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.