You can see how mathematical notation evolved during the last centuries here.
I think everyone here knows that a bad notation can change an otherwise elementar problem into a difficult problem. Just try to do basic arithmetics with roman numbers, for example.
As a computer programmer I know that in some situations programming language notation plays a critical rule because some algorithms are better expressed in a particular language than in other languages even considering they all have the same basis: Lambda Calculus, Turing machines, etc
The linguists has their so-called Sapir–Whorf hypothesis which "…holds that the structure of a language affects the ways in which its respective speakers conceptualize their world, i.e. their world view, or otherwise influences their cognitive processes."
Then, I ask: is there any field in Math that studies Math's notation and its influence for good or for bad in Math itself?
Modifying the fragment on the paragraph above:
is it possible that the notation, the symbols and the language used in Math affects the ways in which Mathematicians conceptualize their world and influences their cognitive processes?
Best Answer
On a quite different tack, you might well be interested in Mohan Ganesalingham's The Language of Mathematics: A Linguistic and Philosophical Investigation (Springer 2013).
The author is an outstanding mathematician (Senior Wrangler, no less), and has a degree in linguistics, and now works in computer science. The book is based on a prize-winning thesis. I mention those facts in case the word "philosophical" in the sub-title puts you off! Mohan seriously knows his stuff.