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Conjecture in algebraic geometry
In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism
Section_conjecture
Open problem on 3x+1 and x/2 functions
problems in mathematics The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple
Collatz_conjecture
Theorem in geometric topology
In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about
Poincaré_conjecture
Prime differing from another prime by two
contain at least m primes. Moreover (see also the next section) assuming the Elliott–Halberstam conjecture and its generalized form, the Polymath Project wiki
Twin_prime
2000, six remain unsolved to date: Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
German mathematician (born 1974)
for the section conjecture", Lecture Notes in mathematics 2054, Springer 2013 (Habilitation thesis) "The Brauer–Manin obstruction for sections of the fundamental
Jakob_Stix
Monster and modular connection
included "Moonshine" as a section in its list of notable properties of the monster group. Borcherds proved the Conway–Norton conjecture for the Moonshine Module
Monstrous_moonshine
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
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
On unit fractions adding to 4/n
problems in mathematics The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer n {\displaystyle
Erdős–Straus_conjecture
Theory in number theory
Galois groups of number fields and mixed-characteristic local fields. Section conjecture Class field theory Fiber functor Neukirch–Uchida theorem Belyi's theorem
Anabelian_geometry
Unsolved problem in computational complexity theory
Unique Games Conjecture true? More unsolved problems in computer science In computational complexity theory, the unique games conjecture (often referred
Unique_games_conjecture
Conjecture about gaps between prime numbers
Andrica's conjecture (named after Romanian mathematician Dorin Andrica (es)) is a conjecture regarding the gaps between prime numbers. The conjecture states
Andrica's_conjecture
Relates rational elliptic curves to modular forms
statement was known as the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture, or the modularity conjecture for elliptic curves. The theorem states
Modularity_theorem
French mathematician (1928–2014)
principal Scheme (mathematics) Section conjecture Semistable abelian variety Sheaf cohomology Stack (mathematics) Standard conjectures on algebraic cycles Sketch
Alexander_Grothendieck
Conjecture on zeros of the zeta function
problems in mathematics In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even
Riemann_hypothesis
Mathematical conjecture
(SYZ) conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics. The original conjecture was
SYZ_conjecture
Number divisible only by 1 and itself
. {\displaystyle 2k.} Andrica's conjecture, Brocard's conjecture, Legendre's conjecture, and Oppermann's conjecture all suggest that the largest gaps
Prime_number
Mathematical conjecture
In differential geometry, Yau's conjecture is a mathematical conjecture which states that any closed Riemannian 3-manifold has infinitely many smooth
Yau's_conjecture
William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of
Thurston elliptization conjecture
Thurston_elliptization_conjecture
field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee
Four_exponentials_conjecture
On generating functions from counting points on algebraic varieties over finite fields
In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them
Weil_conjectures
Conjecture in physics
weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities in the context of
Cosmic_censorship_hypothesis
Directed graph with no directed cycles
Press, p. 19, ISBN 978-0-12-324245-7. Weisstein, Eric W., "Weisstein's Conjecture", MathWorld{{cite web}}: CS1 maint: overridden setting (link) McKay, B
Directed_acyclic_graph
Condition on transcendence of numbers
chapter 2, section 1. Ramachandra, (1967/68). Waldschmidt, (1988), corollary 2.2. Waldschmidt, (2005), theorem 1.4. Waldschmidt, (2005), conjecture 1.5 Roy
Six_exponentials_theorem
Set of conjectures in algebraic geometry
In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology
Standard conjectures on algebraic cycles
Standard_conjectures_on_algebraic_cycles
Visualization of the prime numbers
a high asymptotic density of them, although there is a well-supported conjecture as to what that asymptotic density should be. In 1932, 31 years prior
Ulam_spiral
Topological concept in algebraic geometry
field extensions). Anabelian geometry, for example Grothendieck's section conjecture, seeks to identify classes of varieties which are determined by their
Étale_fundamental_group
Shape containing unit line segments in all directions
dimensions. The Kakeya conjecture is closely related to the restriction conjecture, Bochner-Riesz conjecture and the local smoothing conjecture. In February 2025
Kakeya_set
In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential
Grothendieck–Katz p-curvature conjecture
Grothendieck–Katz_p-curvature_conjecture
Curves of genus > 1 over the rationals have only finitely many rational points
This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. The conjecture was later generalized
Faltings'_theorem
the zero section. More unsolved problems in mathematics In mathematics, more specifically symplectic topology, the nearby Lagrangian conjecture, is an open
Nearby_Lagrangian_conjecture
Disproved conjecture in number theory
In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was presented by Leonhard Euler in 1778 to the Academy
Euler's sum of powers conjecture
Euler's_sum_of_powers_conjecture
Non-orientable mathematical surface
surface of a Klein bottle; this is the only exception to the Heawood conjecture, a generalization of the four color theorem, which would require seven
Klein_bottle
Estimatation in number theory
log e ( x ) {\displaystyle \log _{e}(x)} . In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an
Cramér's_conjecture
Generalization of Fermat's Last Theorem and of Catalan's conjecture,
theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. The conjecture states that the equation
Fermat–Catalan_conjecture
Whether a manifold which is a homotopy sphere is a sphere
In the mathematical area of topology, the generalized Poincaré conjecture is a statement that a manifold that is a homotopy sphere is a sphere. More precisely
Generalized Poincaré conjecture
Generalized_Poincaré_conjecture
Two-dimensional shape
octagon is a region in the plane found by Karl Reinhardt in 1934 and conjectured by him to have the lowest maximum packing density of the plane of all
Smoothed_octagon
American mathematician (1946–2012)
complicated. The conjecture was proved by Grigori Perelman in 2002–2003. Thurston and Dennis Sullivan generalized Lipman Bers' density conjecture from singly
William_Thurston
Conjecture in graph theory
Sidorenko's conjecture is a major conjecture in the field of extremal graph theory, posed by Alexander Sidorenko in 1986. Roughly speaking, the conjecture states
Sidorenko's_conjecture
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
Mathematics award
was found in 1993. In 2006, Grigori Perelman, who proved the Poincaré conjecture, refused his Fields Medal, stated "I'm not interested in money or fame;
Fields_Medal
conjecture may refer to one of several conjectural statements from differential geometry and topology attributed to Heinz Hopf. The Hopf conjecture is
Hopf_conjecture
Perfect graphs have neither odd holes nor odd antiholes
length at least 5) nor odd antiholes (complements of odd holes). It was conjectured by Claude Berge in 1961. A proof by Maria Chudnovsky, Neil Robertson
Strong_perfect_graph_theorem
Would relate vector bundles over a regular Noetherian ring and over a polynomial ring
A[t_{1},\dots ,t_{n}]} . The conjecture is named for Hyman Bass and Daniel Quillen, who formulated the conjecture. The conjecture is a statement about finitely
Bass–Quillen_conjecture
Interplay between observation, experiment, and theory in science
empirical observations based on those predictions. A hypothesis is a conjecture based on knowledge obtained while seeking answers to the question. Hypotheses
Scientific_method
Mathematics concept
algebra of the Galois image. This conjecture is known only in particular cases. Through generalisations of this conjecture, the Mumford–Tate group has been
Mumford–Tate_group
Geometry problem on tiling by hypercubes
In geometry, Keller's conjecture is the conjecture that in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes
Keller's_conjecture
Unsolved conjecture in number theory
In number theory, the Lander, Parkin, and Selfridge conjecture concerns the integer solutions of equations which contain sums of like powers. The equations
Lander, Parkin, and Selfridge conjecture
Lander,_Parkin,_and_Selfridge_conjecture
Topological theorem
R3 is either constant or not contained within an open hemisphere. As conjectured by Louis Nirenberg and proved by Robert Osserman in 1959, in this form
Osserman–Xavier–Fujimoto theorem
Osserman–Xavier–Fujimoto_theorem
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
Brazilian mathematician
with André Neves, he proved the Willmore conjecture. Since then, among proving other important conjectures, Marques and Neves greatly extended Almgren–Pitts
Fernando_Codá_Marques
In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds. It is named after Takao Fujita, who formulated
Fujita_conjecture
Complete manifolds of non-negative sectional curvature largely reduce to the compact case
generalizing a 1969 result of Gromoll and Wolfgang Meyer. The related soul conjecture, formulated by Cheeger and Gromoll at that time, was proved twenty years
Soul_theorem
Type of steel used in Middle Eastern swordmaking
Macroscopic section of crucible steel (left) and false color labeling (right) showing rafts rich in carbide-forming elements (CFEs), which lead to clustered
Damascus_steel
Sprite stemming from Germanic mythology
but placed the discussion of it under the "Wild man of the woods" section conjecturing the use of güttel as synonymous to götze (i.e., sense of 'idol')
Kobold
Pseudometric of complex manifolds
(2004), Conjecture 9.2, Lang (1986), Conjecture 5.8. Campana (2004), Conjecture 9.20. Kobayashi (1998), Theorem 3.5.31. Kobayashi (1998), section 7.2. Kobayashi
Kobayashi_metric
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a
Carathéodory_conjecture
Compounding sum paid for the use of money
irrational representations of e Lindemann–Weierstrass theorem People Jakob Bernoulli John Napier Leonhard Euler Related topics Schanuel's conjecture v t e
Compound_interest
Conjecture on forbidden minors of matroids
Rota's excluded minors conjecture is one of a number of conjectures made by the mathematician Gian-Carlo Rota. It is considered an important problem by
Rota's_conjecture
Fractal named after mathematician Benoit Mandelbrot
closed unit disk. Mandelbrot had originally conjectured that the Mandelbrot set is disconnected. This conjecture was based on computer pictures generated
Mandelbrot_set
Australian and American mathematician (born 1975)
resolved or made progress on a number of conjectures. In 2012, Green and Tao announced proofs of the conjectured "orchard-planting problem," which asks
Terence_Tao
Mathematical function associated to algebraic varieties
2018-03-29. Retrieved 2022-04-13. Birch and Swinnerton-Dyer Conjecture at Clay Mathematics Institute Section C.16 of Silverman, Joseph H. (1992), The arithmetic
Hasse–Weil_zeta_function
Mathematical theory
spheres has a longer history of investigation, from which the Kepler conjecture is most well-known. Atoms in crystal structures can be simplistically
Finite_sphere_packing
Legendary single-horned horse-like creature
pomegranate tree surrounded by a fence, in a field of flowers. Scholars conjecture that the red stains on its flanks are not blood but rather the juice from
Unicorn
Reaction that combines atomic nuclei
S. Department of Energy. Retrieved 13 February 2026. F. Winterberg "Conjectured Metastable Super-Explosives formed under High Pressure for Thermonuclear
Nuclear_fusion
Pharaoh of Egypt from 51 to 30 BC
Cleopatra's mother being a member of an Egyptian priestly family as "pure conjecture," adding that either Cleopatra V or a concubine "probably of Greek origin"
Cleopatra
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
American mathematician (1927–2010)
covering set {3, 5, 7, 13, 19, 37, 73}. Five years later, he and Sierpiński conjectured that 78,557 is the smallest Sierpinski number, and thus the answer to
John_Selfridge
Framework of superstring theory
unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University
M-theory
Problem in discrete geometry
n}})} , and offered a prize of $500 for either proving or disproving the conjecture. Paul Erdős' 1946 lower bound of g(n) = Ω(n1/2) was successively improved
Erdős distinct distances problem
Erdős_distinct_distances_problem
and given by an equation y3 = Q(x) where Q is of degree 4. The gonality conjecture, of M. Green and R. Lazarsfeld, predicts that the gonality of the algebraic
Gonality of an algebraic curve
Gonality_of_an_algebraic_curve
Compact astronomical body
hair conjecture proposes that dynamic gravitational collapse always results in an object characterized with only these three properties. The conjecture is
Black_hole
Theorem in graph theory
Berger was originally a conjecture proposed by Paul Erdős, and before being proved was known as the Erdős–Menger conjecture. It is equivalent to Menger's
Menger's_theorem
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
Partition of a graph into spanning subgraphs
Unsolved problem in mathematics Conjecture: If n is odd and k ≥ n, then G is 1-factorable. If n is even and k ≥ n − 1 then G is 1-factorable. More unsolved
Graph_factorization
Riemannian manifold with SU(n) holonomy
superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to
Calabi–Yau_manifold
Sum of inverse squares of natural numbers
the proof. A proof is also possible assuming Weil's conjecture on Tamagawa numbers. The conjecture asserts for the case of the algebraic group SL2(R) that
Basel_problem
Creationist hypothesis
Inquirer. 43 (3): 57–59. Kathleen McVey, ed. (1994). "Commentary on Genesis. Section I.22". St. Ephrem the Syrian: Selected Prose Works. The Fathers of the
Omphalos_hypothesis
Chemical element with atomic number 87 (Fr)
francium was referred to as eka-caesium or ekacaesium because of its conjectured existence below caesium in the periodic table. It was the last element
Francium
Natural number
Mathematics Institute". www.claymath.org. Retrieved 2020-08-25. "Poincaré Conjecture | Clay Mathematics Institute". 2013-12-15. Archived from the original
7
Video-sharing platform
to extremist videos, little systematic evidence exists to support this conjecture", and that such exposure was "heavily concentrated among a small group
YouTube
American mathematician
B. (2001) [1994], "Osserman conjecture", Encyclopedia of Mathematics, EMS Press Weisstein, Eric W. "Nirenberg's Conjecture". MathWorld. Hoffman, David;
Robert_Osserman
Millennium Prize Problem
showing the existence of a mass gap. Both of these topics are described in sections below. The Millennium problem requires the proposed Yang–Mills theory to
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Biblical Figure
priesthood and titles connected with the Second Temple. It has also been conjectured that the suffix "-zedek" may have been or become a reference to a Canaanite
Melchizedek
Field of knowledge
across mathematics. A prominent example is Fermat's Last Theorem. This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994
Mathematics
British rock musician and songwriter (1946–1991)
statement, which was released the following day: Following the enormous conjecture in the press over the last two weeks, I wish to confirm that I have been
Freddie_Mercury
American domestic terrorist (1942–2023)
subfield effectively ceased to exist after the 1960s, as most of its conjectures had been proven. According to mathematician Donald Rung, if Kaczynski
Ted_Kaczynski
Kepler conjecture, use long computer calculations as well as many pages of mathematical argument. For the computer calculations in this section, the mathematical
List of long mathematical proofs
List_of_long_mathematical_proofs
Unidentified plant used as a seasoning and medicine
Thapsia gummifera has been suggested as another possibility. Another conjecture is that it was simply a high-quality variety of asafoetida, a common seasoning
Silphium
German astronomer and mathematician (1571–1630)
mentioned Kepler's discoveries in his work. He postulated the Kepler conjecture. Kepler influenced among others Isaac Newton, providing one of the foundations
Johannes_Kepler
defined, i.e., independent of the choice of the desingularization. A basic conjecture is that the pluricanonical ring is finitely generated. This is considered
Canonical_ring
French mathematician
geodesics. The first problem in the minimal submanifolds section of Yau's list (Yau's conjecture) asks whether any closed three-manifold has infinitely
Antoine_Song
Branch of algebraic geometry concerned with counting solutions
Gromov–Witten invariants and mirror symmetry gave significant progress in Clemens conjecture. Enumerative geometry is very closely tied to intersection theory. More
Enumerative_geometry
Invariant of algebraic varieties and of more general schemes
Motivic Homology Theories. (AM-143). Section 4. Suslin, Andrei; Voevodsky, Vladimir (2000). "Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients"
Motivic_cohomology
Observation on the growth of integrated circuit capacity
This section is in list format but may read better as prose. You can help by converting this section, if appropriate. Editing help is available. (March
Moore's_law
First-century Jewish preacher and religious leader
are in doubt thereof; they have no knowledge thereof save pursuit of a conjecture; they slew him not for certain. But Allah took him up unto Himself. Allah
Jesus
1977 single by Eagles
producer Bill Szymczyk, there were 33 edits on the two‑inch master. The final section features a guitar battle between Joe Walsh (who had replaced Bernie Leadon
Hotel_California
1995 publication in mathematics
They conjectured that every rational elliptic curve is also modular. This became known as the Taniyama–Shimura conjecture. In the West, this conjecture became
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Probability of making type I errors when performing multiple hypotheses tests
inequalities for ordered MTP2 random variables: a proof of the Simes conjecture". The Annals of Statistics. 26 (2): 494–504. doi:10.1214/aos/1028144846
Family-wise_error_rate
SECTION CONJECTURE
SECTION CONJECTURE
Boy/Male
American, Anglo, Australian, British, English, French
From Baron's Estate; From the Town Near the Sea
Boy/Male
English
From the farm by the sea.
Boy/Male
Hindu, Indian
Boiled or Baked Buckwheat; Section
Boy/Male
English Anglo Saxon
From the farm by the sea.
Boy/Male
American, Australian, British, Christian, English
Village of Rushes; Rush Settlement
Boy/Male
Hindu, Indian
A Section; Portion; Festival; Strong; Occassion
Surname or Lastname
English
English : occupational name for a sexton or churchwarden, from Middle English sexteyn ‘sexton’ (Old French secrestein, from Latin sacristanus).Irish (Munster and midlands) : reduced Anglicized form of Gaelic Ó Seastnáin ‘descendant of Seastnán, Seasnán’, a personal name meaning ‘bodyguard’, from seasuighim ‘to resist’, ‘to defend’.
Boy/Male
British, English, Indian, Russian
Work
Boy/Male
British, English
Church Custodian
Surname or Lastname
English
English : variant of Sessions.
Girl/Female
Tamil
Action
Boy/Male
Shakespearean
The Tragedy of Macbeth' Attendant to Macbeth.
Boy/Male
Tamil
Action
Boy/Male
American, British, English, French
From the Town Near the Sea
Boy/Male
Vietnamese
Section.
Boy/Male
Hindu
Action
Girl/Female
American, Hindu, Indian
Selection
Surname or Lastname
English
English : habitational name from a place in Lancashire, so called from Old Norse sef ‘rush’ + Old English tūn ‘enclosure’, ‘settlement’.
Boy/Male
English
From Sefton; town in the rushes.
Biblical
station;
SECTION CONJECTURE
SECTION CONJECTURE
Girl/Female
Tamil
Goddess Lakshmi, Foremost, Best, First, Night
Girl/Female
Biblical Hebrew
How good is God.
Boy/Male
Hindu
Musical, Lord Shiva
Girl/Female
Arabic
With Beautiful Eyes
Boy/Male
Hebrew American
Abbreviation of Joshua 'Jehovah is salvation.
Boy/Male
Hindu
Lord Vishnu
Girl/Female
Hindu
Who speaks truth, Mother of Vyasa (formerly Matsyagandha  Mother of Vyasa (from the union with Parasara Rishi))
Boy/Male
English
Rhyming- a historical blacksmith with supernatural powers.
Boy/Male
Hindu, Indian, Marathi
All Heroic
Girl/Female
Tamil
SECTION CONJECTURE
SECTION CONJECTURE
SECTION CONJECTURE
SECTION CONJECTURE
SECTION CONJECTURE
n.
One of the portions, of one square mile each, into which the public lands of the United States are divided; one thirty-sixth part of a township. These sections are subdivided into quarter sections for sale under the homestead and preemption laws.
n.
A lesson or selection, esp. of Scripture, read in divine service.
n.
The act of cutting, or separation by cutting; as, the section of bodies.
v. t.
To place; to set; to appoint or assign to the occupation of a post, place, or office; as, to station troops on the right of an army; to station a sentinel on a rampart; to station ships on the coasts of Africa.
v. t.
To give sanction to; to ratify; to confirm; to approve.
a.
Of or pertaining to a sections or distinct part of larger body or territory; local.
n.
The act of secreting or concealing; as, the secretion of dutiable goods.
n.
The mutual or reciprocal action of chemical agents upon each other, or the action upon such chemical agents of some form of energy, as heat, light, or electricity, resulting in a chemical change in one or more of these agents, with the production of new compounds or the manifestation of distinctive characters. See Blowpipe reaction, Flame reaction, under Blowpipe, and Flame.
n.
The figure made up of all the points common to a superficies and a solid which meet, or to two superficies which meet, or to two lines which meet. In the first case the section is a superficies, in the second a line, and in the third a point.
n.
The things sold by auction or put up to auction.
n.
Movement; as, the horse has a spirited action.
a.
The act of choosing; choice; selection.
v. t.
To sell by auction.
n.
An engagement between troops in war, whether on land or water; a battle; a fight; as, a general action, a partial action.
n.
Any action in resisting other action or force; counter tendency; movement in a contrary direction; reverse action.
n.
An action induced by vital resistance to some other action; depression or exhaustion of vital force consequent on overexertion or overstimulation; heightened activity and overaction succeeding depression or shock.
n.
A right of action; as, the law gives an action for every claim.
n.
See Exsection.
a.
Consisting of sections, or capable of being divided into sections; as, a sectional steam boiler.
v. t.
To make mention of; to speak briefly of; to name.