Nicholas Cooke in "Handbook of Musical Analysis" says something that has always influenced me very deeply:

> All notation is analysis

Obviously he's talking in the specific context of musical notation, but it seems true in other fields too. Choosing how to notate seems a very important analytical decision and certain forms of notation help or hinder analysis.

Feynman diagrams for example famously help to understand the maths underlying particle interactions.

Roman numerals (for a different example) make all kinds of arithmetic much harder than in Arabic notation.