This above is exactly the example I would give. Raising and lowering operators and Christoffel Symbols are critical to having an ability to talk about Reimann C

This above is exactly the example I would give. Raising and lowering operators and Christoffel Symbols are critical to having an ability to talk about Reimann Curvature (General Relativity). However, there are many abstract concepts (zero, I, infinity, pi, e) where notation and symbolism can dramatically improve intuition. Similarly, there are notations for different groups, or simply types number systems, N J R C. Hey, why not floats and strings too? In addition, there are also many functions that we use/define (sin, cosh, B, P Y), which are basis sets for the solution of various differential and partial differential equations. Failure to use some of these notations makes explaining oneself (even to yourself) almost impossible and using a different notation will frustrate others.