> Nevertheless, mathematical notation has serious deficiencies. In particular, it lacks universality, and must be interpreted differently according to the topic, according to the author, and even according to the immediate context.

I personally disagree to the premise of this paper.

I think notation that is separated from visualization and ergonomics of the problem has a high cost. Some academics prefer a notation that hides away a lot of the complexity which can potentially result in "Eureka" realizations, wild equivalences and the like. In some cases, however, it can be obfuscating and be prone to introducing errors. Yet, it's a important tool in communicating a train of thought.

In my opinion, having one standard notation for any domain/ closely related domains is quite stifling of creative, artistic or explorative side of reasoning and problem solving.

Also, here's an excellent exposition about notation by none other than Terry Tao https://news.ycombinator.com/item?id=23911903

If you are interested in mathematical notations, check out Terry Tao's comment [0][1] on desirable properties of math notations. It was discussed not long ago [2].

[0] https://en.wikipedia.org/wiki/Terence_Tao

[1] https://mathoverflow.net/questions/366070/what-are-the-benef...

[2] https://news.ycombinator.com/item?id=23911903