Actually, making my own notation is how I start puzzling out any problem. When one reformulates a problem, the appearance keeps changing but the problem is still there. It often takes multiple reformulations to "see" a problem, unencumbered by artifacts of birth.
The other day an EE grad student came to my office to show me his lab's research. After changing notation a couple of times, I was able to recognize that their novel combinatorial problem was an instance of graph coloring.
If I may humbly add, try making your own notation and playing around with it. Very rapidly one realizes just how hard a problem good notation is.