[username90]

> In my experience, the intuitive "experience of the knowledge" was much more striking than the eventual unfolding and application of the logic in that case.

In math applications doesn't matter, just the beauty of the revelation. Understanding how everything in math is connected is the main goal of the field, so understanding more of it is never pointless.

But if we talk about applications then it is that if A and B are the same then all theorems derived for A also works for B and vice versa. This is very important since it automatically multiplies our productivity and learning rate! One such epiphany which many falters on is that x and y doesn't matter, they could be z or µ or whatever. Another which many struggles with but usually overcomes is that 10 + 30 is just as easy to compute as 1 + 3.