The language of mathematics or mathematical language is an extension of the

natural language In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages ...

(for example

English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...

) that is used in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and in

science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

for expressing results (

scientific law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...

theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...

s, proofs,

logical deduction Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false ...

s, etc) with concision, precision and unambiguity.

Features

The main features of the mathematical language are the following. * Use of common words with a derived meaning, generally more specific and more precise. For example, " or" means "one, the other or both", while, in common language, "both" is sometimes included and sometimes not. Also, a " line" is straight and has zero width. * Use of common words with a meaning that is completely different from their common meaning. For example, a mathematical

ring Ring may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell :(hence) to initiate a telephone connection Arts, entertainment and media Film and ...

is not related to any other meaning of "ring".

Real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

s and

imaginary number An imaginary number is a real number multiplied by the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square of an imaginary number is . Fo ...

s are two sorts of numbers, none being more real or more imaginary than the others. * Use of

neologism A neologism Greek νέο- ''néo''(="new") and λόγος /''lógos'' meaning "speech, utterance"] is a relatively recent or isolated term, word, or phrase that may be in the process of entering common use, but that has not been fully accepted int ...

s. For example

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" ...

. * Use of

symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...

s as words or phrases. For example,

A=B

and

\forall x

are respectively read as "

A

equals

B

" and * Use of

formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwee ...

s as part of sentences. For example: "

e=mc^2

''represents quantitatively the

mass–energy equivalence In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...

.''" A formula that is not included in a sentence is generally meaningless, since the meaning of the symbols may depend on the context: in this is the context that specifies that is the

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

of a

physical body In common usage and classical mechanics, a physical object or physical body (or simply an object or body) is a collection of matter within a defined contiguous boundary in three-dimensional space. The boundary must be defined and identified by t ...

, is its

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

, and is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

. * Use of mathematical jargon that consists of phrases that are used for informal explanations or shorthands. For example, "killing" is often used in place of "replacing with zero", and this led to the use of '' assassinator'' and '' annihilator'' as technical words.

Understanding mathematical text

The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example the sentence "''a

free module In mathematics, a free module is a module that has a basis – that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in t ...

is a

module Module, modular and modularity may refer to the concept of modularity. They may also refer to: Computing and engineering * Modular design, the engineering discipline of designing complex devices using separately designed sub-components * Mo ...

that has a

basis Basis may refer to: Finance and accounting * Adjusted basis, the net cost of an asset after adjusting for various tax-related items *Basis point, 0.01%, often used in the context of interest rates * Basis trading, a trading strategy consisting ...

''" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of ''basis'', ''module'', and ''free module''. H. B. Williams, an

electrophysiologist Electrophysiology (from Greek , ''ēlektron'', "amber" etymology of "electron"">Electron#Etymology">etymology of "electron" , ''physis'', "nature, origin"; and , ''-logia'') is the branch of physiology that studies the electrical properties of bi ...

, wrote in 1927:

Features

Understanding mathematical text

See also

References

Further reading

Linguistic point of view

In education