Mathematics · Curated list
Geometry, Algebra, Arithmetic and 27 more, ranked by how much of the world has written about each one.
Most written-about first. Each description summarises the field's Wikipedia article, which its name links to.
1
Branch of mathematics
The part of mathematics that deals with the properties of space: how far apart figures are, and their shapes, sizes and positions relative to one another. With arithmetic, it ranks among the oldest mathematical branches.
Wikidata · Photo: Anonymous painter,15th century, Public domain
2
Branch of mathematics
The mathematics of abstract systems, called algebraic structures, and of how expressions are manipulated inside them. It extends arithmetic by bringing in variables, and operations beyond the familiar ones such as addition and multiplication.
Wikidata · Photo: Jamie Twells, Public domain
3
Branch of elementary mathematics
An elementary part of mathematics covering operations on numbers: adding, subtracting, multiplying and dividing. Taken more broadly it also takes in raising to powers, extracting roots and working out logarithms.
Wikidata · Photo: Master Uegly, Public domain
4
Area of geometry, about angles and lengths
The study of how the angles of triangles relate to the lengths of their sides. Its trigonometric functions, in particular, connect each angle of a right triangle with ratios between the lengths of that triangle's sides.
Branch of mathematics that studies sets
A branch of mathematical logic concerned with sets, which can loosely be thought of as collections of objects. A set may gather objects of any kind, but set theory as a mathematical subject mainly deals with the objects that matter to mathematics generally.
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7
Branch of pure mathematics
A part of mathematics chiefly about the integers and about arithmetic functions. Its practitioners study the primes, along with objects built from the integers or defined by generalising them.
Wikidata · Photo: Glosser.ca, CC BY-SA 3.0
8
Branch of mathematics
The mathematics of those properties of a geometric object that survive continuous deformation, such as bending, stretching, twisting or crumpling, provided nothing is torn, glued, passed through itself, or has holes opened or closed.
Wikidata · Photo: David Benbennick, CC BY-SA 3.0
Methods for numerical approximations
The study of algorithms that solve problems of continuous mathematics. They work with real or complex variables, and generally combine symbolic manipulation with numerical approximation.
11
Subfield of mathematics
Formal logic studied as part of mathematics. Its main subfields are recursion theory, set theory, proof theory and model theory.
12
Mathematical models of strategic interactions
A field of applied mathematics that treats interactions between several agents as "games" of strategy played by "players". It offers a scientific way to describe, predict, weigh up and choose between options, often aiming to get the most utility for one or more players.
Wikidata · Photo: Patrick M. Emerson, CC BY-SA 4.0
Branch of mathematics concerning probability
The mathematics of probability, also called probability calculus. Probability can be interpreted in several ways, but this branch handles it rigorously, stating it through a set of axioms.
14
Mathematical model of the physical space
A mathematical system credited to the ancient Greek mathematician Euclid, who set it out in his geometry textbook, the Elements. His method was to take a few axioms, or postulates, that seem intuitively right and derive many further propositions, or theorems, from them.
Study of discrete mathematical structures
The mathematics of structures that are "discrete" rather than "continuous", such as integers, graphs and logical statements.
Application of mathematical methods to other fields
Mathematical methods put to work in other fields: physics, biology, medicine and engineering, but also industry, business, finance, social science and computer science. It therefore joins mathematical science with specialist knowledge.
17
Branch of mathematics
Also called modern algebra, the part of algebra that studies algebraic structures: sets with particular operations acting on their elements. Lattices, modules, rings, vector spaces, fields, groups and algebras over a field are all examples.
Wikidata · Photo: Michel Bakni, Public domain
18
Branch of discrete mathematics
A part of mathematics mainly about counting, used both as a tool and as a goal in itself, and about certain properties of finite structures. It is tied to many other areas of mathematics and is applied everywhere from logic and statistical physics to evolutionary biology and computer science.
Wikidata · Photo: Original uploader was Chmbrlnd at en.wikibooks, CC BY-SA 4.0
Branch of mathematics that studies the properties of groups
The branch of abstract algebra that studies groups. Groups are central to abstract algebra: rings, fields, vector spaces and other familiar structures can all be viewed as groups given extra operations and axioms.
20
Study of geometry using a coordinate system
Geometry done with a coordinate system. It is also called Cartesian geometry or coordinate geometry, and stands in contrast to synthetic geometry.
Wikidata · Photo: Cham pour wikipedia.fr, transféré sur Commons par Anarkman, Public domain
21
Area of discrete mathematics
The study, in mathematics and computer science, of graphs: structures used to represent relations between pairs of objects. Such a graph is made of vertices, with edges connecting them.
Wikidata · Photo: David Eppstein, CC0
22
Study of rates of change
A subfield of calculus that studies how fast quantities change.
Wikidata · Photo: Engelbert Niehaus, CC BY 4.0
23
Algebraic manipulation of "true" and "false"
A branch of algebra, belonging to both mathematics and mathematical logic, that departs from elementary algebra in two respects.
Wikidata · Photo: User:Vaughan Pratt, CC BY 3.0
24
Field of mathematics and science based on non-linear systems and initial conditions
A branch of mathematics that is also an interdisciplinary area of science. It looks at the deterministic laws and underlying patterns of dynamical systems whose behaviour depends very strongly on their initial conditions.
Wikidata · Photo: Computed in Fractint by Wikimol, Public domain
25
Branch of applied mathematics
The development of mathematical methods for physics and their use there. Defined more broadly, it also covers mathematical ideas that physics has inspired, an area called physical mathematics.
Wikidata · Photo: Yulia Meshkova, CC BY 4.0
26
Branch of mathematics studying functions of a complex variable
Traditionally known as function theory of a complex variable, this part of mathematical analysis looks at functions with complex values, in one complex variable or several. Number theory, algebraic geometry, applied mathematics, functional analysis and analytic combinatorics all draw on it, and in physics so do thermodynamics, hydrodynamics, twistor theory and quantum mechanics.
27
Calculus of vector-valued functions
Also called vector analysis, the branch of mathematics that differentiates and integrates vector fields, mostly in three-dimensional Euclidean space, ℝ³. The name is sometimes used for all of multivariable calculus, which also includes partial differentiation and multiple integration.
Wikidata · Photo: JuanManwell, CC BY-SA 3.0
28
Branch of mathematics
The mathematical study of shapes and spaces that are smooth, also called smooth manifolds, and of their geometry. It relies on methods from linear algebra, multilinear algebra and vector calculus.
Wikidata · Photo: Brews ohare, CC BY-SA 3.0
29
Branch of mathematics
A part of mathematics that tackles geometric problems with abstract algebra, drawing above all on commutative algebra. In its classical form it studies the zeros of polynomials in several variables; the modern approach widens that in a few directions.
Wikidata · Photo: Jakob.scholbach at English Wikipedia, CC BY-SA 3.0
30
Two geometries based on axioms closely related to those specifying Euclidean geometry
Two geometries built on axioms close to those of Euclidean geometry. Since Euclidean geometry sits where metric geometry and affine geometry meet, a non-Euclidean one comes either from swapping the parallel postulate for another axiom, or from using quadratic forms other than the definite ones that metric geometry relies on.
Every Wikidata item that is an area of mathematics, and that has its own English Wikipedia article, ranked by the number of Wikimedia sites with a page about it — Wikipedia's language editions, mostly, and sister projects such as Wikiquote. That counts how many communities independently thought it worth describing, and nobody can buy a place on it. The top 30 are shown.
Fetched from Wikidata on 2026-09-25. Each description is this site's summary of the entry's Wikipedia article, which its name links to: the wording is ours, the facts are Wikipedia's, licensed CC BY-SA 4.0. To correct an entry, correct it there; the next refresh carries the change.
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