Are all group of mathematical notations a mathematical statement? I am not sure if this is the right stackexchange, but I wanted to ask if all group of mathematical notations are a mathematical statement. I want to ask this, because it seems to me that it's not the case, but I don't know what are the other classes a group of mathematical notations can fall under. It seems it's not the case, because a statement seeks to claim something as the truth, and not all group of mathematical notations seek to do that. By mathematical notations, I mean mathematical symbols.
 A: I may be misreading your question, but I'd say no. For example, $\pi$ is used to denote the ratio of a circle's circumference to its diameter and so simply denotes a (irrational) real number as opposed to any sort of statement. 
Additionally, mathematical symbols can be grouped in a way that renders them meaningless; for example, 
$$a^\varnothing-\sum_{\text{David Hilbert}}\prod_!\iint^=.$$
As an aside, there are also meaningful mathematical statements which are impossible to prove (at least with the current, standard axioms, and,  I suppose, assuming their consistency). For example,
$$2^{\aleph_0} = \aleph_1.$$
Caveat: Of course, someone can come along and define some new notation. This may render a once meaningless string meaningful. 
A: Just like any language, mathematics has grammar and vocabulary. There are meaningful ways to put symbols together, and meaningful ways to arrange groups of symbols, and these are essentially defined by a combination of assertion and consensus - by which I mean, anyone can say what something means but then everyone needs to agree on that for it to ultimately have meaning, at least in that context.
For example, I can't just go around talking about the mathfulness of something and expect you to understand that. Similarly, I can't just write $3++4$ and expect you to know what that might represent. However, I can say that "mathfulness" means "the ability to express something in a mathematical formulation", and then when I talk about the mathfulness of circular motion you have an idea of what I'm getting at. I can also say that $++$ is defined as an operator on two numbers such that $a++b := a + b + a \times b$, and now you know that $3++4 = 19$.
But someone else can say that "mathfulness" means "density of mathematical notation", and talk about the trends in mathfulness of journal articles. And they can also define $a++b := a^b + b^a$ and say that $3++4 = 145$. And then we need to have a way to distinguish those different meanings, which will depend on the context in which they're used and whether one meaning is used more often than the other and hence recognised more often.
