MATHEMATICS

 Mathematics , the science of structure,

order, and relation that has evolved from

elemental practices of counting,

measuring, and describing the shapes of

objects. It deals with logical reasoning and

quantitative calculation, and its

development has involved an increasing

degree of idealization and abstraction of

its subject matter. Since the 17th century,

mathematics has been an indispensable

adjunct to the physical sciences and

technology, and in more recent times it

has assumed a similar role in the

quantitative aspects of the life sciences.

In many cultures—under the stimulus of

the needs of practical pursuits, such as

commerce and agriculture—mathematics

has developed far beyond basic counting.

This growth has been greatest in societies

complex enough to sustain these activities

and to provide leisure for contemplation

and the opportunity to build on the

achievements of earlier mathematicians.

All mathematical systems (for example,

Euclidean geometry ) are combinations of

sets of axioms and of theorems that can

be logically deduced from the axioms.

Inquiries into the logical and

philosophical basis of mathematics reduce

to questions of whether the axioms of a

given system ensure its completeness and

its consistency. For full treatment of this

aspect, see mathematics, foundations of .

This article offers a history of

mathematics from ancient times to the

present. As a consequence of the

exponential growth of science, most

mathematics has developed since the 15th

century CE, and it is a historical fact that,

from the 15th century to the late 20th

century, new developments in

mathematics were largely concentrated in

Europe and North America . For these

reasons, the bulk of this article is devoted

to European developments since 1500.