Mathematics

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With 420,278 views on Saturday, 10 October 2026 our article of the day is Mathematics.

Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is widely used to model and solve problems in science, engineering, technology, economics, and everyday life.

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 quantitative study of approximation and convergence), 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, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration.

Mathematics is essential in science and engineering; it is widely used in every field of knowledge and in everyday life, as soon as data are manipulated, shapes, patterns, and structures are studied, and logical reasoning is needed. Although mathematics is widely used to model empirical phenomena, its results are established by deductive proof rather than by experiment. The relationship between mathematical truth, logic, and reality is a subject of philosophical debate. 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 rigor 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 60 first-level areas of mathematics.

This recording reflects the Wikipedia text as of 02:55 UTC on Sunday, 11 October 2026.

For the full current version of the article, see Mathematics on Wikipedia.

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