[Koshkin]

> Mathematical notation is for stating mathematical facts or propositions.

And as such it is way too often abused. Because the (original, and the most useful) purpose of mathematical notation is to enable calculation, i.e., in a general sense, to make it possible to obtain results by manipulating symbols according certain rules.

[layer8]

I see the steps of a calculation as stating a sequence of mathematical facts, so that’s just an instance of the general definition.

[Koshkin]

Sure, but the whole point is to avoid the need to do that! Manipulating symbols is the way to automate reasoning, i.e. to get to a result while completely ignoring said "facts." Using the symbols to merely "state the facts" is abuse (of the reader, mostly).