No, since anyone is free to invent and use whatever notation they prefer. That’s how mathematical notation has evolved so far. People come up with new notation all the time.

"Free" here is a bit abstract. In what way is an undergraduate mathematician free to use their own notation, as opposed to the notation of their lecturer, textbooks, and examination papers? You can think in your own terms, but mathematics has to be taught and communicated with some kind of consensus - and unless you're lucky enough to be the first in the field, that consensus has preceeded you.

Mathematics is completely meritocratic. If you invent a notation that is better than some existing notation, people WILL use it, without asking for your credentials.

I think that's a naive statement, and it's also not really relevant to the original point being made, which is that existing mathematical notation can be difficult to grok.

Inventing new notation does not help with existing material - and that material is what makes mathematicians. People who can put up with old notation, especially if it is bad, are much more likely to become mathematicians: that gives a survivorship bias.

Besides which, you are welcome to invent your own notation, but good luck trying to get anyone to adopt it, particularly if the mathematical field involved is studied enough. Inertia is very strong, even in very abstract disciplines - aren't physicists still treating current as flowing the wrong direction?

Though when you are writing a paper, it's useful to pick standard notation.

But yeah, when working something mathematical out for the first time, picking / making up the right notation is crucial.

sure unless you quit because you struggled to learn what was in place.

Inertia

The most likely place to be hanging around mathematicians is at a school, and that's also where you would expect to hear students complaining about notation as an impediment to learning.

I don’t think it is a given that students are good judges about what impedes them from learning.

Having said that, I personally have never had issues with notation in mathematics nor did I have the impression others I helped had. IMO, abstraction is the main stumbling block, not notation.

I’m talking about the math institutions at the two universities I attended, I took a lot of phd classes. But same with students, the complaint has never been about notation. In fact the only people that seem to complain about notation is computer programmers who find it too loose, but that is precisely its power.