Mathematics is a language. And the most important part of a language is abstraction. And abstraction in Mathematics only comes from understanding, and practising problems. But yes, it's important to accompany formulas with what the variables denote (rather than what they mean). Then the reader should spend time searching for the meaning. If the author really knows what (s)he is writing, (s)he will definitely give enough information for the reader to disambiguate/understand its meaning.

Let me give you an example:
All of us 'know' the formula of a straight line in two dimensions:

• [math]y = mx + c [/math]

I ought to write what the variables and constants mean. So I uncover the first level of abstraction:

• Given constant real numbers [math]m[/math] and [math]c[/math], the equation [math]y = mx + c[/math] denotes a straight line, where [math]y[/math] and [math]x[/math] are dependent and independent real variables respectively. Here, [math]m[/math] and [math]c[/math] denote the slope of the line, and its [math]y[/math]-intercept respectively.

The next question from the reader could be: what is a constant? A real number? A variable? A dependent/independent variable? A slope? An intercept? Assume that the reader knows what a real number is (because it would take more space/time to explain it here). So, in purely mathematical terms, following would be uncovering another level of abstraction:

• A set is a well-defined collection of objects.
• A proposition is a sentence that is either TRUE or FALSE.
• Given a proposition [math]P(x)[/math] for an object [math]x[/math], the set of all values for which the proposition holds is denoted by [math]\{x~|~P(x)\}[/math].
• The Cartesian product of two sets [math]A[/math] and [math]B[/math] is defined as [math]A \times B = \{(a, b)~|~(a \in A) \wedge (b \in B)\}[/math]
• A relation [math]R[/math] from [math]A[/math] to [math]B[/math] is defined as a subset of [math]A \times B[/math]. That is, [math]R \subseteq A \times B[/math]
• A function [math]f[/math] from [math]A[/math] to [math]B[/math] is a relation from [math]A[/math] to [math]B[/math] with the property that [math]a \in A \implies \exists ! b \in B[/math] such that [math](a, b) \in f[/math]. Such a function is denoted as [math]f : A \rightarrow B[/math], and if [math](a, b) \in f[/math], we can write [math]b[/math] as [math]f(a)[/math].
• An operation [math]\ast[/math] on a set [math]A[/math] is defined as a function [math]\ast: A \times A \rightarrow A[/math].
• On the set of real numbers [math]\mathbb{R}[/math], define two operations [math]+[/math] and [math]\cdot[/math], namely addition and multiplication respectively (assume that the reader knows what a real number is, and how to add and multiply two real numbers). Multiplication of [math]a, b \in \mathbb{R}[/math] is sometimes denoted by [math]ab[/math] instead of [math]a \cdot b[/math], and take precedence over [math]+[/math], when written ambiguously.
  
• Let [math]m, c \in \mathbb{R}[/math] be fixed. Then the function [math]f:\mathbb{R} \rightarrow \mathbb{R}[/math], defined by [math]x \mapsto mx + c[/math], [math]\forall x \in \mathbb{R}[/math], denotes a straight line. Sometimes, it's convenient to represent [math]f(x)[/math] as [math]y[/math], where [math]x[/math] is called the independent variable, and [math]y[/math], the dependent variable in [math]\mathbb{R}[/math]

We can stop here! But we haven't yet defined everything: e.g., [math]\in[/math], [math]\wedge[/math], [math]\exists[/math], [math]![/math], [math]\mathbb{R}[/math], [math]+[/math] and [math]\cdot[/math] in [math]\mathbb{R}[/math], and many more. A good exercise is to think how to define the graph of a function.