> 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

This feels like the types programming vs. none typed programming.

There are efforts in math to build "enterprise" reasoning systems. For these it makes sense to have a universal notation system (Lean, Coq, the likes).

But for a personal exploration, it might be better to just jam in whatever.

My personal strife in this space is more on teaching: Taking algebra classes, etc. where the teacher is not consistent nor honest about the personal decision and preference they have on notation - I became significantly better at math when I started studying type theory and theory of mechanical proofs.

The problem the article is talking about is that those different notations are used for super basic stuff that really do not need any of that.