Search Results - Mathematics

Mathematics

Mathematics is a field of study that discovers and organizes methods, theories, and theorems that are developed and proved either in response to the needs of empirical sciences or the needs of mathematics itself. There are many areas of mathematics, including number theory (the study of integers and their properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the study of approximating continuous changes), and set theory (presently used as a foundation for all mathematics).

Mathematics involves the description and manipulation of abstract objects that are either abstractions from nature or purely abstract entities that are stipulated to have certain properties, called ''axioms''. Mathematics uses pure reason to prove the properties of objects through ''proofs'', which consist of a succession of applications of deductive rules to already established results. These results, called ''theorems'', include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of the theory under consideration.

Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application but often find practical applications later.

Mathematical written records first appeared in Ancient Egypt and Mesopotamia, but the concept of proof and its associated mathematical rigour began in Ancient Greek mathematics, exemplified in Euclid's ''Elements''. Mathematics was primarily divided into geometry and arithmetic until the 16th and 17th centuries, when algebra and infinitesimal calculus evolved into new fields. Since then, the interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematic use of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics.

Provided by Wikipedia