I spoke at the Leonardo museum in March, 2017 as part of their Math Medley event. The purpose of this 15-minute talk was to help introduce a non-mathematical audience to pure math research by discussing one of the big open problems in algebraic geometry. In particular, I tried to convey that lots of math research is going on to this day. I also tried to demonstrate that, though it may look complicated and esoteric, modern math research is still trying to answer some basic and very natural questions.