Are languages such as notational,mathematics rightly called artificial languages ratherthan natural languages.?

There are different opinions about calling mathematics as a natural language. It is felt by many that mathematics also has a structure, vocabulary, grammar etc.. Wikipedia gives definitions of language: a systematic means of communicating by the use of sounds or conventional symbols WordNet a system of words used in a particular discipline WordNet the code we all use to express ourselves and communicate to others Speech & Language Therapy Glossary of Terms a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements Noam Chomsky These definitions describe language in terms of the following components: A vocabulary of symbols or words A grammar consisting of rules of how these symbols may be used A community of people who use and understand these symbols A range of meanings that can be communicated with these symbols Like any language, mathematics also has words which have different meanings. For example square means squaring a number. ...  more