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Use of mathematics as a philosophical framework
referred to as mathematicism. Although we do not have writings of Pythagoras himself, good evidence that he pioneered the concept of mathematicism is given
Mathematicism
Field of knowledge
Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical
Mathematics
Application of mathematical methods to other fields
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business,
Applied_mathematics
Collection of mathematical objects
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects:
Set_(mathematics)
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Association of one output to each input
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function
Function_(mathematics)
Set with associative invertible operation
In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following
Group_(mathematics)
System of symbolic representation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling
Mathematical_notation
Cosmological theory
proposes the existence of mathematical entities; a form of mathematicism in that it denies that anything exists except mathematical objects; and a formal
Mathematical universe hypothesis
Mathematical_universe_hypothesis
Branch of mathematics
Mathematical analysis is the branch of mathematics that studies functions, spaces, and operators through quantitative methods of approximation and convergence
Mathematical_analysis
Max Tegmark's mathematical universe hypothesis (or mathematicism) goes further than Platonism in asserting that not only do all mathematical objects exist
Philosophy_of_mathematics
Basic framework of mathematics
Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory
Foundations_of_mathematics
Study of discrete mathematical structures
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one
Discrete_mathematics
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,
Mathematical_object
Expression which is not assigned an interpretation
In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system
Undefined_(mathematics)
Scientific journal
Mathematical Reviews is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of
Mathematical_Reviews
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned
Mathematics_and_art
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern
History_of_mathematics
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Generalization of vector spaces from fields to rings
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)
Module_(mathematics)
Set of all points in a function's domain that all map to some single given point
In mathematics, the fiber (US English) or fibre (British English) of an element y {\displaystyle y} under a function f {\displaystyle f} is the preimage
Fiber_(mathematics)
Description of a system using mathematical concepts and language
mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical
Mathematical_model
Topics referred to by the same term
Look up mathematics in Wiktionary, the free dictionary. Mathematics is a field of knowledge. Mathematics may also refer to: Mathematics (producer), hip-hop
Mathematics_(disambiguation)
2D surface which extends indefinitely
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero
Plane_(mathematics)
Property of two varying quantities with a constant ratio
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant
Proportionality_(mathematics)
Tool to track locally defined data attached to the open sets of a topological space
Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian
Sheaf_(mathematics)
Study of mathematical algorithms for optimization problems
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria
Mathematical_optimization
Mathematics independent of applications
mathematics, pure mathematics is an informal term to describe the study of mathematical concepts independently of any application outside mathematics
Pure_mathematics
Function equal to cos x + i sin x
In mathematics, cis is a function defined by cis x = cos x + i sin x, where cos is the cosine function, i is the imaginary unit and sin is the sine function
Cis_(mathematics)
Collection of objects and morphisms
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked
Category_(mathematics)
All numbers between two given numbers
In mathematics, an interval is the set of all real numbers lying between two fixed endpoints with no "gaps". For example, the set of real numbers consisting
Interval_(mathematics)
Form of mathematical proof
Mathematical induction is a method for proving that a statement P ( n ) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that
Mathematical_induction
Mathematical modeling of psychological theories and phenomena
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes
Mathematical_psychology
248-dimensional exceptional simple Lie group
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same
E8_(mathematics)
Application of mathematical and statistical methods in finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling
Mathematical_finance
Property determining comparison and ordering
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects
Magnitude_(mathematics)
Generalization of mass, length, area and volume
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions
Measure_(mathematics)
Directed graph which is also a multigraph
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows
Quiver_(mathematics)
Operation combining two oriented knots
In mathematics, a knot is an embedding of the circle (S1) into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered
Knot_(mathematics)
Point of reference in Euclidean space
In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry
Origin_(mathematics)
Generalization of a sequence of points
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a function whose domain is a directed set
Net_(mathematics)
Open set containing a given point
In topology and mathematical analysis, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to
Neighbourhood_(mathematics)
Region between two concentric circles
In mathematics, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware
Annulus_(mathematics)
Condition of an optimization problem which the solution must satisfy
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily
Constraint_(mathematics)
Operation on the subsets of a set
In mathematics, a subset of a larger set is closed under a given operation on the larger set if performing that operation on members of the subset always
Closure_(mathematics)
Development of mathematics in South Asia
The tradition of Indian mathematics flourished in South Asia from circa 1200 BCE until the late 18th century, when it merged into a global discipline
Indian_mathematics
Type of puzzle
Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between
Mathematical_puzzle
Function that is its own inverse
In mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse, f(f(x)) = x for all x in the domain
Involution_(mathematics)
Algebraic structure with addition, multiplication, and division
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on
Field_(mathematics)
Conjecture on zeros of the zeta function
problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics In mathematics
Riemann_hypothesis
Property of being an even or odd number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For
Parity_(mathematics)
Addition, multiplication, division, ...
In mathematics, an operation is a function that takes as input a fixed number of elements of a set and returns an element of the same set. For example
Operation_(mathematics)
Equation that is satisfied for all values of the variables
In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might
Identity_(mathematics)
Number of "holes" of a surface
In mathematics, genus (pl.: genera) has a few different, but closely related, meanings. Intuitively, the genus is the number of "holes" of a surface.
Genus_(mathematics)
Special subset of a partially ordered set
In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear
Filter_(mathematics)
Fixed number that has received a name
names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and π occurring
Mathematical_constant
Constant equal to twice pi
The number τ (/ˈtaʊ, ˈtɔː, ˈtɒ/ ; spelled out as tau) is a mathematical constant that is the ratio of a circle's circumference to its radius. It is exactly
Tau_(mathematics)
Algebraic structure associated with a topological space
In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely related usages. First, there is the homology
Homology_(mathematics)
Inputs for which a function's value is non-zero
In mathematics, the support of a real-valued function f {\displaystyle f} is the subset of the function's domain consisting of those elements that are
Support_(mathematics)
Function acting on function spaces
In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes
Operator_(mathematics)
Anxiety towards math
Mathematical anxiety, also known as math phobia and math anxiety, is a feeling of tension and anxiety that interferes with the manipulation of numbers
Mathematical_anxiety
Limiting case which is different from the rest of the class
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than)
Degeneracy_(mathematics)
Mathematics of number-placement puzzle
Mathematics can be used to study Sudoku puzzles to answer questions such as "How many filled Sudoku grids are there?", "What is the minimal number of
Mathematics_of_Sudoku
Plane figure, bounded by circle
in statistics. It most commonly occurs in operations research in the mathematics of urban planning, where it may be used to model a population within
Disk_(mathematics)
American domestic terrorist (1942–2023)
YOO-nə-bom-ər), was an American mathematician and domestic terrorist. A mathematics prodigy, he abandoned his academic career in 1969 to pursue a reclusive
Ted_Kaczynski
Arithmetic operation
division appear in various algebraic structures, different ways of defining mathematical structure. Those in which a Euclidean division (with remainder) is defined
Division_(mathematics)
Number property of being positive or negative
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered
Sign_(mathematics)
Aesthetic value of mathematics
Mathematical beauty is a type of aesthetic value that is experienced in doing or contemplating mathematics. The testimonies of mathematicians indicate
Mathematical_beauty
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
Technique to make a model more generalizable and transferable
In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts
Regularization_(mathematics)
Mathematics course taught in the Faculty of Mathematics, University of Cambridge
The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. In its classical 19th century
Mathematical_Tripos
Mapping from a Euclidean space to itself
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of
Reflection_(mathematics)
Symbol representing a mathematical object
In mathematics, a variable (from Latin variabilis 'changeable') is a symbol, typically a letter, that refers to an unspecified mathematical object. One
Variable_(mathematics)
Differential map between manifolds whose differential is everywhere surjective
In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential pushforward is everywhere surjective. It is a
Submersion_(mathematics)
Property that is not changed by mathematical transformations
In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations
Invariant_(mathematics)
Study of computation
As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation
Computer_science
Function or value which does not change
In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value);
Constant_(mathematics)
Umbrella term for technical disciplines
mathematics (STEM) is an umbrella term used to group together the related technical disciplines of science, technology, engineering, and mathematics.
Science, technology, engineering, and mathematics
Science,_technology,_engineering,_and_mathematics
Supposition or system of ideas intended to explain something
as it is expressed in the formal language of mathematical logic. Theories may be expressed mathematically, symbolically, or in common language, but are
Theory
Number
Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers
0
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
Motion of particles in a fluid
In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics.
Flow_(mathematics)
Simple Lie group; the automorphism group of the octonions
In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g 2 , {\displaystyle {\mathfrak
G2_(mathematics)
Relationship between two sets, defined by a set of ordered pairs
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. As an example, "is less than" is
Relation_(mathematics)
Interdisciplinary field of research
Mathematical sociology is an interdisciplinary field of research concerned with the use of mathematics within sociological research. Starting in the early
Mathematical_sociology
Value approached by a mathematical object
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are
Limit_(mathematics)
Area of mathematics using condensed sets
Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which replaces a topological space by a certain sheaf of sets, in order
Condensed_mathematics
geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set
Symmetry_in_mathematics
Basic notion of sameness in mathematics
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical
Equality_(mathematics)
Characteristic of conic sections
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity
Eccentricity_(mathematics)
Indian mathematician (1887–1920)
contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered
Srinivasa_Ramanujan
Infinite sum
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus
Series_(mathematics)
Branch of applied mathematics
development of mathematical ideas inspired by physics, known as physical mathematics. There are several distinct branches of mathematical physics, and these
Mathematical_physics
Teaching, learning, and scholarly research in mathematics
In contemporary education, mathematics education (known in Europe as the didactics or pedagogy of mathematics) is the practice of teaching, learning, and
Mathematics_education
Mathematical relation making a non-equal comparison
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most
Inequality_(mathematics)
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Circulation density in a vector field
Hodges. 1880. Earliest Known Uses of Some of the Words of Mathematics tripod.com Mathematical methods for physics and engineering, K.F. Riley, M.P. Hobson
Curl_(mathematics)
Measure of the shape of a function
Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents
Moment_(mathematics)
Set of points that satisfy some specified conditions
given distance of a fixed point, the center of the circle. In modern mathematics, similar concepts are more frequently reformulated by describing shapes
Locus_(mathematics)
Mathematics award
International Congress of Mathematicians (ICM) of the International Mathematical Union (IMU), a convention which takes place every four years. The name
Fields_Medal
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