Why is it that math is considered as a language? :shrug:

because everything can be expressed by it

Not according to some people. According to some, certain mathematical ideas have only one way of being defined or described, too. I think people with those sorts of ideas should keep quiet more often, however.

because everything can be expressed by it
Try to express by formal math, the Earth is revolving around Sun and not vice-versa.

Try to express by formal math, the Earth is revolving around Sun and not vice-versa.

relativity does that.

Well I posted this in another thread but for convenience here it is again ....

Mathematics is a language. And languages allow us to represent ideas so that we may communicate them to others and record them for posterity. But more importantly it allows us to think in terms of "what if" and thus deal with and possibly plan for and control the future. Imagine if there were no vocal or sign languages how limited we would be.
The specific sublanguage Algebra deals with shapes, functions and transformations [among other topics]. The example above that x squared plus y squared equals 2 is a precise description of the locus of points the square root of two away from the origin.
A cirlce. In fact all quadratic equations in 2 variables describe one of 4 conic sections;
circle, parabola, ellipse or hyperbola. Higher order polynomials describe more active shapes precisely too.

Why is Matematics a language ?
Because it is an exact and elegant group of symbols representing ideas that are one subset of our reality.
This is why physicists need it and use it to explain the natural world.
But it would exist even if there were no scientists.

Try explaining why the earth revolves around the sun. Relativity does that.

Yes.
But try explaining relativity first in English.
Then describe/explain it with Math.
This illustrates the elegance and power of Mathematics.

Off the top on my head........

Mathematics deals with nouns (objects), verbs (operations), adjectives (object qualifiers/quantifiers), adverbs (operation qualifiers/quantifiers), all put together with an agreed and coherent syntax. There are also, very loosely, synonyms (equalities), similes (equivalence relations), analogies (isomorphisms), and, er, whatever.

Loosely defined, a language is an alphabet, and a set of production rules.
There are mappings, or connections, between elements in the alphabet, and the set of rules (the grammar), this is where things like nouns and verbs emerge. You can define a language mathematically, like a restricted or context-free grammar (or a machine language). Human language would only be mathematical to some extent, or maybe there's a built in chaos factor...

P.S. What do you call writing a new language in another language? Like a new compiler in C, or a new algebra in some other mathematical language? You can define a machine language with an ATN grammar.

ATN stands for augmented transition network. A transition network is a directed graph, that "looks" at input symbols or "tokens", and changes or connects to a different node in the graph, based on the token (by comparing the token with a subset from the "alphabet"), something like a Turing machine looking at an input tape (but the input isn't "consumed" by the ATN, it's read-only; the output is a separate "tape").

The graph is just a list of states. A state can have one or more transitions (to other states in the graph). If there's no transition, or the input symbol doesn't match any transistion, the next (successor) state is "transitioned" to. The graph is by default a sequential list.

An augmented TN, has additional actions (procedures, functions) that can be called before a transition occurs.

Fairly complex languages (command-line languages, assemblers with directives and macros, compilers, etc), can be constructed. Maintaining a complex graph gets a bit tedious, though.

This is a good twist on the topic I started called:What are the meaning of Numbers? This is basicsally the same topic!!! I will have to follow it more when there is time!!!

Because it has symbols, and symbols communicate.

Study Symbolic Logic. If you obtain the knowledge of enough of the symbolic representations, you can actually convey thoughts/ideas, and even notions. Purely with symbols.
One often encountered is the idea of Sigma representing an Expansion Series. You can manipulate this idea further with branch logic.

A neat one is building an entire lever system, which typically is about two sentences of nothing but symbols, figures, and equations. Anyone can then build this, given the knowledge.