Mathematics

Logarithmic scale A logarithmic scale maps quantities to their logarithm so wide-ranging values become manageable; used for sound, earthquakes, pH, light, and many scientific charts and instruments.

Logarithmic spiral A self-similar plane curve with constant angle between radius and tangent, occurring in nature and used in mathematics, engineering and art. Also called equiangular or growth spira…

Logic programming: principles, history and practical uses Logic programming An introduction to logic programming, its core concepts (facts, rules, unification, backtracking), history, variants and common applications such as AI, databases and natural langu…

Logical conjunction (AND) Logical conjunction Logical conjunction, commonly called AND, is a fundamental binary operation of logic that returns true only when all its operands are true. It has algebraic properties, digital-cir…

Logical negation (NOT) — definition, properties, and uses Logical negation Logical negation (NOT) is the unary operation that inverts truth values. Explains symbols, truth table, key laws, differences across logics and computing, and practical examples.

Logical quantifier An explanation of logical quantifiers: their meaning, notation (∀, ∃), semantics, scope and interaction with negation; examples, variants (unique and generalized quantifiers), and…

Long and short scales: naming systems for large numbers Long and short scales Two systems for naming large powers of ten. The short scale advances by thousands (10^3), the long scale by millions (10^6); they use the same words for different values and can ca…

Long ton (imperial ton) Long ton The long ton is the traditional British ton of 2,240 pounds, historically used for shipping and trade in the UK and some Commonwealth countries; it differs from the short ton and m…

Lorenz attractor: chaotic solutions, history, and significance Lorenz attractor The Lorenz attractor is a set of chaotic trajectories of a three‑variable ODE system introduced by Edward Lorenz as a simple model of atmospheric convection. It illustrates sensiti…

Loss function (cost function) in statistics and machine learning Loss function A loss function assigns a numerical penalty to a prediction or decision. This article explains definitions, common types (MSE, MAE, cross‑entropy, hinge), uses in optimization and…

M (letter) M The letter M is the 13th character of the Latin alphabet. This article explains its sound, shapes, historical origin, common uses (including Roman numeral and SI symbol) and typogr…

Magma (algebraic structure) Magma (mathematics) A magma is the most basic algebraic structure: a set equipped with a single closed binary operation. This article covers definition, examples, basic properties, history, and relati…

Magnitude: measures of size in mathematics, astronomy, seismology and more Magnitude Magnitude denotes the size, extent, or strength of something. Used in mathematics (norms), astronomy (apparent/absolute brightness), seismology (earthquake scales) and everyday con…

Magnitude (mathematics) Magnitude denotes the size or extent of a mathematical object. It appears in many forms—length, area, measure, norm, absolute value, cardinality—and underlies comparison and orderi…

Majority: meaning, types, and role in voting and decisions Majority Overview of the concept of majority — definitions, common variants (absolute, relative/plurality, supermajority), history, uses in voting and law, and distinctions from minority an…

Mandelbrot set: definition, properties, history, visualisation and variations Mandelbrot set A compact guide to the Mandelbrot set: its iterative definition on the complex plane, visual and mathematical properties, historical context, examples, notable facts and common gen…

Manifold (mathematics): spaces locally equivalent to Euclidean space Manifold Overview of mathematical manifolds: spaces that are locally like Euclidean n-space, assembled from coordinate charts and atlases. Explains examples (curves, surfaces, hyperbolic pl…

Maple (computer algebra system) Maple (CAS) Maple is a commercial computer algebra system by Maplesoft that integrates symbolic and numeric computation, visualization, a programming language, and tools for mathematics, engin…

Margin of Error Margin of error measures sampling uncertainty in survey results; it depends on sample size, variability, and confidence level and helps interpret polls and estimates.

Maß (Mass): traditional German beer measure Maß Maß — a traditional German liquid measure once ≈1.069 litres, now commonly the one-litre beer mug (Maß) used at Oktoberfest, beer gardens and in Bavarian beer culture.

Mathematical analysis: foundations, branches and applications Mathematical analysis Mathematical analysis studies limits, continuity, differentiation, integration and infinite processes. It forms the rigorous backbone of calculus and underpins many areas of pure a…

Mathematical induction: principles, variants, and applications Mathematical induction Mathematical induction is a proof technique for propositions indexed by natural numbers. This article explains its principle, common variants, examples, typical mistakes, and conne…

Mathematical logic Mathematical logic is the discipline that studies formal systems of reasoning, their structure, limits, and applications to mathematics and computing.

Mathematical model: concept, types, construction and uses Mathematical model A mathematical model represents a real system with mathematical language. This article explains types, how models are built and tested, their uses across sciences and engineering,…

Mathematical notation: symbols, structure, history, and uses Mathematical notation An overview of mathematical notation: its elements (symbols, variables, operators), historical development, diagrammatic forms, conventions, and role across mathematics and science…

Optimization in mathematics: theory, problem types, and common solution methods Mathematical optimization Overview of mathematical optimization: theory, problem classes (convex, integer, multiobjective, stochastic), model formulation, and common solution methods from calculus and LP to…

Mathematical physics: concepts, methods, and applications Mathematical physics Mathematical physics develops and applies mathematical structures and techniques to formulate, analyze, and solve physical problems, linking pure mathematics and theoretical physic…

Mathematical proof A mathematical proof is a logical demonstration that a statement follows from agreed assumptions. This article explains what proofs are, common techniques, history, uses, and notab…

Mathematical Reviews A reviewing service and bibliographic database from the American Mathematical Society offering expert summaries, subject classification and searchable records for mathematics, stat…

Mathematician: roles, areas, history, methods and applications Mathematician A mathematician studies mathematics, creating proofs, models and theories. This article outlines typical roles, key branches, historical development, methods, and practical applica…

Mathematics: concepts, branches, history, and applications Mathematics A clear introduction to mathematics: its central ideas, main branches, historical development, and practical uses across science, engineering, business and everyday life.

Mathematics Genealogy Project A web database that documents doctoral-level academic lineages in mathematics: advisors, students, thesis titles, institutions and related metadata for research, verification, and…

Mathematics Subject Classification (MSC) Mathematics Subject Classification A hierarchical alphanumeric system used to categorize mathematical literature for indexing, searching, and bibliographic organization, maintained by mathematical reviewing services…

Matrix (mathematics): definition, properties, and applications Matrix (mathematics) A matrix is a rectangular array of numbers or symbols arranged in rows and columns. This article explains structure, common operations, types, brief history, and principal applicat…

Maximum and Minimum: Definitions, Types, and Mathematical Significance Maximum and minimum Overview of maximum and minimum (extrema), their formal definitions, global vs local distinctions, calculus criteria, historical context, examples and common applications.

Maya Calendrical System: Interlocking Ritual and Solar Cycles Maya calendar Overview of the Maya calendrical system: how 260-day ritual and 365-day solar cycles interlock, plus the Long Count, their origins, uses in ceremony and agriculture, and modern leg…

Maze: types, history, design, and practical uses Maze A maze is a puzzle built from paths and barriers. This article explains types, structure, history, differences from labyrinths, common solving methods, and practical applications i…

Mean (average): definitions, types, and uses in mathematics and statistics Mean An accessible overview of the mean: what it is, common types (arithmetic, geometric, harmonic, weighted), statistical role, properties, examples, and differences from other average…

Measurement: concept, units, methods and importance Measurement Overview of measurement: defining quantities, common units and scales, instruments and methods, history and standards, plus practical uses and distinctions like accuracy, precision…

Mebibyte (MiB): definition, history, conversions and practical use Mebibyte A mebibyte (MiB) is a binary-based unit of digital information equal to 1,048,576 bytes (2^20). This article explains its definition, history, conversions, uses and common confusio…

Median (measure of central tendency) Median The median is the middle value that divides a dataset or distribution into two equal halves. This article explains calculation, properties, variants, history, uses and distinctions…

Meet-in-the-middle attack A cryptanalytic technique that reduces the cost of breaking composed encryption by trading computation for memory; notably used against naive double-encryption schemes such as earl…

Megasecond A megasecond is one million seconds (10^6 s), equal to about 11.6 days. It is an SI-derived time interval used for expressing large durations and relating seconds to metric multipl…

Mental calculation (mental maths) Mental calculation Mental calculation is performing arithmetic in the mind without writing or using external tools; it relies on methods, memory strategies and practice for fast, accurate results and…

Meridian arc Distance measured along a meridian (constant longitude) between two latitudes; a fundamental concept in geodesy for determining Earth’s shape, mapping datums and converting angular…

Mersenne prime A prime number of the form 2^p − 1, where p is prime. Mersenne primes connect to perfect numbers, are central to large-prime searches, and are efficiently tested by specialized alg…

Metre (meter): the SI base unit of length Metre The metre (meter) is the SI base unit of length, defined since 1983 by the distance light travels in vacuum in 1/299,792,458 of a second. It originated from a French Revolutionary…

Metric space A metric space is a set equipped with a distance function satisfying non-negativity, identity of indiscernibles, symmetry and the triangle inequality; foundational in analysis, top…