matematik

Matematik is the study of numbers, quantities, shapes, patterns, and changes, expressed through symbols and formal reasoning. It seeks to understand abstract relationships and to provide tools for describing and analyzing the natural and engineered world. Mathematics is both a science and a language used across disciplines.

Mathematics is commonly divided into pure mathematics, which investigates mathematical structures for their own sake, and applied mathematics, which develops methods for solving real-world problems. Pure branches include algebra, geometry, number theory, calculus, topology, and logic. Applied branches include statistics, numerical analysis, optimization, computational mathematics, and mathematical physics.

Mathematics has ancient roots in counting and measurement from civilizations such as Mesopotamia and Egypt. Greek mathematicians developed formal proofs and axiomatic reasoning. Later contributions came from Indian, Chinese, and Islamic scholars, who advanced algebra and numerical notation. The invention of calculus in the 17th century marked a turning point. In the 19th and 20th centuries, the emphasis shifted toward rigor and abstraction with developments in set theory, logic, and formalism, leading to modern mathematical foundations and computer-assisted methods.

Mathematics relies on precise definitions, axioms, and deductive proofs. It also involves modeling real phenomena with abstract structures and using computation to explore complex problems. While proofs provide certainty within a given framework, mathematical models may approximate reality.

Mathematics underpins science, engineering, economics, and technology. It supports data analysis, cryptography, optimization, simulations, and algorithm design. Education in mathematics aims to develop logical thinking, problem solving, and the ability to abstract patterns.