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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)
Mathematical theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold
Singularity_theory
Hypothetical event
The technological singularity, often simply called the singularity, is a hypothetical event in which technological growth accelerates beyond human control
Technological_singularity
Condition in which spacetime itself breaks down
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that
Gravitational_singularity
Topics referred to by the same term
Look up Singularity or singularity in Wiktionary, the free dictionary. Singularity or singular point may refer to: Mathematical singularity, a point at
Singularity
Matrix decomposition
(1965). "Calculating the singular values and pseudo-inverse of a matrix". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical
Singular_value_decomposition
Key results in general relativity on gravitational singularities
Big Bang singularity and the typical singularity inside a non-rotating, uncharged Schwarzschild black hole are spacelike. Timelike singularities: These
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Phenomenon within general relativity
curvature singularity at the Cauchy horizon known as the mass-inflation singularity, the Cauchy horizon singularity, the infalling singularity, or the "fat
Mass_inflation
Location around which a function displays irregular behavior
essential singularity of a function is a "severe" singularity near which the function exhibits striking behavior. The category essential singularity is a "left-over"
Essential_singularity
Hypothetical phenomenon
In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon. When there exists at least one causal
Naked_singularity
Has no other singularities close to it
In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it. In other words, a complex number
Isolated_singularity
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
Mathematical concept describing isolated singularity of an algebraic surface
a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex
Du_Val_singularity
2005 non-fiction book by Ray Kurzweil
embraces the term "the singularity", which was popularized by Vernor Vinge in his 1993 essay "The Coming Technological Singularity." Kurzweil describes
The_Singularity_Is_Near
Point on a curve where motion must move backwards
type A2-singularity. Let f (x, y) be a smooth function of x and y and assume, for simplicity, that f (0, 0) = 0. Then a type A2-singularity of f at (0
Cusp_(singularity)
Concept in algebraic geometry
does not is given by the isolated singularity of x2 + y3z + z3 = 0 at the origin. Blowing it up gives the singularity x2 + y2z + yz3 = 0. It is not immediately
Resolution_of_singularities
Singularity or discontinuity only resulting from the choice of coordinate system
In mathematics and physics, a coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame that can be removed
Coordinate_singularity
Attribute of a mathematical function
\over z(z-1)}} it is apparent that the singularity at z = 0 {\displaystyle z=0} is a removable singularity and then the residue at z = 0 {\displaystyle
Residue_(complex_analysis)
In mathematics, more particularly in the field of algebraic geometry, a scheme X {\displaystyle X} has rational singularities, if it is normal, of finite
Rational_singularity
Expression which is not assigned an interpretation
function is undefined, is called a singularity. Some different types of singularities include: Removable singularities - in which the function can be extended
Undefined_(mathematics)
Solution to the Einstein field equations
Schwarzschild metric has a singularity for r = 0, which is an intrinsic curvature singularity. It also seems to have a singularity on the event horizon r
Schwarzschild_metric
American computer scientist and writer (1944–2024)
taught mathematics and computer science at San Diego State University. He was the first wide-scale popularizer of the technological singularity concept
Vernor_Vinge
Point without a tangent space
In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric
Singular point of an algebraic variety
Singular_point_of_an_algebraic_variety
English mathematician, mathematical physicist (born 1931)
only an apparent singularity, similar to the well-known apparent singularity at the event horizon of a black hole. The latter singularity can be removed
Roger_Penrose
Topics referred to by the same term
infinite cardinal number that is not a regular cardinal Singular point of a curve, in geometry Singularity Singulair, Merck trademark for the drug Montelukast
Singular
Degree of differentiability of a function or map
smoothness for parametric curves Quasi-analytic function Singularity (mathematics) – Point where a mathematical object behaves irregularly Sinuosity – Ratio of
Smoothness
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_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)
Type of surface singularity used in algebraic geometry
algebraic geometry, an elliptic singularity of a surface, introduced by Philip Wagreich in 1970, is a surface singularity such that the arithmetic genus
Elliptic_singularity
Partial differential equation
soliton The first two singularity models arise from Type I singularities, whereas the last one arises from a Type II singularity. In four dimensions very
Ricci_flow
Russian mathematician (1937–2010)
equations, and singularity theory." State Prize of the Russian Federation (2007), "for outstanding contribution to development of mathematics." Shaw Prize
Vladimir_Arnold
Concept in differential equation mathematics
coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction
Regular_singular_point
Singularities of algebraic varieties
In mathematics, canonical singularities are a class of singularities that appear on the canonical model of an algebraic variety, and terminal singularities
Canonical_singularity
Branch of mathematics studying functions of a complex variable
branch of mathematical analysis that investigates functions of a complex variable of complex numbers. It is helpful in many branches of mathematics, including
Complex_analysis
Concept in complex analysis
variable. It is the simplest type of non-removable singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function
Zeros_and_poles
Undefined point on a holomorphic function which can be made regular
{\text{sinc}}(z)={\frac {\sin z}{z}}} has a singularity at z = 0 {\displaystyle z=0} . This singularity can be removed by defining sinc ( 0 ) := 1
Removable_singularity
General relativity model near spacetime singularities
relativity has a page on the topic of: BKL singularity A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe
BKL_singularity
Computer algebra system
commutative and non-commutative algebra, algebraic geometry, and singularity theory. Singular has been released under the terms of GNU General Public License
Singular_(software)
2022 novel by John Banville
theory, a mathematical concept of space and time which predicted multiple universes. He published his theories in a paper entitled "On singularities and the
The_Singularities
Gravitational singularity of a rotating black hole
A ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring. When a
Ring_singularity
Type of function in mathematics
{\displaystyle 1} , because the nearest singularity is at z = − 1 {\displaystyle z=-1} . Complex singularities can determine the radius of convergence
Analytic_function
Type of function
it is common for a function which contains a mathematical singularity to be referred to as a 'singular function'. This is especially true when referring
Singular_function
Square roots of the eigenvalues of the self-adjoint operator
In mathematics, in particular in functional analysis, the singular values of a compact operator T : X → Y {\displaystyle \,T\!:X\rightarrow Y} acting
Singular_value
Method for assigning values to integrals
a singularity on an integral interval is avoided by limiting the integral interval to the non-singular domain. Depending on the type of singularity in
Cauchy_principal_value
Functions in mathematics
harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however, we can make the solution
Harmonic_function
American mathematician (1943–2024)
a closed manifold with a finite-time singularity, Hamilton developed methods of rescaling around the singularity to produce a sequence of Ricci flows;
Richard_S._Hamilton
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)
Class of discontinuous functions
discontinuous at their singular points. Singularity functions have been heavily studied in the field of mathematics under the alternative names of generalized
Singularity_function
Conjecture in physics
Penrose–Hawking singularity theorems, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe
Cosmic_censorship_hypothesis
Russian mathematician (born 1966)
research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the
Grigori_Perelman
Increase in the rate of technological change through history
century, leading to a singularity. Kurzweil elaborates on his views in his books The Age of Spiritual Machines and The Singularity Is Near. In the natural
Accelerating_change
Power series with negative powers
In mathematics, the Laurent series of a complex function f ( z ) {\displaystyle f(z)} is a representation of that function as a power series which includes
Laurent_series
In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally
Theta_divisor
Methods of mathematical approximation
In mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related
Perturbation_theory
In mathematics, an ordinary singularity of an algebraic curve is a singular point of multiplicity r where the r tangents at the point are distinct (Walker
Ordinary_singularity
Theorem in geometric topology
Unlike the heat flow, the Ricci flow could run into singularities and stop functioning. A singularity in a manifold is a place where it is not differentiable:
Poincaré_conjecture
Association of one output to each input
everywhere except for isolated singularities, but whose value may "jump" if one follows a closed loop around a singularity. This jump is called the monodromy
Function_(mathematics)
Used to count, measure, and label
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth. Individual
Number
Functions in harmonic analysis mathematics
\mathbb {R} ^{n}\to \mathbb {R} } is singular along the diagonal x = y {\displaystyle x=y} . Specifically, the singularity is such that | K ( x , y ) | {\displaystyle
Singular_integral
Concept of complex analysis
it can be made to contain only the singularity of c {\displaystyle c} due to nature of isolated singularities. This may be used for calculation in
Residue_theorem
Theorem in complex analysis
{\displaystyle \mathbb {C} \cup \{\infty \}} . Viewed this way, the only possible singularity for entire functions, defined on C ⊂ C ∪ { ∞ } {\displaystyle \mathbb
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
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
Scientific field of study
two millennia, physics, chemistry, biology, and certain branches of mathematics were part of natural philosophy, but during the Scientific Revolution
Physics
German mathematician
longstanding problem in minimal surface theory. He has also worked on singularity formation in the mean curvature flow and Ricci flow, solving a question
Simon_Brendle
American computer scientist and AI researcher
PhD in mathematics from Temple University under the supervision of Avi Lin in 1990, at age 23. Goertzel is the founder and CEO of SingularityNET, a project
Ben_Goertzel
Mathematical behavior near singularities
algebraic geometry and differential geometry behave as they "run round" a singularity. As the name implies, the fundamental meaning of monodromy comes from
Monodromy
Description of the degeneracy of a function
In mathematics, and in particular singularity theory, an Ak singularity, where k ≥ 0 is an integer, describes a level of degeneracy of a function. The
Ak_singularity
Indian physicist (1923–2005)
demonstrates that singularities arise inevitably in general relativity and is a key ingredient in the proofs of the Penrose–Hawking singularity theorems. Raychaudhuri
Amal_Kumar_Raychaudhuri
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
Russian mathematician
in singularity theory, whose contributions to the subject are fundamental. He has published several books and a variety of papers in singularity theory
Victor_Goryunov
Branch of mathematics
does not cross a singularity. This is useful in evaluating many real integrals, and in the study of functions through their singularities. In operator theory
Mathematical_analysis
hypersurface singularity. This has a similar setup, where a polynomial f {\displaystyle f} with f = 0 {\displaystyle f=0} having a singularity at the origin
Milnor_map
evaluated at the singular configuration (if any exists), then those equations exhibit mathematical singularity. Examples of mechanical singularities are gimbal
Mechanical_singularity
Provides integral formulas for all derivatives of a holomorphic function
In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a
Cauchy's_integral_formula
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Concept in mathematics
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to
Singular_perturbation
American mathematician
Small scales and singularity formation in fluid dynamics". YouTube. 17 October 2018. Retrieved 2019-05-20. "Alexander Kiselev: Singularity formation in models
Alexander Kiselev (mathematician)
Alexander_Kiselev_(mathematician)
Matrix of second derivatives
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued
Hessian_matrix
nature of mathematics and individual mathematical problems into the future is a widely debated topic; many past predictions about modern mathematics have been
Future_of_mathematics
Seven mathematical problems with a US$1 million prize for each solution
Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged
Millennium_Prize_Problems
Hypothetical object of spacetime
general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter, light
White_hole
Field-equations in general relativity
determines the curvature of spacetime. These equations form the core of the mathematical formulation of general relativity. They readily imply the geodesic equation
Einstein_field_equations
Theorem about the range of an analytic function
Picard's Theorem: If an analytic function f {\textstyle f} has an essential singularity at a point w {\textstyle w} , then on any punctured neighborhood of w
Picard_theorem
Mathematical function that preserves angles
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U {\displaystyle U} and V
Conformal_map
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)
Number of times a curve wraps around a point in the plane
In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of
Winding_number
Mathematics award
under 40 years of age at the International Congress of the International Mathematical Union (IMU), a convention which takes place every four years. The name
Fields_Medal
Mathematical idealization of the surface of a body
the classification of the singular points is singularity theory. A singular point is isolated if there is no other singular point in a neighborhood of
Surface_(mathematics)
Mathematical theorem
neighborhood of z = 0. Hence it is an isolated singularity, as well as being an essential singularity. Using a change of variable to polar coordinates
Casorati–Weierstrass_theorem
Second-order partial differential equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its
Laplace's_equation
Topic in systems theory
System relatedness: the effects of a singularity are characteristic of the system. Uniqueness: The nature of a singularity does not arise from the scale of
Singularity_(systems_theory)
Canadian mathematician
Advances in Mathematics. 358 106840. arXiv:1804.07696. doi:10.1016/j.aim.2019.106840. Flat Littlewood polynomials exist (2020) The singularity probability
Julian_Sahasrabudhe
Invariant that plays a role in algebraic geometry and singularity theory
In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued
Milnor_number
In mathematics, the signature defect of a singularity measures the correction that a singularity contributes to the signature theorem. Hirzebruch (1973)
Signature_defect
Australian and American mathematician (born 1975)
harmonic analysis, and additive number theory. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the
Terence_Tao
German mathematician (1885–1955)
Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski
Hermann_Weyl
Probability distribution in measure theory
In mathematics, two positive (or signed or complex) measures μ {\displaystyle \mu } and ν {\displaystyle \nu } defined on a measurable space ( Ω , Σ )
Singular_measure
Area of mathematical analysis
Harmonic analysis is an area of mathematical analysis that emerged from the study of harmonic functions, and especially their boundary behavior. The methods
Harmonic_analysis
Mathematical concept
infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The
Infinity
Point on a curve at which two or more osculating circles are tangent
{\displaystyle A_{1}^{-}} -singularity. A tacnode corresponds to a type A 3 − {\displaystyle A_{3}^{-}} -singularity. In fact each type A 2 n +
Tacnode
SINGULARITY MATHEMATICS
SINGULARITY MATHEMATICS
Girl/Female
Muslim/Islamic
Singularity
Boy/Male
Indian
Singularity
Boy/Male
Muslim
Singularity
Boy/Male
Australian, Vietnamese
Complete; Mathematics
Girl/Female
Arabic, Muslim, Sindhi
Singularity
SINGULARITY MATHEMATICS
SINGULARITY MATHEMATICS
Girl/Female
Australian, Danish, Finnish, Swedish
Happy; Goat
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Following the Rain
Boy/Male
Hindu, Indian, Marathi, Mythological, Oriya, Sanskrit, Traditional
God of the Immovable; Another Name for Shiva
Boy/Male
American, British, English
Swordsman; Germanic Tribe; From Saxonny
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name, with fused preposition d(e), for someone from Airelle in Calvados, France, or Airel in La Manche, Normandy.
Girl/Female
Australian, British, English, German, Latin
Lioness
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Punjabi, Sanskrit, Sikh, Sindhi, Tamil, Telugu
A King; An Ancestor of Lord Rama
Boy/Male
Hindu, Indian, Marathi
Greater; Stronger
Girl/Female
Hindu, Indian, Tamil, Telugu
Blissful; Live Long Life
Girl/Female
American, Arabic, Australian, British, English, Muslim, Russian, Slavic
Wealthy Guardian; Sanctuary; Voice; Call; Born of Sunday
SINGULARITY MATHEMATICS
SINGULARITY MATHEMATICS
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SINGULARITY MATHEMATICS
SINGULARITY MATHEMATICS
n.
The quality or state of being singular; some character or quality of a thing by which it is distinguished from all, or from most, others; peculiarity.
n.
The quality or state of being odd; singularity; queerness; peculiarity; as, oddity of dress, manners, and the like.
v. t.
To make singular or single; to distinguish.
n.
The state or quality of being an island or consisting of islands; insulation.
n.
Celibacy.
n.
The quality or state of being angular; angularness.
n.
Possession of a particular or exclusive privilege, prerogative, or distinction.
n.
One who affects singularity.
n.
Narrowness or illiberality of opinion; prejudice; exclusiveness; as, the insularity of the Chinese or of the aristocracy.
n.
A genus of tropical apocynaceous shrubs having singularly twisted flowers. One species (Strophanthus hispidus) is used medicinally as a cardiac sedative and stimulant.
adv.
Singularly; peculiarly.
adv.
In a singular manner; in a manner, or to a degree, not common to others; extraordinarily; as, to be singularly exact in one's statements; singularly considerate of others.
n.
Singularity; strangeness; eccentricity; irregularity; uncouthness; as, the oddness of dress or shape; the oddness of an event.
adv.
So as to express one, or the singular number.
n.
The quality or state of being peculiar; individuality; singularity.
pl.
of Singularity
adv.
Strangely; oddly; as, to behave singularly.
n.
Anything singular, rare, or curious.
n.
Mixed mathematics.