mathématique

Mathématique, in French linguistic usage, is the field of study that investigates quantities, structures, spaces and changes, using abstract reasoning and symbolic manipulation. Internationally, the discipline is known as mathematics; it encompasses both theoretical development and practical application.

Historically, mathematical activity arose in ancient times with counting and basic geometry. Greek mathematicians laid foundations in logic and deduction. Islamic scholars preserved and expanded Greek works, translating and extending algebra and trigonometry. The European Renaissance and subsequent centuries produced calculus, algebraic geometry, topology, and the formal axiomatic method, culminating in modern mathematical foundations.

Branches include arithmetic, algebra, geometry, analysis (including calculus and real/complex analysis), topology, number theory, probability and statistics, logic, and applied mathematics. Interdisciplinary areas such as computational mathematics and mathematical physics blend methods from several branches.

Mathematics is practiced through definitions, axioms, theorems, and proofs. Notation evolves for precision, with symbols to express operations, limits, sets and functions.

In education and science, mathématique provides tools for modeling, reasoning, and decision making, underpinning sciences, engineering, finance, and data analysis.