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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
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
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)
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. The following
Group_(mathematics)
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
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)
A mathematical object is an abstract entity arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,
Mathematical_object
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)
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
Subfield of mathematics
Mathematical logic is the study of logic within mathematics. This is commonly done by means of formal systems called formal logics that define rules of
Mathematical_logic
Large reference work translated from Soviet source
The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics. The 2002 version contains
Encyclopedia_of_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
Branch of mathematics
Mathematical analysis is the branch of mathematics that studies functions, spaces, and operators through methods of approximation and convergence. It grew
Mathematical_analysis
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)
Embedding of the circle in three dimensional Euclidean space
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)
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)
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)
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
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
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)
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)
Whole number
or subtracting zero from any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers
0
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)
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)
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)
American domestic terrorist (1942–2023)
YOU-na-bom-ər), was an American mathematician and domestic terrorist. A mathematics prodigy, he abandoned his academic career to pursue a reclusive primitive
Ted_Kaczynski
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
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)
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
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)
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
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
Form of mathematical proof
Mathematical induction is a method for proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0),P(1)
Mathematical_induction
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)
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 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)
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)
Mathematics and architecture are related, since architecture, like some other arts, uses mathematics for several reasons. Apart from the mathematics needed
Mathematics_and_architecture
Umbrella term for scientific and 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
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
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
tau) is a mathematical constant, equal to 2π, that has been proposed as an alternative to π by various proponents, who argue that mathematical notation
Tau_(mathematics)
Brackets as used in mathematical notation
In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets ⟨ ⟩, are frequently
Bracket_(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)
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
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
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)
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)
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)
All numbers between two given numbers
In mathematics, an interval is the set of all real numbers lying between two fixed lower or upper bounds ("endpoints") with no "gaps". For example, the
Interval_(mathematics)
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance
Norm_(mathematics)
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
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)
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)
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
Inputs for which a function's value is non-zero
In mathematics, the support of a real-valued function f is the subset of the function's domain consisting of those elements that are not mapped to zero
Support_(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)
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
Notion in mathematics
In mathematics, a mathematical value is a broad term that refers to any definite entity that can be manipulated with operators according to the well-defined
Value_(mathematics)
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)
Map from a vector space to its underlying field
central role in the calculus of variations, mathematical optimization, distribution theory, mathematical physics, and machine learning. An important application
Functional_(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)
Number divisible only by 1 and itself
Pages from year three of a mathematical blog. Graduate Studies in Mathematics. Vol. 117. Providence, RI: American Mathematical Society. pp. 82–86. doi:10
Prime_number
Counterintuitive mathematical object
In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand
Pathological_(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)
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)
Measure of the shape of a function
In mathematics, moments of a function are certain quantitative measures related to the shape of the function's graph. For example, in physics, if the
Moment_(mathematics)
Function that applies a set to itself
In mathematics, a transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e
Transformation_(function)
Generalization of perpendicularity
In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to linear algebra of bilinear forms. Two elements u and
Orthogonality_(mathematics)
Symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
Gerbert studied in Barcelona in his youth. He was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he
Arabic_numerals
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)
Teaching and learning of 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
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
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)
Number taken as representative of a list of numbers
In mathematics, an average of a collection or group is a value that is most central, common, or typical in some sense, and represents its overall position
Average
English computer scientist (1912–1954)
philosophy of artificial intelligence and the Turing pattern concept to mathematical and theoretical biology. Born in London and raised in southern England
Alan_Turing
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)
Mathematically obvious
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or a particularly simple
Triviality_(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
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)
Rap music producer
Ronald Maurice Bean, better known professionally as Mathematics (also known as Allah Mathematics) (born October 21, 1971), is a hip hop producer and DJ
Mathematics_(producer)
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
Point where a mathematical object behaves irregularly
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved
Singularity_(mathematics)
Shape with three sides
Greitzer, S. L. (1967). Geometry Revisited. Anneli Lax New Mathematical Library. Vol. 19. Mathematical Association of America. ISBN 978-0-88385-619-2. Devadoss
Triangle
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
Used to count, measure, and label
A number is a mathematical object used to count, measure, order and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth
Number
Function with a smaller domain
In mathematics, the restriction of a function f is a new function, denoted f|A or f↾A, obtained by choosing a smaller domain A for the original function
Restriction_(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
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)
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)
Plane figure, bounded by circle
disk, a disk with radius one Annulus (mathematics), the region between two concentric circles Ball (mathematics), the usual term for the 3-dimensional
Disk_(mathematics)
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)
Circle with radius of one
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle
Unit_circle
Class of points in a function's domain defined by having the same image by that map
In mathematics, a fiber (US English) or fibre (British English) of a map or function f:X→Y is an equivalence class in X for the relation of having the
Fiber_(mathematics)
Simple curve of Euclidean geometry
inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry
Circle
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
Certain type of mathematics from secondary school onwards
Further Mathematics is the title given to a number of advanced secondary mathematics courses. The term "Higher and Further Mathematics", and the term "Advanced
Further_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)
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