Mathematics

Mathematics is the study of quantity, structure, space, and change, expressed through numbers, symbols, and logical reasoning. It provides a precise language for describing patterns and relationships and underpins the natural sciences, engineering, economics, and many other fields. Mathematical knowledge is built from clearly stated definitions and assumptions, from which further results are proved by rigorous argument.

The subject is divided into several major branches. Arithmetic and basic mathematics deal with numbers and their operations, while algebra generalises arithmetic by using letters to represent unknown or variable quantities and to express general rules. Geometry studies shapes, sizes, and the properties of space, and trigonometry examines the relationships between the angles and sides of triangles. Calculus introduces the ideas of rates of change and accumulation, allowing the analysis of curves and motion, and statistics deals with collecting, summarising, and interpreting data.

Across these branches, mathematics relies on a shared system of symbols, constants, and formulas. Standard notation, including many letters of the Greek alphabet, allows complex ideas to be written compactly and understood internationally. Reference tables of formulas, constants, and important curves support both study and practical calculation. Together these branches and tools form a connected body of knowledge in which results from one area often illuminate another.

Frequently asked questions

What are the main branches of mathematics?

They include arithmetic, algebra, geometry, trigonometry, calculus and statistics, each studying a different aspect of number, shape, change or data.

How does algebra differ from arithmetic?

Arithmetic works with specific numbers, while algebra uses letters to stand for unknown or variable quantities and to express general relationships.

Why does mathematics use Greek letters?

Greek letters provide a large, internationally recognised set of symbols for constants, variables and functions, helping write ideas compactly.