Has this ever happened to you? You’re enjoying your night casually solving some differential equations when you realize the problem that your solving doesn’t describe a smooth solution. That is, you come across a function that you can’t take the derivative of, but it solves a differential equation. In this talk, we’ll be talking about Viscosity Solution theory to expand our horizons and see that if we change our viewpoint on what it means to “solve a differential equation,” then we can make sense of a non-differentiable solution to a differential equation. Once we can talk about such solutions, we can see where their applications lie such as Numerical solutions.