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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
About polynomials in several variables
In mathematics, the Jacobian conjecture is a conjecture concerning polynomials in several variables that states that if a polynomial function from an n
Jacobian_conjecture
2000, six remain unsolved to date: Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness[when?] P versus NP Riemann
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
German mathematician (1906–1990)
tiling of space with cubes. This led to another 'Keller conjecture': the Keller cube-tiling conjecture from 1930. Subsequently, he worked with Georg Hamel
Ott-Heinrich_Keller
Dutch computer scientist
resolve mathematical conjectures such as the Boolean Pythagorean triples problem, Schur's theorem number 5, and Keller's conjecture in dimension seven.
Marijn_Heule
Tiling by squares of two sizes
Pythagoras with the original inspiration for his theorem. According to Keller's conjecture, any tiling of the plane by congruent squares must include two squares
Pythagorean_tiling
by cubes, there are two cubes that meet face to face. Keller's conjecture is the same conjecture for non-lattice tilings, which turns out to be false in
Hajós's_theorem
American mathematician
Samuel Wendell Williston. Entanglement-assisted classical capacity Keller's conjecture Stabilizer code Quantum capacity "The Mathematical Association of
Peter_Shor
Mathematical proof at least partially generated by computer
human-surveyable (albeit with difficulty, as with the proof of the Robbins conjecture) they do not share the controversial implications of computer-aided proofs-by-exhaustion
Computer-assisted_proof
Hungarian mathematician
face-to-face. Hajós used similar group-theoretic methods to attack Keller's conjecture on whether cube tilings (without the lattice constraint) must have
György_Hajós
American mathematician
divisors of n. He disproved Keller's conjecture in dimensions at least 10. Lagarias has also done work on the Collatz conjecture and Li's criterion and has
Jeffrey_Lagarias
Task of computing complete subgraphs
step in the analysis of certain random processes. In mathematics, Keller's conjecture on face-to-face tiling of hypercubes was disproved by Lagarias &
Clique_problem
Polyhedron that tiles space by translation
these symmetries may involve rotations, not just translations. Keller's conjecture, on tilings by translated copies of cubes and hypercubes that are
Parallelohedron
German mathematician (1880–1975)
Notes Math. 207, Springer-Verlag, 1971 Analytic hierarchy process Keller's conjecture Stieltjes transformation Jacobi–Perron algorithm Scott, W. T. (1955)
Oskar_Perron
Discrete probability distribution
question culminated in a proof in 2020 by Nathan Keller and Ohad Klein of the following conjecture. Conjecture. Let X = ∑ i = 1 n a i X i {\displaystyle X=\sum
Rademacher_distribution
Space-filling system of square prisms
meet face-to-face with any other cube, results of Oskar Perron on Keller's conjecture prove that (like the cubes within each prism of the tetrastix) every
Tetrastix
American mathematician (born 1992)
to the Jacobian conjecture, a problem in algebraic geometry begun by Ludwig Kraus in 1884 and formally posed by Ott-Heinrich Keller in 1939. The example
Levent_Alpöge
Stark Distinguished University Professor of Mathematics; disproved Keller's conjecture in dimensions at least 10 Hugh L. Montgomery, professor emeritus;
List of University of Michigan faculty and staff
List_of_University_of_Michigan_faculty_and_staff
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
German mathematician (1869–1940)
Teubner, 1953. Eisenstein reciprocity Hilbert class field Keller's conjecture Kummer–Vandiver conjecture Principalization (algebra) "Philipp Furtwängler - Biography"
Philipp_Furtwängler
Textbook on the use of group theory in studying tessellations
theory, but a generalization of this question to non-lattice tilings (Keller's conjecture) was disproved shortly before the publication of the book, in part
Algebra_and_Tiling
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
American-German physicist, engineer (1927–1999)
temple of quantum computing. p. 26 – 27. Retrieved 11 January 2005. The 'Landauer' formula Stuyvesant math team Physicists confirm Landauer's conjecture
Rolf_Landauer
Czech mathematician (1857–1886)
two-variable case of the Jacobian conjecture more than half a century before Ott-Heinrich Keller proposed the conjecture in its general form in 1939. Kraus's
Ludwig_Kraus
2021 American science fiction TV series
mathematical subfield of psychohistory, as a reward for solving a complex conjecture. They are both arrested on charges of treason; Seldon because his model
Foundation_(TV_series)
Dutch–German cartographer
activities during this period are unclear, but based on his later works it is conjectured that he spent time in Poland where he may have worked as a military engineer
Andreas_Cellarius
Graph representation in quantum mechanics
and Tasaki (AKLT) in 1987, as a rigorous example supporting the Haldane conjecture for integer-spin Heisenberg chains; the same authors also constructed
Tensor_network
Theory in the philosophy of science
of the Boundaries of Science (1999) and other works, and by Evelyn Fox Keller in Making Sense of Life: Explaining Biological Development with Models,
Unity_of_science
Positive integer of the form (2^(2^n))+1
who conjectured that all Fermat numbers are prime. Indeed, the first five Fermat numbers F0, ..., F4 are easily shown to be prime. Fermat's conjecture was
Fermat_number
allegations were used as a deliberate pretext for war. Various unsubstantiated conjectures were put forward that the weapons might have been hidden or sent elsewhere
Iraq and weapons of mass destruction
Iraq_and_weapons_of_mass_destruction
Perelman COURANT Fields Medal winner; proved soul conjecture and Thurston's geometrization conjecture Leopold B. Felsen POLY Professor at Boston University;
List of New York University alumni
List_of_New_York_University_alumni
American former attorney (born 1952)
Linda V. Parker stated that the plaintiffs had only offered "theories, conjecture, and speculation" of potential vote switching, that the "ship has sailed"
L._Lin_Wood
Observation that no scientific discovery is named after its discoverer
of Eponymy". James & Wells. Retrieved 15 August 2026. "Letter to Helen Keller". American Foundation for the Blind. 1903. Diamond, Arthur M. Jr. (December
Stigler's_law_of_eponymy
Prime such that p^2 divides 2^(p-1)-1
numbers as well as more general subjects such as number fields and the abc conjecture. As of 2026[update], the only known Wieferich primes are 1093 and 3511
Wieferich_prime
Award for advancements in discrete mathematics
with a fixed angle Nathan Keller and Noam Lifshitz for The junta method for hypergraphs and the Erdős–Chvátal simplex conjecture Source: American Mathematical
Fulkerson_Prize
Algebraic variety that is a moduli space for principally polarized abelian varieties
Parshin showed that the Mordell conjecture (now known as Faltings' theorem) would hold if the Shafarevich finiteness conjecture was true by introducing Parshin's
Siegel_modular_variety
Decade
eraser to remove pencil marks. Joseph-Louis Lagrange proves Bachet's conjecture. The Baron d'Holbach's (anonymous) materialist work Le Système de la Nature
1770s
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
ISSN 1941-6016. Marklof, Jens, The Berry–Tabor conjecture (PDF) Barba, J.C.; et al. (2008). "The Berry–Tabor conjecture for spin chains of Haldane–Shastry type"
Quantum_chaos
Italian-born American mathematician (1923–2023)
and the result became known as the Calabi conjecture. In 1957, Calabi published a paper in which the conjecture was stated as a proposition, but with an
Eugenio_Calabi
Sculpture from the Parthenon in Athens
of an infant but there is no infant on the frieze. "Interpretation and conjecture″ (above) discusses challenges to the prevailing view of the frieze, most
Parthenon_Frieze
1977 single by Eagles
(2005). 1000 Record Covers. Taschen. ISBN 3-8228-4085-8. Ferguson, Kevin; Keller, Chris (May 15, 2014). "20 things to know about Hotel California". 89.5
Hotel_California
Possible fate of the universe
run down as work is converted to heat because of the second law. The conjecture that all bodies in the universe cool off, eventually becoming too cold
Heat_death_of_the_universe
label) (b. 1947) Eugenio Calabi, 100, Italian-born mathematician (Calabi conjecture, Calabi–Yau manifold, Calabi flow) (b. 1923) Gerry Shamray, 66, comic
2023 deaths in the United States (July–September)
2023_deaths_in_the_United_States_(July–September)
invalidating the catastrophic scenario that some experts had initially conjectured. In September 2020, David Beasley, executive director of the World Food
Economic impact of the COVID-19 pandemic
Economic_impact_of_the_COVID-19_pandemic
American mathematician
B. (2001) [1994], "Osserman conjecture", Encyclopedia of Mathematics, EMS Press Weisstein, Eric W. "Nirenberg's Conjecture". MathWorld. Hoffman, David;
Robert_Osserman
1607 historical work by Walter Raleigh
are many digressions: one, "wherein is maintained the liberty of using conjectures in history"; another, "Of the Several Commandments of the Decalogue";
The History of the World (Raleigh)
The_History_of_the_World_(Raleigh)
State of matter
material with superfluid properties. In the case of helium-4, it has been conjectured since the 1960s that it might be possible to create a supersolid. Starting
Supersolid
this is false for surfaces of positive geometric genus. Jacobian conjecture. Keller asked this as a question in 1939, and in the next few years there
List_of_incomplete_proofs
Extinct class of simple animals
fossil was interpreted as an arthropod, later as a proarticulatan, then conjectured as possibly a frond-like organism. Current scientific consensus now recognizes
Vendiamorpha
South African diver (1974–1994)
was lost on ascent around 50 metres (160 ft) from the surface. They conjectured he had probably lost consciousness either because of oxygen toxicity
Deon_Dreyer
Arabic word for god
The more commonly used standalone word for God in Arabic is Allah, conjectured to be a compound form of the Arabic definite article Al ('the') + Ilah
Ilah
Heroic character from The Lord of the Rings
Frankish kingdoms. The Catholic author Joseph Pearce and others have conjectured, without evidence, that Aragorn's name is derived from the Kingdom of
Aragorn
Wife of Wolfgang Amadeus Mozart (1762–1842)
biographical myths about her first husband Johann Traeg – Cliff Eisen's conjecture for how Constanze quickly addressed her financial situation after her
Constanze_Mozart
2007 mass shooting in Baghdad, Iraq
sergeant from Sparta, Tennessee, and Paul Slough, an army veteran from Keller, Texas. A sixth Blackwater guard, Jeremy Ridgeway of California, struck
Nisour_Square_massacre
Paleolithic artifact from Congo
who stated: "A single bone may well collapse under the heavy weight of conjectures piled onto it." Similarly, George Joseph, in "The Crest of the Peacock:
Ishango_bone
2002 spy novel by Daniel Silva
accuses Rolfe of performing various services to the Nazi regime. He even conjectures that Rolfe allowed Jews to deposit their money in his bank and then turned
The English Assassin (Silva novel)
The_English_Assassin_(Silva_novel)
Species of tropical plant
species. However, as no other wild specimens have been found, this is still conjecture. The plant is grown widely throughout Southeast Asia and South Asia. Though
Pandanus_amaryllifolius
Hypothetical travel into the past or future
arguments led Stephen Hawking to formulate the chronology protection conjecture, suggesting that the fundamental laws of nature prevent time travel, but
Time_travel
Type of prime number
If any others exist, they must be greater than 2 × 1013. It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson
Wilson_prime
Generic name for various green iron layered double hydroxide
the sulfate in the intercalation layer, before the reduction. It was conjectured that green rust may be formed in the reducing alkaline conditions below
Green_rust
Major goddess in Hinduism
defeat of a group of demons. But Kinsley notes: "it is little more than conjecture to identify her with the later goddess Satī-Pārvatī, although [..] later
Parvati
One of six awards by the Wolf Foundation
fields, major advances on fundamental conjectures, and for settling Fermat's Last Theorem. 1996/97 Joseph B. Keller United States for his profound and
Wolf_Prize_in_Mathematics
Ethical point of view that extends inherent value to all living things
Darwin's Notebook on Transmutation of Species (1837): If we choose to let conjecture run wild, then animals, our fellow brethren in pain, diseases, death,
Biocentrism_(ethics)
Italian sculptor and architect (1598–1680)
Press, 2011), pp. 294–296, nn. 4–12; see also p. 128, n. 2 for Mormando's conjecture about the reason for the non-execution of the Benediction Loggia commission
Gian_Lorenzo_Bernini
98, Austrian-born mathematician (Graham–Pollak theorem, Gilbert–Pollak conjecture) Phil Regan, 89, baseball player (Los Angeles Dodgers, Chicago Cubs) and
2026 deaths in the United States
2026_deaths_in_the_United_States
Argentine writer (1899–1986)
intimate depths of his being, can wish it to triumph. I shall risk this conjecture: Hitler wants to be defeated. Hitler is blindly collaborating with the
Jorge_Luis_Borges
cancer. Eugenio Calabi, 100, Italian-born American mathematician (Calabi conjecture, Calabi–Yau manifold, Calabi flow). Bob Dahl, 54, American football player
Deaths_in_September_2023
Ancient Greek storyteller (620–564 BCE)
13th century who made a recension of The Aesop Romance in which it is conjectured that Aesop might have been Ethiopian, given his name. But according to
Aesop
Christian apostle and missionary (c. 5 – c. 64/65)
MacDonald 2004, p. 109. 1 Corinthians 14:34–36 Achtemeier 1985, p. 882. Keller 2010. Romans 16:3–4 1 Corinthians 1:11 Romans 16:1–2 Romans 16 Allison Barr
Paul_the_Apostle
Aspect of Chinese history
ancestry. Various nomadic tribes, such as the Yuezhi, Saka, and Wusun are conjectured to be part of the migration of Indo-European speakers who were settled
History_of_Xinjiang
American white supremacist hate group
court cases, exposés by disgruntled members, newspaper reports, and conjecture to describe the organization's activities. Almost all major national newspapers
Ku_Klux_Klan
American author and humorist (1835–1910)
all-powerful for good or evil, He is not in His right mind". At other times, he conjectured sardonically that perhaps God had created the world with all its tortures
Mark_Twain
Unpredictable phenomenon in complex systems
principles may involve more than just systematic logic, and could require conjectures suggested by experiments, simulations or insight. It has been suggested
Emergence
Propagation of information or matter faster than the speed of light
violations", and invoked Hawking's speculative chronology protection conjecture which suggests that feedback loops of virtual particles would create "uncontrollable
Faster-than-light
American writer (1842 – c. 1914)
(Macmillan, 2025) .online Eckhardt, Jason. "Across the Borderlands of Conjecture with Mr Bierce." Studies in Weird Fiction 4 (Fall 1988), 26–31. Fatout
Ambrose_Bierce
List of scientists who are Christians
method of evaluating determinants, led them to the Alternating Sign Matrix conjecture, now a theorem. Heinrich Hertz (1857–1894): German physicist who first
List of Christians in science and technology
List_of_Christians_in_science_and_technology
X1966 Mathematician Christophe Breuil X1989 Proved the Taniyama–Shimura conjecture together with Fred Diamond, Richard Taylor and Brian Conrad in 1999 Édouard
List of École polytechnique alumni
List_of_École_polytechnique_alumni
American beekeeping innovator
what is coming along this line, much better than any one living could conjecture the final outcome of Columbus' experiment.... — Gleanings in Bee Culture
Amos_Root
Series of air-to-ground attacks during the Iraqi insurgency
happened here in Iraq. We lost our country and our lives were destroyed. Bill Keller of The New York Times wrote, "But in its zeal to make the video a work of
July 12, 2007, Baghdad airstrike
July_12,_2007,_Baghdad_airstrike
Astronomical high energy transient pulse
(not especially coming from the galactic plane); consequently they are conjectured to be of extragalactic origin. Because of the isolated nature of the
Fast_radio_burst
Prime Minister of Italy (1972–73; 1976–79; 1989–92)
According to Andreotti's lawyers, the prosecution case was based on conjecture and inference, without any concrete proof of direct involvement by Andreotti
Giulio_Andreotti
American poet and suffragist
with her youngest brother through woods where trails were a matter of conjecture, and frequented by Native Americans, she visited practically all of Northern
Anna_M._Morrison_Reed
Qualitative research methodology
York: Routledge. Popper, K. (1963). Science: Conjectures and refutations. In K. R. Popper (Ed.), Conjectures and refutations: The growth of scientific knowledge
Grounded_theory
American writer (1728–1814)
political commentary yet: in 1775 Warren published The Group, a satire conjecturing what would happen if the British king abrogated the Massachusetts charter
Mercy_Otis_Warren
Universe/multiverse, to which authors were major contributors)] and recent conjectures about quantum gravity". 6 April U.S. Space Command, based on information
2022_in_science
Composition by Johann Sebastian Bach
The ornamentation of the penultimate note is a matter of interpretive conjecture, as no authentic ornament sign or trill is indicated, unlike in the B
Prelude and Fugue in F minor, BWV 857
Prelude_and_Fugue_in_F_minor,_BWV_857
even said to have married into the Imperial Family. By 700, it has been conjectured, perhaps one third of all Japanese aristocrats may have been of relatively
Korean influence on Japanese culture
Korean_influence_on_Japanese_culture
Italian mathematician (born 1984)
models. Also, together with Joaquim Serra, he proved the De Giorgi's conjecture for boundary reaction terms in dimension lower than five, and he improved
Alessio_Figalli
Mythical figure
wild woman or holzmoia are pointed out to be invalid, though Russell conjectures animal pelts may have been worn. The glossary source given as "Gloss
Wild_man
Pyrotechnic composition of metal powder and metal oxide
proven not to be the fault of the thermite reaction alone, but instead conjectured to be a combination of that and the burning of hydrogen gas that filled
Thermite
Distant planetesimals in the Solar System
trajectories, and longer times implied elliptical orbits. Leuschner conjectured that better statistics would show that comets had elliptical orbits and
Oort_cloud
American Nazi organization (1936-1941)
focused attention upon the Nazi movement in the United States and inspired conjectures as to its strength and influence. "Vonsiatsky Espionage". FBI.gov. Federal
German_American_Bund
on the solutions of the tameness, virtual Haken, and virtual fibering conjectures" James P. Allison – professor at UC Berkeley (1985–2004); 2014 Breakthrough
List of University of California, Berkeley faculty
List_of_University_of_California,_Berkeley_faculty
Medium consisting of pages of text or images
textbook that helps young children master reading and writing. It is thus conjectured that the earliest Indo-European writings may have been carved on beech
Book
Largest species of toothed whale
sperm whale's eyes afford good vision and sensitivity to light. They conjectured that sperm whales use vision to hunt squid, either by detecting silhouettes
Sperm_whale
Japanese dance
best" Araki 1964, pp. 68–69: "only conjecture". Araki (1964), pp. 68–69. Sasano (1943), pp. 69, 72–73. Kimbrough, R. Keller (2008), Preachers, Poets, Women
Kōwakamai
is ergodic Fields medalist Maryam Mirzakhani proved the long-standing conjecture that William Thurston's earthquake flow on Teichmüller space is ergodic
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Disorder of depression and mood episodes
possible mechanisms connecting cytokine levels to mood changes. They conjecture that immune dysfunction is relevant to some but not all bipolar disorder
Bipolar_disorder
Freiherr von Eichendorff and writers Christian Friedrich Hebbel, Gottfried Keller, Irene Frisch, Heinrich Hoffmann, Sir Muhammad Iqbal, José Rizal, W. Somerset
List of Heidelberg University people
List_of_Heidelberg_University_people
Interdisciplinary theory
414–424. doi:10.1037/a0031769. PMID 23398182. S2CID 7839454. Rabelo AL, Keller VN, Pilati R, Wicherts JM (2015). "No Effect of Weight on Judgments of Importance
Embodied_cognition
travel, tourism, insurance
KELLERS CONJECTURE
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