Straddling the theory + practice divide is always vexing, and I do this a lot when working at a research lab. The following note from an essay by Don Knuth is interesting:
The word 'theory' actually comes from the same root as the word 'theater'. .... the root word 'θέα' (a sight) led to (a place for viewing), (a spectator), and (a seeing, a spectacle).
And what about 'practice'. It's another Greek word, indeed another theatrical word: Practice means performance.
thus we can say that theory is to practice as rigor is to vigor.
-- from 'Theory and Practice II', in Selected papers in Computer Science
Knuth's point is not that theory is in any way subservient to practice: far from it. What he does argue is that theory far removed from practice becomes stale and ossified. His arguments, fleshed out over a series of articles, are more nuanced than I can do justice to in this note; suffice it to say that he wants to foster a far more active interaction between theory and practice than mathematicians (and theoretical computer scientists) are possibly comfortable with.
The essay ends with a beautiful bit of word play on the root word for theorem and the related root word for God:
Let us not confuse big-Omicron with big-Omega in making a theology out of theory. Let us rather practice what we preach. This will not only give the world better applications, it will ultimately give the world better theory.