I have to write a statement of interest for a math reu application. I was going to just write a formal essay. Then I thought, maybe I can write this essay in the form of a proof with lemmas and a theorem which will say that I will be a good fit for your program. Do you think this is stupid? It's okay if you do. I've never written any kind of application before for math. I want your honest opinion. Do you think it is too informal? Do you think a lot of people do this?