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In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of
Gradient_conjecture
Aharoni-Korman conjecture also known as the fishbone conjecture Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture Bunkbed conjecture Chinese
List_of_conjectures
conjectures, Bourgain-Tzafriri conjecture and R ε {\displaystyle R_{\varepsilon }} -conjecture) Ahlfors measure conjecture (Ian Agol, 2004) Gradient conjecture
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Chinese mathematician
geometrization conjecture. Additionally, he posted a third article in which he gave a shortcut to the proof of the famous Poincaré conjecture, for which the
Huai-Dong_Cao
Russian mathematician (born 1966)
analysis of Ricci flow, and proved the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open problem
Grigori_Perelman
French mathematician (1923–2002)
transversality theorem. Another example of this line of work is the Thom conjecture, versions of which have been investigated using gauge theory. From the
René_Thom
Numerical ordinary differential equations Bendixson–Dulac theorem Gradient conjecture Recurrence plot Limit cycle Initial value problem Clairaut's equation
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
Fractal named after mathematician Benoit Mandelbrot
animations serve to highlight the gradient boundaries. Animated gradient structure inside the Mandelbrot set Animated gradient structure inside the Mandelbrot
Mandelbrot_set
Partial differential equation
Thurston's geometrization conjecture, Hamilton produced a number of results in the 1990s which were directed towards the conjecture's resolution. In 2002 and
Ricci_flow
Polish mathematician
Kurdyka and Adam Parusinski, Tadeusz Mostowski solved René Thom's gradient conjecture in 2000. List of Polish mathematicians Mostowski model 1968 & 1976:
Andrzej_Mostowski
Chinese-American mathematician (born 1949)
recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered
Shing-Tung_Yau
American mathematician (1943–2024)
of results and ideas for using it to prove the Poincaré conjecture and geometrization conjecture from the field of geometric topology. Hamilton's work on
Richard_S._Hamilton
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a
Carathéodory_conjecture
Millennium Prize Problem
and it is a product of the velocity vector v and the gradient operator ∇. Because the gradient operator is a linear operator, the term (v · ∇)v is nonlinear
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
Matrix of partial derivatives of a vector-valued function
scalar-valued function of several variables is (the transpose of) its gradient and the gradient of a scalar-valued function of a single variable is its derivative
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Symplectic topology tool
now called symplectic Floer homology, in his 1988 proof of the Arnold conjecture in symplectic geometry. Floer also developed a closely related theory
Floer_homology
Romanian-American mathematician (born 1977)
Giorgi's conjecture about global solutions to certain semilinear equations, that he proved up to dimension 8. It is to be noticed that the conjecture turns
Ovidiu_Savin
American mathematician (born 1930)
regarding his work habits while proving the higher-dimensional Poincaré conjecture. He said that his best work had been done "on the beaches of Rio." He
Stephen_Smale
Conjecture in symplectic geometry
In mathematics, and especially symplectic geometry, the Thomas–Yau conjecture asks for the existence of a stability condition, similar to those which appear
Thomas–Yau_conjecture
Discrete probability distribution
inequalities as well as anti-concentration inequalities like Tomaszewski's conjecture. Let {xi} be a set of random variables with a Rademacher distribution
Rademacher_distribution
Particular knot energy
property because it prevents self-intersection and ensures the result under gradient descent is of the same knot type. Invariance of Möbius energy under Möbius
Möbius_energy
American mathematician
known as the "multiplicity-one" conjecture. Richard Bamler and Bruce Kleiner proved the multiplicity-one conjecture in a 2023 preprint. Ilmanen received
Tom_Ilmanen
Equations of motion for viscous fluids
the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The Navier–Stokes
Navier–Stokes_equations
Differential operator in mathematics
or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols
Laplace_operator
Lighthouse off the northwest coast of Scotland
railway was built to facilitate the transport of provisions up the steep gradients from the landing places. At that time, the light consumed twenty barrels
Flannan_Isles_Lighthouse
embedding or immersion. Ricci flow, as in the solution of the Poincaré conjecture, and Richard S. Hamilton's proof of the uniformization theorem Calabi
Geometric_flow
Algorithm for finding zeros of functions
square of known area could be effectively approximated, and this is conjectured to have been done using a special case of Newton's method, described
Newton's_method
Chinese mathematician (born 1958)
conjecture that K-stability would be sufficient to ensure the existence of a Kähler-Einstein metric became known as the Yau-Tian-Donaldson conjecture
Tian_Gang
Extends the Jordan curve theorem to characterize the inner and outer regions
differential topology, CRC Press, ISBN 9781439831601 Smale, Stephen (1961), "On gradient dynamical systems", Annals of Mathematics, 74 (1): 199–206, doi:10.2307/1970311
Schoenflies_problem
Optical illusion
effect in 1865, conjecturing that filtering is performed in the retina itself, by lateral inhibition among its neurons. This conjecture is supported by
Mach_bands
Physical phenomenon
the transport of charged particles in a plasma resulting from spatial gradients in particle density and, in many cases, temperature. In contrast to diffusion
Plasma_diffusion
Void between celestial bodies
planets may successfully transport life forms to another habitable world. A conjecture is that just such a scenario occurred early in the history of the Solar
Outer_space
Brazilian mathematician (1940–2025)
bifurcations, attractors and chaotic systems. He proposed the Palis' conjectures (which form the Palis' program), which influenced the development of
Jacob_Palis
Class of algorithms that find approximate solutions to optimization problems
computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly
Approximation_algorithm
Theory in differential topology
depends on neither.) The pair ( f , g ) {\displaystyle (f,g)} gives us a gradient vector field. We say that ( f , g ) {\displaystyle (f,g)} is Morse–Smale
Morse_homology
Russian mathematician (1930–2004)
{\displaystyle 2\pi } , or the Gauss curvature and the gradients of the curvatures are bounded on S. The conjecture was proven by Brendan Guilfoyle and Wilhelm Klingenberg
Victor_Andreevich_Toponogov
a class of optimal sphere eversions, the minimax eversions. Willmore conjecture White, James H. (1973). "A global invariant of conformal mappings in space"
Willmore_energy
American mathematician
Golub offered a US$500 prize for “the construction of a 3-term conjugate gradient like descent method for non-symmetric real matrices or a proof that there
Vance_Faber
Differential geometry conjecture
The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about
Yamabe_problem
Topological space that locally resembles Euclidean space
the Poincaré conjecture. After nearly a century, Grigori Perelman proved the Poincaré conjecture (see the Solution of the Poincaré conjecture). William Thurston's
Manifold
River in Italy
river valley decreases from 0.35% in the west to 0.14% in the east, a low gradient. Along its path lie 450 standing lakes. Almost all of the rest of the non-Italy
Po_(river)
General relativity model near spacetime singularities
spatial gradients do enter these equations non-trivially. Subsequent analysis by a large number of authors has shown that the BKL conjecture can be made
BKL_singularity
Abstraction of bar-and-joint frameworks
small scales of distance by its gradient, a vector for each vertex specifying its speed and direction. The gradient describes a linearized approximation
Rigidity_matroid
Sequence of locally optimal choices
a given triangle that maximize the total area of the circles; it is conjectured that the same greedy algorithm is optimal for any number of circles.
Greedy_algorithm
Method to solve optimization problems
John von Neumann to discuss his simplex method, von Neumann immediately conjectured the theory of duality by realizing that the problem he had been working
Linear_programming
Machine learning model for speech
training translation. The model was trained using the AdamW optimizer with gradient norm clipping and a linear learning rate decay with warmup, with batch
Whisper (speech recognition system)
Whisper_(speech_recognition_system)
Mathematical optimization problem restricted to integers
Reis, Victor; Rothvoss, Thomas (2023-03-26). "The Subspace Flatness Conjecture and Faster Integer Programming". Hildebrand, Robert (2016-10-07). "FPT
Integer_programming
Type of partial differential equation
heat of melting. By T 1 {\displaystyle T_{1}} we mean the limit of the gradient as x {\displaystyle x} approaches Γ t {\displaystyle \Gamma _{t}} from
Free_boundary_problem
Subfield of convex optimization
expectation the ratio is always at least 0.87856.) Assuming the unique games conjecture, it can be shown that this approximation ratio is essentially optimal
Semidefinite_programming
Structures Using the OBurnett Equations in Combination with the Holian Conjecture". Fluids. 6 (12): 427. Bibcode:2021Fluid...6..427J. doi:10.3390/fluids6120427
Burnett_equations
biquaternion conjugate diameters four-vector four-acceleration four-force four-gradient four-momentum four-velocity hyperbolic orthogonality hyperboloid model
List of mathematical topics in relativity
List_of_mathematical_topics_in_relativity
Formation of mountain ranges
surrounding mountain-building. With hindsight, we can discount Dana's conjecture that this contraction was due to the cooling of the Earth (aka the cooling
Orogeny
Discrete analog of a derivative
time-domain method (FDTD) Finite volume method FTCS scheme Gilbreath's conjecture Newton–Raphson method Sheffer sequence Summation by parts Time scale calculus
Finite_difference
Russian-French mathematician
Riemannian metric of positive scalar curvature, which had been a major conjecture previously resolved by Schoen and Yau in low dimensions. In 1981, Gromov
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Italian mathematician
very general Lusin type theorem for gradients asserting that every Borel vector field can be realized as the gradient of a continuously differentiable function
Giovanni Alberti (mathematician)
Giovanni_Alberti_(mathematician)
Number, approximately 3.14
decimal digits of π appear to be evenly distributed, but no proof of this conjecture has been found. Mathematicians have attempted to extend their understanding
Pi
Hamilton, Yamabe flow is for noncompact manifolds, and is the negative L2-gradient flow of the (normalized) total scalar curvature, restricted to a given
Yamabe_flow
Point where the derivative of a function is zero or undefined (in certain cases)
several real variables, a critical point is a value in its domain where the gradient norm is equal to zero (or undefined). This sort of definition extends to
Critical_point_(mathematics)
Relationship between derivatives and integrals
calculation of gradients) are actually closely related. Calculus as a unified theory of integration and differentiation started from the conjecture and the proof
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Process of calculating the causal factors that produced a set of observations
question of whether it is possible to hear the shape of a drum. Weyl conjectured that the eigenfrequencies of a drum would be related to the area and
Inverse_problem
Relativistic quantum mechanical wave equation
1925 by Samuel Goudsmit and George Uhlenbeck. Shortly after, it was conjectured by Schrödinger to be the missing link in acquiring the correct Sommerfeld
Dirac_equation
American mathematician
which claimed to provide a proof for William Thurston's geometrization conjecture, using Richard Hamilton's theory of Ricci flow. Perelman's papers attracted
John_Lott_(mathematician)
scientific context. While theory in colloquial usage may denote a hunch or conjecture, a scientific theory is a set of principles that explains an observable
List of common misconceptions about science, technology, and mathematics
List_of_common_misconceptions_about_science,_technology,_and_mathematics
Australian carnivorous marsupial
to S. moornaensis have been found in New South Wales, and it has been conjectured that these two extinct larger species may have hunted and scavenged.
Tasmanian_devil
DNA analysis of Jewish populations
evidence predating the 15th century on the other, leave much room for conjecture and speculation. Linguistic evidence, however, does not support the theory
Genetic_studies_of_Jews
observable in most cases, a reaction mechanism is often a theoretical conjecture based on thermodynamic feasibility and what little support can be gained
Glossary_of_chemistry_terms
Evolutionary effects of sexual selection on humans
remain passive, but select the more agreeable partners." Charles Darwin conjectured that the male beard, as well as the hairlessness of humans compared to
Sexual_selection_in_humans
On converting relations to functions of several real variables
for 3-manifolds, the capstone of his proof of Thurston's geometrization conjecture, can be understood as an extension of the implicit function theorem. Inverse
Implicit_function_theorem
Concept in topology
manifolds. For a start, it almost immediately proves the generalized Poincaré conjecture. Before Smale proved this theorem, mathematicians became stuck while trying
H-cobordism
Tropical atmospheric circulation feature
disequilibrium. The broad ascent and descent of air results in a pressure gradient force that drives the Hadley circulation and other large-scale flows in
Hadley_cell
Chinese science award
geometry to solve several long-standing problems and proving Ax-Schanuel’s conjecture for Shimura varieties." 2023 Kaiming He "fundamental contributions to
Future_Science_Prize
German mathematician (born 1958)
Penrose inequality, which is a special case of the more general Penrose conjecture in general relativity. After finishing high school in 1977, Huisken took
Gerhard_Huisken
traditions suggesting that the Revis family has African ancestry. It has been conjectured that the presence of this haplogroup may date from the Roman era when
Genetic history of the British Isles
Genetic_history_of_the_British_Isles
Mixed-breed dog with socio-environmental typology
ranging from whiter variants of the wild-type agouti to warmer (yellow–red gradient) intensities. Brazil was the first to acknowledge the cultural significance
Caramelo_(dog)
Migrations out of the Proto-Indo-European homeland
Proto-Germanic language. David Anthony, in his "revised Steppe hypothesis", conjectures that the spread of the Indo-European languages probably did not happen
Indo-European_migrations
English polymath (1642–1727)
experimental philosophy involves clearly distinguishing hypotheses—unverified conjectures—from propositions established through phenomena and generalised by induction
Isaac_Newton
Fastest curve descent without friction
it and his problem had to wait for advances in mathematics. Galileo's conjecture is that "The shortest time of all [for a movable body] will be that of
Brachistochrone_curve
Partial differential equation describing the evolution of temperature in a region
passed for all permanent temperature gradients to establish themselves in space, after which these spatial gradients no longer change in time (as again
Heat_equation
Particle accelerator at Lawrence Berkeley National Laboratory
Piccioni, and William Wenzel in 1956. Confirmation of the charge symmetry conjecture in 1955 led to the Nobel Prize for physics being awarded to Emilio Segrè
Bevatron
Country in South Asia
particular, carries a huge amount of silt out of Nepal but sees extreme drop in Gradient in Bihar, causing severe floods and course changes, and is, therefore,
Nepal
French mathematician, physicist and engineer (1854–1912)
far-reaching consequences. Early in the 20th century he formulated the Poincaré conjecture, which became, over time, one of the famous unsolved problems in mathematics
Henri_Poincaré
Galaxy containing the Solar System
first began to conjecture that the Milky Way is a barred spiral galaxy, rather than an ordinary spiral galaxy, in the 1960s. These conjectures were confirmed
Milky_Way
Physical theory with fields invariant under the action of local "gauge" Lie groups
geometrical ideas of general relativity to include electromagnetism, conjectured that Eichinvarianz or invariance under the change of scale (or "gauge")
Gauge_theory
Set of statistical processes for estimating the relationships among variables
versus the number of independent variables in the model. One method conjectured by Good and Hardin is N = m n {\displaystyle N=m^{n}} , where N {\displaystyle
Regression_analysis
Theory of gravitation as curved spacetime
recently come to prominence in the context of what is called the Maldacena conjecture). Given the difficulty of finding exact solutions, Einstein's field equations
General_relativity
Type of machine learning model
Some researchers characterize LLMs as "alien intelligence". For example, Conjecture CEO Connor Leahy considers untuned LLMs to be like inscrutable alien "Shoggoths"
Large_language_model
"Contact topology and hydrodynamics. I. Beltrami fields and the Seifert conjecture", Nonlinearity, 13 (2): 441–448, Bibcode:2000Nonli..13..441E, doi:10
Beltrami_vector_field
include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives and integrals in alternative
List_of_theorems
Pictorial representation of the behavior of subatomic particles
the television sit-com The Big Bang Theory, in the episode "The Bat Jar Conjecture". PhD Comics of January 11, 2012, shows Feynman diagrams that visualize
Feynman_diagram
Mathematical descriptions of the properties of certain cells in the nervous system
Radar-like detection procedure. As shown in Fig. 6, the key idea of the conjecture is to account for neurotransmitter concentration, neurotransmitter generation
Biological_neuron_model
List of largest planets by size
ISSN 1476-4687. PMID 40399630. Ramm, D. J.; et al. (2016). "The conjectured S-type retrograde planet in ν Octantis: more evidence including four
List_of_largest_exoplanets
Algorithm for supervised learning of binary classifiers
learn an XOR function. It is often incorrectly believed that they also conjectured that a similar result would hold for a multi-layer perceptron network
Perceptron
American annual mathematics conference
manifold Wu-Yi Hsiang, Sphere packing and spherical geometry: The Kepler conjecture and beyond Alan Nadel, On the geometry of Fano varieties Grigori Perelman
Geometry_Festival
Hypothesis that complex extraterrestrial life is improbable and extremely rare
the numerical values of quite a few of the factors below can only be conjectured. They cannot be estimated simply because we have but one data point:
Rare_Earth_hypothesis
Instances of subjective experience
discoveries arise, these authors argue, from ontologically promiscuous conjectures[clarification needed] that do not come from current data. The authors
Qualia
Tidal force experienced by objects subject to the gravitational field of a galaxy
the Oort cloud of the Solar System. Tidal forces are dependent on the gradient of a gravitational field, rather than its strength, and so tidal effects
Galactic_tide
To find the minimal surface with a given boundary
single embedded spheres. Mathematics portal Physics portal Double Bubble conjecture Dirichlet principle Plateau's laws Stretched grid method Bernstein's problem
Plateau's_problem
Every Riemannian manifold can be isometrically embedded into some Euclidean space
19891440113. MR 1037168. Isett, Philip (2018). "A proof of Onsager's conjecture". Annals of Mathematics. Second Series. 188 (3): 871–963. arXiv:1608.08301
Nash_embedding_theorems
Major river in the western United States and Mexico
agricultural irrigation and urban water supply. Its large flow and steep gradient are used to generate hydroelectricity, meeting peaking power demands in
Colorado_River
In mathematics, invariant of square matrices
Cayley–Menger determinant Dieudonné determinant Slater determinant Determinantal conjecture Lang 1985, §VII.1 "Determinants and Volumes". textbooks.math.gatech.edu
Determinant
GRADIENT CONJECTURE
GRADIENT CONJECTURE
Boy/Male
Muslim
Radiant
Boy/Male
Muslim
Radiant
Boy/Male
Tamil
Pradhyun | பà¯à®°à®¤à¯à®¯à¯à®‚நÂ
Radiant
Pradhyun | பà¯à®°à®¤à¯à®¯à¯à®‚நÂ
Boy/Male
Tamil
Radiant
Girl/Female
Tamil
Radiant
Boy/Male
Indian
Radiant
Male
French
French form of Roman Latin Gratian, GRATIEN means "pleasing, agreeable."
Boy/Male
Muslim
Radiant
Boy/Male
Indian
Radiant
Boy/Male
Tamil
Radiant
Girl/Female
Tamil
Ujjvala | உஜà¯à®œà¯à®µà®¾à®²à®¾
Radiant
Ujjvala | உஜà¯à®œà¯à®µà®¾à®²à®¾
Boy/Male
Muslim
Radiant
Boy/Male
Tamil
Pradyun | பà¯à®°à®¤à®¯à¯à®¨
Radiant
Pradyun | பà¯à®°à®¤à®¯à¯à®¨
Boy/Male
American, British, English
Gray-haired; Son of the Gray Family; Son of Gregory
Boy/Male
Tamil
Radiant
Boy/Male
Indian
Radiant
Girl/Female
Tamil
Suprabha | ஸà¯à®ªà¯à®°à®ªà®¾
Radiant
Suprabha | ஸà¯à®ªà¯à®°à®ªà®¾
Boy/Male
British, English
Great
Surname or Lastname
Swedish
Swedish : unexplained.German : unexplained.English : unexplained.
Girl/Female
Latin
Grace.
GRADIENT CONJECTURE
GRADIENT CONJECTURE
Boy/Male
Sikh
Divine knowledge attained naturally
Girl/Female
Tamil
Praneetha | பà¯à®°à®¨à®¿à®¤à®¾Â
Led forward, Conducted, Advanced, Promoted, Pure water
Boy/Male
American, British, English
Mighty Spearman; One who Saves; The Fictional Character Jorel Father of Superman
Girl/Female
Arabic, Muslim
Like Nightingale
Girl/Female
Indian
Silken
Boy/Male
Indian, Tamil
Line on Any Particular Raaga from Tamil
Boy/Male
Arabic, Muslim
Servant of the Master or King
Girl/Female
Celtic
Serves God.
Girl/Female
Arabic
Best of Everything / Everyone
Girl/Female
Tamil
Kalasaveri | கலாஸாவேரீ
Name of a Raga
GRADIENT CONJECTURE
GRADIENT CONJECTURE
GRADIENT CONJECTURE
GRADIENT CONJECTURE
GRADIENT CONJECTURE
a.
Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.
a.
Beamy; radiant.
a.
Radiating; radiant.
a.
Shining; radiant.
n.
State of being gracilent; slenderness.
a.
Adapted for walking, as the feet of certain birds.
n.
Alt. of Gradine
a.
Bright; shining; radiant; sheen.
a.
Moving by steps; walking; as, gradient automata.
n.
A graded ascending, descending, or level portion of a road; a gradient.
pl.
of Gradino
n.
A step or raised shelf, as above a sideboard or altar. Cf. Superaltar, and Gradin.
a.
Beaming with vivacity and happiness; as, a radiant face.
a.
Emitting beams; radiant.
n.
The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.
n.
The rate of regular or graded ascent or descent in a road; grade.
a.
Giving off rays; -- said of a bearing; as, the sun radiant; a crown radiant.
a.
Especially, emitting or darting rays of light or heat; issuing in beams or rays; beaming with brightness; emitting a vivid light or splendor; as, the radiant sun.
n.
Inclination; ascent or descent; a gradient.
n.
A part of a road which slopes upward or downward; a portion of a way not level; a grade.