Hi everyone! For my 480 talk this week I will be discussing the topic of chaos within mathematics. I will start with the history of the first appearance of chaos, and give a description of what this concept really is in math. I will show some other examples of chaos, and then dive into the main focus of my talk. This will be the Lorenz Equations and their chaotic behavior. We will analyze this dynamical system and see what makes it so unpredictable. As a consequence, there are many other mathematical topics that can be studied using the Lorenz equations and variations of them.