"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