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The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.
In mathematics, a symbolic language is a language that uses characters or symbols to represent concepts, such as mathematical operations, expressions, and statements, and the entities or operands on which the operations are performed.
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
If mathematics is a language, it is a different type of language from natural languages. Indeed, because of the need for clarity and specificity, the language of mathematics is far more constrained than natural languages studied by linguists.
A formal language is a language that is defined by a formal system. Like languages in linguistics , formal languages generally have two aspects: the syntax is what the language looks like (more formally: the set of possible expressions that are valid utterances in the language)
List of letters used in mathematics, science, and engineering; ISO 31-11; Language of mathematics; List of mathematical jargon; Mathematical notation; Notation in probability and statistics; Physical constants; List of logic symbols; Glossary of mathematical symbols; Mathematical operators and symbols in Unicode; List of mathematical functions
Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice , quasi-empiricism in mathematics , and so-called folk mathematics , oral traditions ...