Mathematics

Tensor (mathematics and physics) Tensor A tensor is a multilinear mathematical object used across mathematics, physics and engineering to represent scalars, vectors, linear maps and higher-order relationships between spa…

Terasecond and longer time spans Terasecond and longer A terasecond (Ts) equals one trillion seconds (10^12 s), about 31,700 years. Overview of its scale, related larger SI multiples (petasecond to quettasecond), uses, and notable conv…

Term (mathematics) A mathematical term is a single element of an expression—such as a number, variable, or product of them—used in algebra, polynomials, sequences, and formal logic; terms can be comb…

Tessellation (tiling of the plane) Tessellation Arrangement of shapes that covers a surface without gaps or overlaps; covers basic types, mathematical theory, history, and applications.

Tesseract — the four-dimensional hypercube Tesseract A tesseract (4‑cube) is the four-dimensional analogue of a cube: a regular convex 4‑polytope composed of eight cubic cells, studied in geometry, visualization, and theoretical cont…

Tet (Teth) — the ninth letter of the Hebrew alphabet Teth Tet (also Teth) is the ninth letter of the Hebrew alphabet, traditionally representing an emphatic t, carrying the numeric value 9, and tracing its shape and name to ancient Semiti…

Tetracontagon (40-sided polygon) Tetracontagon A tetracontagon is a forty-sided polygon. This article explains its key properties, regular form, formulas, constructibility, symmetry, star variants and common uses in geometry an…

Tetradecagon (14-sided polygon) Tetradecagon A tetradecagon is a polygon with fourteen sides and vertices. This article explains its regular form, angle measures, symmetry, star forms, constructibility, formulas and common oc…

Tetrahedron (triangular pyramid) Tetrahedron A tetrahedron is a polyhedron with four triangular faces, four vertices and six edges. This article explains its geometry, types, history, uses, and notable mathematical properties…

Tetration: the hyperoperation after exponentiation Tetration Tetration is the fourth hyperoperation: iterated exponentiation. It grows faster than exponentials, has special notation (e.g. a ↑↑ n or ^{n}a), and admits inverse operations and a…

Theorem (mathematics): definition, proof methods, and importance Theorem A theorem is a mathematical statement established by proof from axioms. This article explains structure, common proof methods, historical examples, uses, and distinctions from conj…

Gauss's Theorema Egregium — the intrinsic curvature of surfaces Theorema egregium Theorema Egregium states that Gaussian curvature of a surface is an intrinsic property: it can be computed from distances on the surface and does not change under bending without s…

Theory of computation Study of what problems computers can solve and how efficiently, covering computability, complexity, automata, formal languages, and applications in algorithms, cryptography, and ve…

Theta: Greek letter, history, and scientific uses Theta Theta (Θ, θ) is a Greek letter used in language, numerals, science, and mathematics; it has a long history from ancient phonetics to modern symbolic roles.

Third Normal Form (3NF) in Relational Database Design Third normal form Third normal form (3NF) is a database-design principle that reduces redundancy and anomalies by removing transitive dependencies; it requires 2NF and additional constraints on func…

Timeline of Women in Mathematics Chronological overview of women's participation in mathematics: early figures, institutional changes, notable contributions, milestones in recognition, and ongoing efforts to broad…

Timeline of Women in Mathematics in the United States Chronological overview of American women mathematicians: pioneers, educators, wartime programmers, institutional milestones, notable figures and ongoing challenges in the U.S. math…

Ton (unit) — short ton, long ton, and metric tonne explained Ton Overview of the ton as a unit of mass: definitions of the short ton, long ton (imperial), and the metric tonne, plus history, common uses, conversions, and important distinctions.

Topological space A topological space is a set equipped with a collection of open sets that formalize nearness and continuity. Definitions, examples, constructions, key properties, and applications…

Topology: the mathematical study of space, continuity and shape Topology An introduction to topology: its basic concepts, main branches (point-set, algebraic, differential), history, examples, and applications across mathematics and science.

Toroid (geometry) A toroid is a doughnut-like geometric form produced by revolving a plane figure about an external axis; it includes tori and related ring-shaped solids with applications in topolog…

Torsion: twisting in biology, mathematics, medicine and mechanics Torsion Torsion denotes a twisting or rotation and appears across disciplines: gastropod development, several mathematical notions, mechanical torque and spring behavior, and medical emerg…

Torus: geometry, topology, types, measurements and applications Torus A torus is a ring-shaped surface or solid formed by revolving a circle. Studied in geometry and topology, it has major and minor radii, closed-form area and volume, and several dis…

Transcendental number A transcendental number is a real or complex number that is not a root of any nonzero polynomial with integer coefficients; examples, history, properties and why they matter.

Transfinite number Numbers that extend beyond all finite values, including transfinite cardinals (alephs) and ordinals (ω and beyond); fundamental to set theory, sizes of infinity, and ordering of in…

Transformation (mathematics) Transformation A mathematical transformation is a rule that maps points between coordinate systems or within a space. It includes linear, affine, projective and non‑linear types and is central to…

Transitivity (mathematics) Transitivity is a structural property of a binary relation: whenever a relation links a to b and b to c, it also links a to c. It underpins equivalence relations and partial orders…

Transpose (matrix operation) Transpose The transpose of a matrix or vector swaps rows and columns. This article explains the definition, basic properties, common notation, examples, and where the transpose is used in ma…

Transposition Transposition is the action of changing positions or order; the term appears across mathematics, music, genetics, cryptography, law and medicine with distinct technical meanings.

Trapezoid (Trapezium) — Definition, Properties, and Uses Trapezoid A trapezoid (US) or trapezium (UK) is a four‑sided polygon with at least one pair of parallel sides. This article explains terminology, properties, formulas, special cases, and com…

Travelling Salesman Problem (TSP) Travelling salesman problem The Travelling Salesman Problem (TSP) is a foundational combinatorial optimization problem that asks for the shortest possible route visiting each node once and returning to the st…

Triacontadigon (32-sided polygon) Triacontadigon A triacontadigon is a polygon with 32 sides. This article summarizes its geometry, regular form, symmetry, diagonal count, constructibility, star variants, history, and common uses…

Triacontagon (30-sided polygon) Triacontagon A triacontagon, or 30-gon, is a polygon with thirty edges and vertices. The regular triacontagon has interior angles of 168°, central angle 12°, and is constructible with straighte…

Triangle (basic geometry and properties) Triangle A triangle is a three-sided polygon in plane geometry. This article explains its defining features, types, key formulas, notable centers, history and common applications.

Triangular number A triangular number equals the sum of the first n natural numbers, forming equilateral dot arrangements. Defined by n(n+1)/2, it appears in combinatorics, geometry, and number theo…

Trigonometric functions Trigonometric function Functions relating angles to ratios of triangle sides or coordinates on the unit circle; fundamental in geometry, analysis, physics, engineering and signal processing.

Trigonometry: functions, principles, history, and applications Trigonometry Survey of trigonometry: definitions, main functions and identities, historical development, practical uses in science and engineering, and how it relates to geometry and the unit c…

Trillion A trillion is a large cardinal number used in counting, science and finance; its numeric value differs between short and long scales and corresponds to 10^12 in the short scale.

Truncated differential cryptanalysis A form of differential cryptanalysis that tracks partially specified differences through a cipher; useful for analyzing block and stream ciphers when full bitwise differences are i…

Truncated icosahedron An Archimedean solid formed by truncating a regular icosahedron: 12 pentagons and 20 hexagons, 60 vertices and 90 edges. Familiar as the classic soccer-ball pattern and the C60 mol…

Truncated octahedron A truncated octahedron is a uniform Archimedean solid with 14 faces (8 hexagons, 6 squares), 36 edges and 24 vertices; it can fill space and arises by truncating an octahedron's ve…

Tuple: ordered finite sequences in mathematics and computing Tuple A tuple is a finite ordered list of elements. This article explains notation, properties, relations to sets and products, uses in mathematics, databases and programming, and common…

Turing complete (Turing completeness in computation) Turing complete Turing complete describes a system capable of performing any computation a Turing machine can, given enough time and memory. It is a central concept in computability, programming l…

Twin prime A twin prime pair are two prime numbers that differ by two. This article explains their properties, examples, historical results, open questions and related prime-pair types.

Twin prime conjecture Conjecture that there are infinitely many pairs of primes that differ by two. Overview, definitions, history, major results, methods, and related open problems in prime gaps and nu…

Type I and Type II Errors in Hypothesis Testing Type I and type II errors An accessible explanation of Type I (false positive) and Type II (false negative) errors in statistical hypothesis testing, their probabilities (α, β), the power of a test, trade-o…

Uncountable set A set too large to be placed in a one-to-one list with the natural numbers. Examples include the real numbers and any nontrivial interval; Cantor proved uncountability with a diago…

Unit — meanings, uses, and notable forms Unit Concise overview of the term “unit”: its meanings in measurement, mathematics, organizations, military and culture, with examples, history, and distinctions.