The purpose of positive economics is to make accurate statements about economic phenomena. I also believe this is the purpose of any science. Scientists attempt to make accurate statements about their object of study. The hard part is determining what statements are true.
I also believe that all of mathematical economics falls under the umbrella of economic statements. Equations and models make statements about economic variables. Geometrical pictures make statements about economic variables also.
So basically I think theoretical economics goes like this:
1. Make an economic statement (hypothesis)
2. Determine the validity of the economic statement
In my opinion, testing economic statements (step 2) is the most important part of economics. Building a DSGE model is cool, but it's only a statement. I believe it's more important to find evidence that supports or disputes an economic statement in order to determine its accuracy. That's why I'm a big fan of econometrics and the empirical revolution in economics. I'm inspired by innovative methods that determine the validity of economic statements.
I believe one of the most common mistakes in modern economics is too much time spent building complex formal economic statements and not enough emphasis testing the validity of those statements. I believe economic statements do not need to be complex in order to be testable.