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Home > Mathematics as a language


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The central question involved in discussing mathematics as a language can be stated as follows :
What do we mean when we talk about the language of mathematics ? To what extent does mathematics meet generally accepted criteria of being a language ?

A secondary question is :

If it is valid to consider mathematics as a language, does this provide any new insights into the origins of mathematics, the practice of mathematics or the philosophy of mathematics ?.

1 What is a language?

To answer the first question, we need some definitions of language. See the article on language for several possible definitions. Other definitions are :-

These definitions describe language in terms of the following components :-

To expand on the concept of mathematics as a language, we can look at each of these components within mathematics itself.

2 The vocabulary of mathematics

Mathematical notation has assimilated symbols from many different alphabets and fonts. It also includes symbols that are specific to mathematics, such as

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 mathematics - examples are groupIn mathematics, a group is a set, together with a binary operation satisfying certain axioms, detailed below. The branch of mathematics which studies groups is called group theory. The historical origin of group theory goes back to the works of Evariste G, ringIn ring theory, a branch of abstract algebra, a ring is an algebraic structure in which addition and multiplication are defined and have similar properties to those familiar from the integers. History See Ring theory Definition and notation A ring is an a, fieldIn abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication, and division (except division by zero) may be performed and the associative, commutative, and distributive rules hold, which are famil, categoryCategory theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense". See list of category theory topics for a breakdown of relevan.

In other cases, specialist terms have been created which do not exist outside of mathematics - examples are tensorFor more technical Wiki articles on tensors, see the section later in this article. In mathematics, a tensor is a certain kind of geometrical entity which generalizes the concepts of scalar, vector (spatial) and linear operator in a way that is independen, fractalA fractal is a geometric object which is "broken up" in a radical way. The term fractal was coined in 1975 by Benoit Mandelbrot, from the Latin fractus or "broken", in order to call attention to such objects. They are in a number of major aspects differen, functorFor the usage in computer science, see the function object article. In category theory, a functor is a special type of mapping between categories. Functors can be thought of as morphisms in the category of all ( small) categories. Functors were first cons. Mathematical statements have their own moderately complex taxonomy, being divided into axiomFor the algebra software named Axiom, see Axiom (algebra software). For the 1970s Australian rock music group, see Axiom (band). In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built ups, conjectures, theorems, lemmas and corollaries. And there are stock phrases in mathematics, used with specific meanings, such as " if and only if", " necessary and sufficient" and " without loss of generality".



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