Catalyst is an ideal candidate for you for this. The Controller and View code is very much separated from the Model code that you want, and agnostic to the framework code. I'm writing some text mining stuff at the moment, and Catalyst is what I'm using to keep web application logic and problem-domain logic well separated from each other. This (hopefully) makes everything much more maintainable.

Why don't you either a) put all the math stuff in its own set of modules and/or b) have your backend do all the analysis and store it in a middle layer (e.g. DB) for the front end visualization?