Language can be defined as the following: A medium in which communication occurs. However, there may be many misperceptions that mathematics is a language. One may argue that one can utilize numbers to represent certain letters in the alphabet, for example, a= 1, b = 2, c = 3. It is just using numbers, to represent a language. However, this is not mathematics. Numbers themselves can be a language, however numbers are just symbols. Numbers are not mathematics. Do we use mathematics to communicate? No. This is because mathematics is not a language, it is a process of logical reasoning. Yes, we can use any system of language to communicate the process of logic that mathematicians use. However, mathematics itself is not a method of communication. We can explain how to find the value of "x" in an equation in Babylonic cuneiform, or in C++, however, one cannot reach the conclusion without the method of inferring the answer, which is mathematics. Do we use language to find the instantaneous rate of change in a parabolic equation? No. We use a process of logical reasoning called mathematics to solve the problem. We do not use Latin to solve the problem. We do not use Morse code to solve the problem. We can use numbers to solve a problem, however, numbers by themselves are completely meaningless unless mathematics is used to manipulate numbers.
We can define language as: A medium in which communication occurs. Or a system of communication. Or a method to communicate one's thoughts or ideas.
We can define mathematics as: A procedure of manipulating numeric values to reach a desired conclusion. Or a method of finding answers to a numerical problem using logical reasoning. Or a science of numeric value, quantity, and space.
Mathematics is a process, not a medium. Mathematics is a method of reasoning, not a method of communication.
Now, perhaps it is clearly understood why mathematics is not a language; only the poetic can...