Algebraic Geometry: concepts, history, and applications Algebraic geometry Algebraic geometry studies the geometric structure of solutions to polynomial equations, using tools from abstract algebra and topology. It connects number theory, geometry, and co…
Solvability by Radicals: When Polynomial Equations Have Algebraic Solutions Algebraic solution Explore when polynomial roots can be expressed using finite arithmetic and root extractions—solvability by radicals, classic formulas for quadratics/cubics/quartics, Abel–Ruffini l…
Algebraic structure An algebraic structure pairs a set with one or more operations and axioms; it organizes objects by how operations behave and underlies many areas of mathematics and its application…
Algebraic topology: methods for studying shape with algebra Algebraic topology Algebraic topology studies topological spaces by assigning algebraic invariants like groups and rings to capture qualitative features such as holes, connectivity, and higher-dimens…
Algebraic variety An algebraic variety is a geometric object defined by polynomial equations. This article explains basic definitions, types (affine, projective), irreducibility, singularities, hist…
Algorithm: Definition, Structure, History and Applications Algorithm An algorithm is a finite, well-defined sequence of steps to solve a problem or perform a task. Covers definition, parts, history, types, complexity, and typical uses in computing a…
Algorithmic information theory Study of information content and complexity of individual strings using computation and Kolmogorov complexity. Explains core concepts, history, uses, and limits for measuring rando…
Allometry: how size relates to shape, growth and biological scaling Allometry Allometry examines how size affects shape, growth rates and function in organisms. It covers scaling laws, developmental timing, evolutionary change and practical applications in e…
Alpha (Greek letter): origin, forms, and uses Alpha Overview of the Greek letter alpha — its shape and sound, historical origin, numeric value, and wide-ranging uses in language, science, mathematics, and culture.
Alphabet (computer science: formal languages and automata) Alphabet (computer science) A concise overview of the concept of an alphabet in computer science: definition, properties, history, relation to strings and languages, and practical applications in computing an…
Alphanumeric: definition, uses, ambiguity and technical notes Alphanumeric Alphanumeric refers to characters composed of letters and digits. This article explains definitions, practical variations, human-factor choices, examples (aircraft seats, VINs, con…
American Mathematical Society (AMS) American Mathematical Society The American Mathematical Society is a leading professional association advancing mathematical research, education, publications, meetings, and prizes for the mathematics community…
Anagram: definition, history, examples and uses Anagram An anagram rearranges the letters of a word or phrase to form a new word or phrase. This entry explains definitions, conventions, history, notable examples, literary uses, solving…
Analysis: definition, history, methods, and applications Analysis Examination of Analysis — breaking complex subjects into parts to understand them. Covers origins, key features, disciplines that use analysis, differences from synthesis, and comm…
Analytic Geometry (Coordinate or Cartesian Geometry) Analytic geometry Study of geometry using coordinates and algebraic methods; links shapes and equations, enables calculation of distances, slopes, conic sections, and transformations, and underpins…
And: conjunction, logical operator, computing symbol, and typographic sign And Overview of the word 'and' covering its role in language, logic (AND), computing, typographic symbol (&), history, common uses, and distinctions from related connectors.
Angle: definition, measurement, types, history and applications Angle An angle is the figure formed by two rays or lines meeting at a common point. This article explains notation, units (degrees, radians, gradians), classification, examples, history…
Annals of Mathematics A leading peer-reviewed mathematics journal published bimonthly by Princeton University and the Institute for Advanced Study, devoted to rigorous original research in pure mathemat…
Anonymous function (lambda, unnamed function) Anonymous function Overview of anonymous functions (lambdas): definition, syntax, history, common uses, language support, and distinctions from named functions.
Antiderivative (Indefinite Integral) Antiderivative An antiderivative is a function whose derivative equals a given function. This article explains definition, existence and uniqueness, main methods, relation to the fundamental theo…
Antiprism (geometry) Antiprism An antiprism is a polyhedron formed by two parallel, rotated copies of a polygon joined by a band of alternating triangles. It contrasts with prisms and appears in mathematics, che…
Apothem: definition, formulas, examples and uses Apothem The apothem of a regular polygon is the perpendicular segment from the polygon's center to a side; it equals the inradius and appears in area formulas and polygon geometry.
Applied Mathematics: methods, subfields, and practical applications Applied mathematics Applied mathematics develops mathematical models and techniques to solve real-world problems in science, engineering, finance and society, spanning modeling, computation, statistic…
Approximation: concepts, methods, and practical uses Approximation An overview of approximation: what it means, how it differs from exact values, common methods, error and tolerance, historical notes (Archimedes) and practical applications in scie…
Approximation theory: methods, history, and applications Approximation theory Overview of approximation theory: goals, common methods (polynomials, splines, Fourier), historical development, applications in computation and engineering, and important distinct…
Archimedean solid A convex uniform polyhedron with regular polygonal faces and identical vertices; distinct from Platonic solids, prisms or antiprisms. Thirteen (or fifteen counting chiral pairs) cl…
Arcsecond: definition, notation, conversions and astronomical uses Arcsecond An arcsecond is 1/3,600 of a degree (1/60 of an arcminute). Used in astronomy, surveying and geometry, it measures very small angles; 1 arcsec = π/648000 rad ≈ 4.848×10⁻⁶ radians.
Arithmetic: fundamentals, operations, history, education, and applications Arithmetic Arithmetic is the branch of mathematics that studies numbers and basic operations (addition, subtraction, multiplication, division), number types, methods, history, learning, and e…
Arithmetic precision: definitions, representation, rounding, and practical use Arithmetic precision Overview of arithmetic precision: significant digits, decimal places, rounding rules, numeric representation (floating and fixed point), measurement limits, examples, and best prac…
Arity (number of arguments of a function) Arity Arity is the number of arguments or operands a function, operation, or relation accepts. Used in logic, mathematics, and computer science to classify and type expressions and signa…
Association fallacy: guilt by association and honor by association Association fallacy Logical error that attributes qualities to a person or thing solely because of a shared connection; includes guilt by association and honor by association and appears in politics,…
Associativity: definition, examples, and significance in mathematics and computing Associativity Associativity is a property of binary operations meaning grouping does not change the result: (a⋆b)⋆c = a⋆(b⋆c). This article explains the concept, examples, non-examples, history,…
Atomicity (Transactions and Computing) Atomicity Atomicity is the guarantee that a set of operations executes as a single indivisible unit: either every operation completes successfully or none do. It is a core property of transa…
Attack model (cryptography) Attack model An attack model describes what information and capabilities an adversary has when trying to break a cryptographic system, from only ciphertext to adaptive chosen-ciphertext access.
Attribute–Value System Attribute-value system A compact, table-like knowledge representation in which objects (rows) are described by a fixed set of attributes (columns) and each cell records the attribute's value for that obj…
August Ferdinand Möbius German mathematician and astronomer noted for contributions to projective geometry, barycentric ideas and topology, best known for the Möbius strip and work at the University of Le…
Automata theory: abstract machines, formal languages, and computation Automata theory Overview of automata theory, its main models (finite, pushdown, Turing), core definitions, historical origins, applications in computing, and important distinctions and limits.
Automaton: abstract machines, finite-state models, and applications Automaton An automaton is an abstract mathematical machine that reads input symbol by symbol, changes states, and accepts or rejects sequences; used in computing, linguistics, verification a…
Average (mean, median, mode): Concepts, types, and uses Average An average summarizes a set of numbers by a single representative value. This article explains common averages (mean, median, mode), how they differ, calculation examples, uses, an…
Avoirdupois system: traditional system of weight measurement Avoirdupois system Avoirdupois is a system of weight based on a 16-ounce pound (7,000 grains, 453.59237 g). Widely used in the United States and still in use for everyday weights in several English-s…
Axiom (logic and mathematics) Axiom A concise reference on axioms: fundamental statements accepted without proof that form the starting points for logical systems, mathematical theories, and some scientific formulati…
Axiom of Choice Set-theory axiom asserting the ability to choose one element from each of a family of nonempty sets; important equivalents, history, examples, and mathematical consequences.
Babylonian numerals Overview of the Babylonian cuneiform numeral system: its symbols, base-60 positional structure, historical development, uses in astronomy and timekeeping, and its lasting influence…
Bacon number — degrees of separation from Kevin Bacon Bacon number A Bacon number measures how many film-based links separate an actor from Kevin Bacon, using co-appearance as connections; it adapts concepts from graph theory and the Erdős number…
Baker's dozen An informal count of 13 items — one more than a usual dozen — with origins in medieval trade practice; used historically as a safety margin and today as an idiom for an extra item.
Bar chart (bar graph) Bar chart Bar chart: a visual method that uses rectangular bars to compare values across categories. Covers types, components, history, uses, best practices, and distinctions from histograms…
Base — meanings, uses and notable senses Base Overview of the word “base” across mathematics, geometry, chemistry, technology, buildings, military, sport and language, with definitions, examples and distinctions.
Base (geometry): definition, role in polygons and solids Base (geometry) In geometry, a base is a referenced side or face used for measurements and calculations. This article explains its meaning in plane figures and solids, common conventions, and how…
