Ernie’s 3D Pancakes gives us a nice, honest answer for the next time you give a theory talk:
Q: Are there any applications of your results?
A1: Um no, this is a theory talk, why would there be applications?
I once attended a talk by a solid mathematician who spent the last 4 years doing fancy combinatorics. It was as pure as it can be as far as research is concerned. Yet, he kept on talking about the fact that it had applications in Computer Science. Yet, at no point did he make these applications precise or even mention them in passing. It was annoying. Anything can have applications to anything… with enough beer.
Also, I once gave this relatively pure talk where I solve a neat problem which might have some applications, but I solve it in a crazy way just to make a point about how far one can go. At the end of the talk, I’m asked (by a student) what are the applications of my work. Duh! The talk is the application itself.
Anyhow, the lesson here is that some things are really about theory and you should not apologize that it has no known application. Not everything is meant to be applicable. And that’s ok. [Except if you ask a million dollars to do it.]