The derivative of a function, for example, can be written in at least 4 ways (https://en.wikipedia.org/wiki/Notation_for_differentiation)
Also note that https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo... lists only fairly common notation, but already says “may”, “in such-and-so field” or “it is also denoted as” lots of times, and mentions several notations with multiple meanings. The section on brackets, in particular, clearly shows the same notation can mean wildly different things.
There is some notation that’s almost universal, such as using ‘+’ for edition, but that’s the case for programming languages, too.
Are there different notations for propositional logic and predicate logic?
https://en.wikipedia.org/wiki/Quantifier_(logic)#History:
“Frege did not devise an explicit notation for existential quantification, instead employing his equivalent of ~∀x~, or contraposition”
and
“Peirce and Mitchell wrote Πx and Σx where we now write ∀x and ∃x.”
(I like that notation, by the way)
and
“Peirce's approach to quantification also influenced William Ernest Johnson and Giuseppe Peano, who invented yet another notation, namely (x) for the universal quantification of x and (in 1897) ∃x for the existential quantification of x. Hence for decades, the canonical notation in philosophy and mathematical logic was (x)P* to express "all individuals in the domain of discourse have the property P," and "(∃x)P" for "there exists at least one individual in the domain of discourse having the property P." Peano, who was much better known than Peirce, in effect diffused the latter's thinking throughout Europe. Peano's notation was adopted by the Principia Mathematica of Whitehead and Russell, Quine, and Alonzo Church. In 1935, Gentzen introduced the ∀ symbol, by analogy with Peano's ∃ symbol. ∀ did not become canonical until the 1960s.”*
It would be nice to express logical aggregations such as AND and OR across sets like sum and product can be. Since their symbols are not Greek letters, it's not as simple as choosing the capitalized letter.
For that matter, a way of separating map-reduce from the reduction function, so that max, min, or other functions can be expressed uniformly, would also seem like an advancement. Probably it's been done and I'm simply ignorant.
― Alfred North Whitehead, An Introduction to Mathematics