Simplification Depends on Your Next Move
We often speak of "simplifying" as if it were a universal process with a single definition. But as mathematicians know, what constitutes simplification entirely depends on what you intend to do next. In calculus, if you're preparing to integrate, simplification means breaking expressions into smaller pieces.
In other contexts, simplification might mean combining terms into elegant products or quotients. The mathematician's approach reveals a broader truth: simplification isn't about making something uniformly simpler—it's about rearranging complexity in a way that makes your next step more manageable. What appears as a complication in one context might be the perfect simplification in another. The value of simplification lies not in some abstract notion of simplicity, but in how it serves your subsequent purpose.