In 1956 Hans Lewy shocked the world. For decades, people had believed that just like ODEs, well-behaved PDEs should have a general existence theorem, and that it was only a matter of time before it was proven. However, Lewy constructed a very simple example to prove them all wrong. He was in as much shock and awe as they were. We'll talk about this equation and the proof, which coincidentally uses a lot of CR geometry. The talk should be accessible to anyone who has ever taken a partial derivative.