In this talk, I would like to talk about a soft topic which is crucially important for our society: gerrymandering. I am not an expert on this topic of course but I have been doing my own research for a while. I thought I would share some of the topics that I’ve found most interesting with you. We will try to understand what is gerrymandering and how math, especially geometry and of course probabilistic methods, is being efficiently used in the service of democracy to prevent gerrymandering.