The intention of this question is to find practical examples of improved mathematical notation that enabled actual progress in someone's research work.

I am aware that there is a related post Suggestions for good notation. The difference is that I would be interested especially in the practical impact of the improved notation, i.e. examples that have actually created a better understanding of a given topic, or have advanced actual research work on a given topic, or communication about results.

I would be interested in two aspects in particular

(1) **Visibility and efficiency**: Improved and simplified notation that made structures and properties more clearly visible, and that created efficiencies (e.g., using less space and needed less time, dropped unnecessary or redundant details).

(2) **Evolving process**: Mathematical work is constantly creating new objects, i.e. in constant need of new symbols, or using symbols in new ways. And it needs to create a shared understanding about that. Would you have any practical examples of this evolving process, including dead-ends and breakthroughs?

I would be most interested to learn about practical examples, and would be grateful if you were willing to share.