruments sound the way they do.