the language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. this language consists of a substrate of some natural language (for example english) using technical terms and grammatical conventions that are peculiar to mathematical discourse (see mathematical jargon), supplemented by a highly specialized symbolic notation for mathematical formulas. like natural languages in general, discourse using the language of mathematics can employ a scala of registers. research articles in academic journals use a more formal tone than oral exchanges over a scribbled-upon napkin in the university cafeteria. ==what is a language?== here are some 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 each of these components is also found in the language of mathematics. ==the vocabulary of mathematics== mathematical notation has assimilated symbols from many different alphabets and typefaces. it also includes symbols that are specific to mathematics, such as :\forall \ \exists \ \nabla \ \wedge \ \infty. mathematical notation is central to the power of modern mathematics. though the algebra of al-khwÄrizmÄ« did not use such symbols, it solved equations using many more rules than are used today with symbolic notation, and had great difficulty working with multiple variables (which using symbolic notation can simply be called x, y, z, etc.). sometimes formulas cannot be understood without a written or spoken explanation, but often they are sufficient by themselves, and sometimes they are difficult to read aloud or information is lost in the translation to words, as when several parenthetical factors are involved or when a complex structure like a matrix is manipulated. like any other profession, mathematics also has its own brand of technical terminology. in some cases, a word in general usage has a different and specific meaning within mathematicsâexample
Language Philosophy_of_mathematics