mathematike

Mathematike, or mathematics, is the abstract science of quantity, structure, space, and change. It investigates patterns, relationships, and logical consequences using symbolic notation and rigorous proof. The term derives from Greek mathema, meaning something learnt, through mathēmatikḗ, the science of learning, with Latin mathematica shaping the modern word.

Historically, mathematical ideas emerged in ancient civilizations for practical tasks such as counting, surveying, and astronomy. Greek thinkers such as Euclid and Archimedes developed deductive methods and formal proofs that shaped the notion of a mathematical theory. From the medieval Islamic world and later European scholars, algebra and analysis advanced, culminating in calculus by Newton and Leibniz. In the 19th and 20th centuries, mathematics expanded into formal foundations, including set theory and logic, and into increasingly abstract areas such as topology, modern algebra, and category theory. The late 20th and 21st centuries have seen the rise of computational mathematics, numerical analysis, and data-driven approaches that apply mathematical ideas to science and engineering.

Branches of mathematics include pure areas—number theory, algebra, geometry, analysis, topology, and combinatorics—and applied areas such as statistics, probability, applied mathematics, mathematical physics, computational mathematics, and financial mathematics. Mathematics also informs computer science, economics, engineering, biology, and the social sciences.

Methods combine axiomatic reasoning, proof, and model-building with computation and approximation. Mathematics is both a universal language for describing patterns in the natural world and a creative discipline that continually extends its foundations and tools.