Mathematics

Composite number An integer greater than 1 that has a nontrivial divisor; contrasted with prime numbers and described by its prime factorization, examples, tests for compositeness, and some applica…

Computability theory: what can and cannot be computed Computability theory Study of which problems can be solved by algorithmic procedures, central models (Turing machines), main undecidable problems, history, and practical implications.

Computable Function A computable function is a mathematical function for which an effective algorithm exists to produce outputs from inputs in a finite number of steps.

Computation: concepts, models, and applications Computation An overview of computation: what it is, how it is modelled and studied, its history, practical applications, and theoretical limits including computability and complexity.

Computational complexity theory Study of the resources (time, space, randomness) required by algorithms and the classification of problems by their inherent difficulty, including classes like P, NP, and major ope…

Computer Algebra System Software that performs symbolic mathematics: it manipulates expressions, solves equations symbolically, computes derivatives and integrals, simplifies formulas, and aids visualizat…

Computer number formats: binary, octal, hexadecimal, integer and floating point Computer number format Overview of how computers and calculators represent numbers: binary, octal, hexadecimal, integer encodings, fixed-point and IEEE 754 floating point, uses, trade-offs and notable di…

Computus: calculation of the date of Easter Computus Computus is the traditional method for determining the date of Easter. It combines solar and lunar cycles, historical decisions, calendar reforms and algorithms that produce the mo…

Concatenation: joining strings and sequences in language, math, and computing Concatenation Concatenation is the operation of joining two or more strings or sequences end-to-end. It appears in everyday language, formal language theory, programming and database systems; it…

Concentric: shared centers in geometry, design, and nature Concentric Concentric describes shapes or objects that share the same center or origin. Common in geometry (circles, spheres), engineering, art, and natural patterns; distinct from eccentric…

Conceptual metaphor (cognitive metaphor) Conceptual metaphor An account of conceptual metaphor: how one domain of experience is understood in terms of another, its structure, examples, origins in cognitive linguistics, uses, and critical poi…

Cone: geometric shape, types, formulas, and uses Cone A cone is a three-dimensional figure with a circular, elliptic, or polygonal base tapering to an apex. This article covers definitions, varieties, surface and volume formulas, hist…

Congruence (geometry and related uses) Congruence Congruence describes when two figures have identical shape and size. In geometry it is formalized by isometries; applied criteria exist for polygons and triangles and contrasts wit…

Conic section Curves produced by intersecting a plane with a cone: parabolas, ellipses (including circles) and hyperbolas; defined geometrically and algebraically with applications in astronomy,…

Conjecture (mathematics): definition, history, and significance Conjecture An account of mathematical conjectures: what they are, how they differ from theorems, famous examples, and their role in mathematical discovery and research.

Conjugate variables in classical and quantum theory Conjugate variables Pairs of quantities whose order matters under a mathematical operation; central to quantum mechanics (e.g. position and momentum), with distinct mathematical formulation, history a…

Connect Four: rules, play, history and strategy Connect Four Connect Four is a two-player connection game played on a vertical 7×6 grid. Players drop colored discs aiming to make a line of four. The game is simple to learn yet rich in strate…

Consecutive integers Consecutive integer Consecutive integers are whole numbers that follow one another with a difference of one. This article explains their definition, key properties, arithmetic formulas, examples, and…

Consistency (concept) Consistency Consistency is the property of being uniform and noncontradictory across time, elements, or processes; it appears in behavior, logic, science, computing and materials and supports…

Consistency proof (mathematical logic) Consistency proof An overview of consistency proofs in logic: definitions, methods (model-theoretic and proof-theoretic), historical context including Hilbert and Gödel, examples, and important dist…

Constant (mathematics, physics, and computer science) Constant A constant is a fixed value that does not change. This article explains mathematical and physical constants, constants in programming, basic properties, history, examples, and comm…

Constant function A constant function is a map that assigns the same output to every input. This article explains the definition, basic properties, examples, and common uses in calculus, algebra, an…

Constraint (concept and applications) Constraint A constraint is a limitation or condition that restricts possible states or actions. This article surveys meanings, types, methods for handling constraints, history, and common app…

Constructive proof A constructive proof shows that a mathematical object exists by giving a method, explicit example, or algorithm to produce it. It contrasts with non-constructive existence proofs a…

Continuous function A continuous function maps nearby inputs to nearby outputs. This article explains the intuitive idea, the epsilon–delta definition, common variants, examples, and why continuity ma…

Continuum hypothesis A central question in set theory: whether any set has cardinality strictly between the natural numbers and the real numbers. It is independent of the usual Zermelo–Fraenkel axioms.

Contour line (isoline) Contour line A contour line (or isoline) connects points where a variable has the same value. Used on maps and charts to show elevation, pressure, temperature and other continuous fields.

Contradiction (logic and reasoning) Contradiction A contradiction is a pair or set of statements that cannot all be true at the same time. This article explains its formal role in logic, historical origins, examples, and philosoph…

Conversion of units: principles, methods, history and common examples Conversion of units Overview of unit conversion: what it is, how conversion factors and affine transforms work, common examples, rules for precision and dimensional analysis, history and practical tip…

Convex function Overview of convex functions: definition, key characterizations, common examples, basic properties and applications in analysis, optimization and economics.

Convex Regular 4‑Polytopes (Regular Polychora) Convex regular 4-polytope A concise overview of convex regular 4‑polytopes: their defining properties, the six examples discovered by Schläfli, structure and symmetries, historical context, and why they are…

Convex set A convex set is a subset of a vector space that contains the whole line segment between any two of its points. Fundamental in geometry, analysis, optimization, and computational ge…

Conway's Game of Life: a cellular automaton and zero-player simulation Conway's Game of Life A concise encyclopedia overview of Conway's Game of Life: rules, typical patterns, history, significance in computation and examples of use in mathematics, art, and education.

Cook–Levin theorem: SAT as the first NP-complete problem Cook–Levin theorem The Cook–Levin theorem proves that the Boolean satisfiability problem is NP-complete, establishing SAT as a canonical hard problem and underpinning the theory of NP-completeness an…

Coordinate system A coordinate system assigns numbers to points so their positions are uniquely specified. Covers Cartesian, polar, spherical and other systems, uses, history, and how coordinates tr…

Coprime (Relatively Prime) Numbers Coprime Two integers are coprime when their greatest common divisor is 1. This article covers definitions, notation, properties, examples, history, and key applications in arithmetic and c…

Corollary A corollary is a statement that follows readily from a previously proven proposition or theorem; used in mathematics, logic, and everyday language to denote an immediate consequenc…

Correlation in statistics: meaning, measures, and practical considerations Correlation Correlation quantifies the relationship between two variables. This article explains types of correlation, common measures, history, applications, and important cautions about inte…

Coset (group theory) Coset A coset is a translate of a subgroup inside a group. Left and right cosets partition a group, give the index, and lead to quotient groups when the subgroup is normal.

Countable set (mathematics) Countable set A countable set is one whose elements can be put into a list indexed by the natural numbers. This article explains definitions, examples, properties, historical background and key…

Countdown A countdown is a sequence of numbers that decreases toward zero to mark the approach of a planned event. It synchronizes actions, builds anticipation, and appears in launches, broa…

Counting: principles, methods, history and applications Counting An overview of counting as the activity and theory of determining how many items are present, covering basic concepts, historical development, practical methods, mathematical princ…

Crelle's Journal (Journal für die reine und angewandte Mathematik) Crelle's Journal A long-running German mathematics journal founded in 1826 by August Leopold Crelle, known for publishing foundational papers in analysis, algebra and number theory and for its infl…

Crore — South Asian unit equal to ten million Crore A crore is a unit in the South Asian numbering system equal to 10,000,000 (ten million) or 100 lakh, commonly used in India, Pakistan, Bangladesh, Nepal and Sri Lanka for counts an…

Cross product (vector product) Cross product The cross product is a binary operation on two three-dimensional vectors that yields a third vector perpendicular to both, with magnitude equal to the parallelogram area; widely us…

Cross section (geometry) A cross section is the intersection produced when a geometric object is cut by a line or plane; used in mathematics, engineering, and design to analyze shape, area, and internal st…

Cryptanalysis: methods, history, and modern practice Cryptanalysis Study of techniques for recovering plaintext or secret keys from encrypted data. Covers classical methods, attack models, mechanical and digital eras, modern mathematical and side‑…

Cryptographic hash function: properties, history, and applications Cryptographic hash function A cryptographic hash function maps arbitrary input to a fixed-size output used for integrity, authentication, and digital signatures. Covers properties, design history, common atta…