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...
There may also exist types of math that are impossible to represent or reason about with current notation.