The p-adic numbers are incarnations of nonarchimedean fields – fields with a notion of size that doesn’t satisfy the archimedean property. This property says that a small number, when added to itself a massive number of times, becomes a big number. This causes several headaches, and overcoming them has led to the development of some amazing mathematics due to Tate, Raynaud, Huber, and Berkovich. Close to the hearts of many in this department, nonarchimedean fields are ever-present in tropical geometry. In this talk, I will give an introduction to some beautiful and some annoying facts about the p-adic numbers, as we start to get a feel for why things get challenging. For instance, we’ll see that every p-adic triangle is isosceles, and any two intersecting disks are concentric. I will sketch a proof that, in a certain sense, most fields are nonarchimedean. No archimedeans will be harmed in this talk.