May I offer the four-vector notation as an example from physics? Quoting Feynman: > The notation for four-vectors is different than it is for three- > vectors. [...] We write $p_\mu$ for the four-vector, and $\mu$ stands > for the > *four* possible directions $t$, $x$, $y$, or $z$. We could, of course, use any notation we want; do not laugh at notations; invent them, they > are powerful. *In fact, mathematics is, to a large extent, invention > of better notations.* The whole idea of a four- vector, in fact, is an > improvement in notation so that the transformations can be remembered > easily. *The Feynman Lecture on Physics, Volume 1, Chapter 17.* A <A HREF="https://tex.stackexchange.com/questions/274463/feynman-trig-notation-creating-custom-characters">trigonometric notation</A> that Feynman invented in his youth did not catch on. And then of course <A HREF="https://en.wikipedia.org/wiki/Feynman_diagram">Feynman diagrams</A> are perhaps the most celebrated example of an impactful notation in physics.