Answer

I’m not sure I agree with the statement..

If I would agree with it, and try to convince someone, I would point out that a theory that produces non-analytical results, will always require some numeric approximation to deal with experimental predictions or analysis of outcomes. Hence one could say the theoretical work takes a background to a more numeric approach.

People who have the “other” opinion, would probably say the numeric approaches only work *because* of the theoretical basis, and that in fact Nature is also a course-grained simulator if you look close enough – at very close distance suddenly all the third-derivative, fourth-derivative orders you threw away in linearizations suddenly start mattering and the simulation becomes more complex but are driven by theory.

Honestly I think both points make sense and I’m not entirely in agreement with the distinctions being made here, but I have a feeling I will agree once I get more familiar with the course.