I understand mathematical notation, but I do think it generally is best only used when necessary in day-to-day work. Whenever something is of sufficient complexity, trying to keep track of the 10+ variables in a mathematical notation is generally harder than just reading a description.
For a recent example, my thought process yesterday: "So let's see, it says to multiply all of the 'F' functions, from 'm' to 'n'.. 'F' is, what, the base array? OK, so that makes 'm' and 'n'.. hmm. Let's come back to that. OK, so we multiply the product of those 'F's times the product of all 'alpha's of 'm,n' over 'm'.. so alpha is, let's see, the.. message? And... uh.."
Long story short, I finally deciphered it just meant "Multiply the base array of values by the value of each message that comes in that shares a parameter," only it took about 5 minutes instead of 10 seconds.
Think vector notation. Multiply arrays with matrices to get vectors. Add some sum notations and integrals. All that stuff is tedious to express in code but trivial to express in mathematics.
Also, many more scientific concepts such as gradient descent are most easily expressed using the appropriate mathematic operators like the nabla operator for gradients.
You're right, I don't want to give the impression that it's never warranted. Just that it's important to give thought to if a simple description or even a graph might be more efficient in each case.
I try to stay mindful of the limits of short term brain storage.. if there's over 7 unique variables or interval indicators, it might be tough for someone unfamiliar with what's going on to pick it up without wasting extra time noodling on it. When you've got a sum over 'm', a sum over 'm,n', a product sum over 'n,x' and another over 'x', etc.. sometimes it's just easier to bite the bullet and give a visual aid so the reader's not trying to envision all these overlapping regions in his head while still trying to remember what each is supposed to represent in real life.
For a recent example, my thought process yesterday: "So let's see, it says to multiply all of the 'F' functions, from 'm' to 'n'.. 'F' is, what, the base array? OK, so that makes 'm' and 'n'.. hmm. Let's come back to that. OK, so we multiply the product of those 'F's times the product of all 'alpha's of 'm,n' over 'm'.. so alpha is, let's see, the.. message? And... uh.."
Long story short, I finally deciphered it just meant "Multiply the base array of values by the value of each message that comes in that shares a parameter," only it took about 5 minutes instead of 10 seconds.