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Longer titles found: Open Problems in Mathematics (view)

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Argument from ignorance (1,321 words) [view diff] exact match in snippet view article find links to article

the proposition can be called unproven, undecided, inconclusive, an open problem or a conjecture. The term was likely coined by philosopher John Locke

{\displaystyle n} ). All non-palindromic permutable primes are emirps. It is an open problem whether there are infinitely many emirps. Weisstein, Eric W. "Emirp"

with a concrete solution, and identity-based encryption remained an open problem for many years. The first practical implementations were finally devised

{P}}\subsetneq {\mathsf {NP}}} hypothesis) remains unproven. Another open problem is whether NP = co-NP; since P = co-P, a negative answer would imply

Unsolved problem in computer science ⁠ N C = ? P {\displaystyle {\mathsf {NC}}{\overset {?}{=}}{\mathsf {P}}} ⁠ More unsolved problems in computer science

rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the

this became known as Moser's worm problem and as of 2024 remains an open problem. Bell number Berlekamp switching game Salem–Spencer set Secretary problem

algorithm is equivalent to the P versus NP problem, which is a famous open problem in the theory of computing. Nevertheless, as of 2007, heuristic SAT-algorithms

most simplicial spheres cannot be obtained in this way. One important open problem in the field was the g-conjecture, formulated by Peter McMullen, which

proving procedures" and is considered by many to be the most important open problem in the field. It is one of the seven Millennium Prize Problems selected

verified in polynomial time. The problem has been called the most important open problem in computer science. Aside from being an important problem in computational

substituted for quantification over the integers is a notoriously hard open problem. The MRDP theorem (so named for the initials of the four principal contributors

work. The third case, the positive or Fano case, remained a well-known open problem for many years. In this case, there is a non-trivial obstruction to existence

to as the sofa constant. The exact value of the sofa constant is an open problem. The leading solution, by Joseph L. Gerver, has a value of approximately

system of the arithmetic of the even and the odd in and, but it is an open problem in a stronger natural axiom system for the arithmetic of the even and

princess full freedom of locomotion. This game remained a well-known open problem until it was solved by Shmuel Gal in the late 1970s. His optimal strategy

be proved by considering examples). Therefore, W(2, 3) is 9. It is an open problem to determine the values of W(r, k) for most values of r and k. The proof

languages. The "n squares' problem", known also as Büchi's problem, is an open problem from number theory, closely related to Hilbert's tenth problem. Finite

Carleson as advisor. In 2002, Tucker succeeded in solving an important open problem that had been posed by Stephen Smale (the fourteenth problem on Smale's

Hypothesis implies the existence of an ℵ2-Suslin tree, is a longstanding open problem. Glossary of set theory Kurepa tree List of statements independent of

In mathematics, the Casas-Alvero conjecture is an open problem about polynomials which have factors in common with their derivatives, proposed by Eduardo

β-labeling by Alexander Rosa in a 1967 paper on graph labelings. A major open problem in graph theory is the graceful tree conjecture or Ringel–Kotzig conjecture

of identity-based signatures. Identity-based encryption remained an open problem for many years. The pairing-based Boneh–Franklin scheme and Cocks's encryption

is named for Paul Erdős and András Hajnal, who first posed it as an open problem in a paper from 1977. More precisely, for an arbitrary undirected graph

just like the untyped lambda calculus[citation needed]. It is a major open problem in the field whether this is always the case, i.e. whether a (weakly)

question whether every matching extends to a Hamiltonian cycle remains an open problem. The hypercube graph Qn (for n > 1) : is the Hasse diagram of a finite

half-coin which involves negative probability, and the solution of an old open problem of lottery mathematics: in a 5-from-90 lotto the minimum number of tickets

original presentation of a compressed suffix array solved a long-standing open problem by showing that fast pattern matching was possible using only a linear-space

arithmetic; meanwhile, the consistency of NF relative to anything remains an open problem, pending verification of Holmes's proof of its consistency relative to

Comb. Theory Ser B, 30 (1981), 130–135. [1], Open Problem Garden. [2], Open Problem Garden. [3], Open Problem Garden. Zhang, Cun-Quan (1997). Integer Flows

should be emphasized that the Poincaré conjecture has been a well-known open problem in the field of geometric topology since 1904. These results by Hamilton

favorable properties including linear wait, and which extension solved the open problem posted by Leslie Lamport whether there is an algorithm with a constant

polynomial-time ε-approximation algorithm, they resolved a long-standing open problem in optimal control. Their first paper considered time-optimal control

"Weyl problem" in differential geometry, which had been a well-known open problem since 1916. Following his doctorate, he became a professor at the Courant

theory to another primitive operation, the exponential function. It is an open problem whether this theory is decidable, but if Schanuel's conjecture holds

Unsolved problem in mathematics Which finite groups are BI-groups? More unsolved problems in mathematics Babai's problem is a problem in algebraic graph

Fuglede's conjecture is an open problem in mathematics proposed by Bent Fuglede in 1974. It states that every domain of R d {\displaystyle \mathbb {R}

false: this is called the Vaught conjecture and is the main remaining open problem (in 2005) in the theory of the spectrum. Morley's problem was a conjecture

question of whether such infinite growth patterns exist was posed as an open problem by Gravner, Griffeath, and Moore. The chaotic patterns common in this

groups; the classification of isomorphism classes of finite groups is an open problem. Ring isomorphism between rings. Field isomorphisms are the same as ring

constructing Costas arrays. The general enumeration of Costas arrays is an open problem in computer science and finding an algorithm that can solve it in polynomial

pseudorandomness and derandomization, where researchers consider the open problem of whether L = RL. The corresponding nondeterministic space complexity

but the positive characteristic case is (as of 2024) still a major open problem. Essentially all Noetherian rings that occur naturally in algebraic geometry

Milind Sohoni. The goal of the program is to answer the most famous open problem in computer science – whether P = NP – by showing that the complexity

construction of other large NLFSRs with guaranteed long periods remains an open problem. Using bruteforce methods, a list of maximum-period n-bit NLFSRs for

{\displaystyle 1-p} ). Determining the capacity of the deletion channel is an open problem. The deletion channel should not be confused with the binary erasure

In statistics, the topic of location testing for Gaussian scale mixture distributions arises in some particular types of situations where the more standard

decompositions of complete hypergraphs, which solved a long-standing open problem. In addition to his mathematical pursuits, Baranyai was also a professional

powers of 5 greater than 5 itself by marked ruler and compass is an open problem, along with all primes greater than 11 of the form p = 2r3s5t + 1 where

Proving that this is true (or finding a counterexample) remains an open problem. Several important classes of graphs can be defined by or characterized

integers. While the complete classification of integral graphs remains an open problem, the Cayley graphs of certain groups are always integral. Using previous

n ) {\displaystyle O(n)} steps to solve. Perhaps the most important open problem in all of computer science is the question of whether a certain broad

position? More unsolved problems in mathematics The McMullen problem is an open problem in discrete geometry named after Peter McMullen. In 1972, David G. Larman

particular, that almost all Woodall numbers are composite. It is an open problem whether there are infinitely many Woodall primes. As of October 2018[update]

Conjecture", MathWorld Moskovich, D. (June 4, 2012), "Dürer's conjecture", Open Problem Garden Ghomi, Mohammad (2018-01-01), "Dürer's Unfolding Problem for Convex

2005 by Kirsten. Earlier, in 1979, Hashiguchi had also solved another open problem on regular languages, of deciding whether, for a given language A {\displaystyle

C*-algebra. An additive quasitrace is called a trace. It is a major open problem if every quasitrace is a trace. A quasitrace on a C*-algebra A is a map

uncertainty places it in a unique complexity class, making it a significant open problem in computer science. Is graph canonization polynomial-time equivalent

group has intermediate growth, thus providing an answer to an important open problem posed by John Milnor in 1968. The Grigorchuk group remains a key object

the Riemann hypothesis, which has long been regarded as the deepest open problem in mathematics. Given the solution, he calls for more thorough investigation

arrangement is a Koszul algebra; whether the converse is true is an open problem. Stanley, Richard P. (1972). "Supersolvable lattices". Algebra Universalis

famous P = NP? problem, one of the Millennium Prize Problems, is an open problem in the theory of computation. Information theory, closely related to

satisfying the parabolic one. The existence of such an example was an open problem for many years. A variation of the Sierpiński carpet, called the Wallis

embeddings, are important in the theory of approximation algorithms. A major open problem in this area is the GNRS conjecture, which (if true) would characterize

malicious CPU or memory consumption. This attack was previously denoted an open problem in ICN, only heuristic countermeasures available.[vague] In 2016, Aubrey

have the same Alexander and Conway polynomials as the unknot. It is an open problem whether any non-trivial knot has the same Jones polynomial as the unknot

approximate Nash equilibria, but the existence of a PTAS remains an open problem. For constant values of ε, polynomial-time algorithms for approximate

"Semigroups, Antiautomorphisms, and Involutions: A Computer Solution to an Open Problem, I". Mathematics of Computation. 37 (156): 533–545. doi:10.2307/2007445

his award-winning teaching, and for his solution to a long-standing open problem due to Irving Kaplansky on a symmetric *-algebra. Robert Stuart Doran

theory, Büchi's problem, also known as the n squares' problem, is an open problem named after the Swiss mathematician Julius Richard Büchi. It asks whether

local maxima. Every ribbon knot is known to be a slice knot. A famous open problem, posed by Ralph Fox and known as the slice-ribbon conjecture, asks if

varieties of dimension at least 4 over fields of characteristic p, it is an open problem. Originally the problem of resolution of singularities was to find a

branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry of

varieties of dimension at least 4 over fields of characteristic p, it is an open problem. Originally the problem of resolution of singularities was to find a

for x , y ≤ 200 {\displaystyle x,y\leq 200} Field Number theory Conjectured by G. H. Hardy John Edensor Littlewood Conjectured in 1923 Open problem yes

our understanding of computation. The following problem is the main open problem in this area of research: find an explicit polynomial of polynomial degree

but showing the existence of such a polynomial time algorithm is an open problem. Other computational problems with quasi-polynomial time solutions but

the permanent was shown by Grigoriy Kogan. Barnette's conjecture, an open problem on Hamiltonicity of cubic bipartite polyhedral graphs Eulerian path,

unfolding restrict their cuts to the edges of the polyhedron. It is an open problem whether every polyhedron can be cut and unfolded to a simple polygon

{G}}^{2}=\{k^{2}\}_{k=1}^{\infty }} is an additive basis of degree 4. (About an open problem for additive bases, see Erdős–Turán conjecture on additive bases.) Historically

differences between perfect squares and perfect cubes, which remains an open problem as of 2015. Hall's work on continued fractions showed that the Lagrange

predatory interactions between competing species Inverse Galois problem, an open problem in mathematics This disambiguation page lists articles associated with

> 3 {\displaystyle n>3} are poorly understood. For example, it is an open problem whether or not Diff ( S 4 ) {\displaystyle {\text{Diff}}(S^{4})} has

Davenport, began to undertake research in number theory. Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway

c_{r}(Z)} . The theorem was introduced in SGA 5 Exposé I, § 3.1.4. as an open problem. Later, Thomason proved it for large n and Gabber in general. purity

have if they were more informed and enlightened. AI alignment is an open problem for modern AI systems and is a research field within AI. Aligning AI

conjectures due to I. J. Good and Daniel Shanks. The conjecture remains an open problem: several papers give empirical support, but it disagrees with the widely

mathematics to refer to a reward offered to any person willing to take on an open problem. Bounties are offered for solving a particular math problem – ranging

question about the irrationality of Euler's constant γ is a long standing open problem in number theory. Other important numbers which are not known to be irrational

1742 (Latin-German) Field Number theory Conjectured by Christian Goldbach Conjectured in 1742 Open problem Yes Consequences Goldbach's weak conjecture

{\textstyle D} of the graph of the classical Weierstrass function was an open problem until 2018, while it was generally believed that D = 2 + log b ⁡ ( a

The question of whether there are any Lychrel numbers in base 10 is an open problem in recreational mathematics; the smallest candidate is 196. Counting

as Brier had theorized. The cause of Tutankhamun's demise is still an open problem in Egyptology, and Bob Brier still maintains the plausibility of Ay's

characteristic for varieties of dimension at least 4 is (as of 2019) an open problem. Abhyankar, Shreeram (1956), "Local uniformization on algebraic surfaces

topological manifolds not homeomorphic to a simplicial complex was an open problem. In 2013, Ciprian Manolescu posted a preprint on ArXiv showing that there

simple polygon can be triangulated faster than O(n log n) time was an open problem in computational geometry. Then, Tarjan & Van Wyk (1988) discovered an

Pauli's theory, the lack of a strong Curie paramagnetism in metals was an open problem as the leading Drude model could not account for this contribution without

is mostly in optimization. In his thesis, he answered a 20-year-old open problem posed by N. Z. Shor. For this contribution and other contributions to

In mathematics, specifically in combinatorial commutative algebra, a convex lattice polytope P is called normal if it has the following property: given

}[\mathrm {DGumbel} (0,1)]=1.077240905953631072609...} , but it remains an open problem to find a closed form for this constant (it is plausible there is none)

case n = 2) with 2-coloring does not imply WKL0 over RCA0, solving an open problem left by English logician David Seetapun in the 1990s (Liu (2012)). "Math

theorem holds. Many metrics for the M/G/k queue with k servers remain an open problem, though some approximations and bounds are known. M/M/1 queue M/M/c queue

1.  See topological tensor product. Note it is still somewhat of an open problem to define or work out a correct tensor product of topological vector

transformation function of the Collatz conjecture (1 ⇒ 2 ⇒ 4 ⇒ 1 ⇒ ..., it is an open problem if there are any other loops of the Collatz transformation). Another

e} ) then the channel is a deletion channel, and its capacity is an open problem. The BEC was introduced by Peter Elias of MIT in 1955 as a toy example

that every connected component has a strong orientation. An important open problem involving bridges is the cycle double cover conjecture, due to Seymour

square aspect ratio, we arrive at the Gauss Circle Problem, an unsolved open problem in mathematics.) Note that formulas estimating the gross dies per wafer

follows. An extension of this is the assumption of a solution to an open problem. This weaker kind of deductive reasoning will get used in current research

Some suggestions have been made on this issue but this is still an open problem since none of them have gathered significant support. The teleological

conjecture for the classical capacity of quantum channels, a long standing open problem in quantum Shannon theory. He and Michael Freedman formulated the NLTS

dilute and dense regimes of attracting pairs of fermions is still an open problem, which now attracts a lot of attention within the field of ultracold

an apparent horizon condition. Proving such an inequality remains an open problem in general relativity, called the Penrose conjecture. In episode 6 of

but was unable to produce a proof for this result, leaving it as an open problem in 1895. In the early decades of the 20th century, the main areas of

of the Bolza surface, although providing a rigorous proof is still an open problem. Following this pattern, one may reasonably conjecture that Bring's surface

Problems such as performance metrics for the M/G/k queue remain an open problem. Various scheduling policies can be used at queueing nodes: First in

{\displaystyle k\leq n=3.4\times 10^{11}} in 1993, but the conjecture remains an open problem. Instead of evaluating n rows, Odlyzko evaluated 635 rows and established

originally posed by Pietro Mengoli in 1644, and by the 1730s was a famous open problem, popularized by Jacob Bernoulli and unsuccessfully attacked by many of

Problems such as performance metrics for the M/G/k queue remain an open problem. Various scheduling policies can be used at queueing nodes: First in

coupling. This hierarchy in the fermion masses remains a profound and open problem in theoretical physics. Higgs–Yukawa couplings are not fixed constants

rank-1 tensors, where R is minimal. Computing this decomposition is an open problem.[clarification needed] Canonical polyadic decomposition (CPD) is a variant

optimal. However, the log n factor was eliminated by Devai, who raised the open problem whether the same optimal O(n2) upper bound existed for hidden-surface

that is unexpected and powerful. Polchinski notes that an important open problem in quantum gravity is to develop holographic descriptions of gravity

general solution to the prediction of the function of a protein remains an open problem. Most efforts have so far been directed towards heuristics that work

possible solutions to the structured tails problem, but it remains an open problem. Interpretation of quantum mechanics Many-worlds interpretation Philosophy

produce only even amicable pairs, so they are of no interest for the open problem of finding amicable pairs coprime to 210 = 2·3·5·7, while over 1000 pairs

I. Washington: Carnegie Institution of Washington. p. 6. "The oldest open problem in mathematics" (PDF). Harvard.edu. Retrieved 16 June 2023. Oddperfect

Galois theory, the Galois group of F/M is G. On the other hand, it is an open problem whether every finite group is the Galois group of a field extension of

dimensions, classification of the possible Calabi–Yau manifolds is an open problem, although Yau suspects that there is a finite number of families (albeit

at least in simulation, such as in morphogenetic robotics. Another open problem is the understanding of the relation between the key phenomena investigated

relativity and quantum field theory into a quantum gravity theory is still an open problem in physics. Emmy Noether proved the Noether's theorem in 1918 relating

that has o ( n 3 + ϵ ) {\displaystyle o(n^{3+\epsilon })} events is an open problem. The smallest enclosing disk of a set of n moving points can be ε-approximated

But there is no proof that it is, in fact, the only method. It is an open problem to determine whether the discrete log assumption is equivalent to the

inequality can be used to derive homomorphism inequalities. A major open problem relating homomorphism densities is Sidorenko's conjecture, which states

fields) have a finite mass-gap with regard to the vacuum state. Another open problem, connected with this conjecture, is a proof of the confinement property

of PNE; a complete characterization of such networks is posed as an open problem. Mlichtaich analyzes the effect of network topology on the efficiency

with a specified Hamiltonian cycle as its cycle of sides, remains an open problem. Carpenter's rule problem, on continuous motion of a simple polygon into

to the hidden subgroup problem for the dihedral group. It is a major open problem to understand how well quantum algorithms can perform for this task,

geometry Topological vector spaces Collision detection Conjectured by Hermann Minkowski Open problem No Generalizations Hahn–Banach separation theorem

the field of transcendental number theory, which remains an important open problem to this day. Schanuel was a professor emeritus of mathematics at University

instance, 24 is friendly, with its smallest friend 91,963,648. It is an open problem whether there are infinitely large clubs of mutually friendly numbers

y − 1 = 0 {\displaystyle xy-1=0} and x > 0 {\displaystyle x>0} . One open problem in real algebraic geometry is the following part of Hilbert's sixteenth

= 2 , 3 {\displaystyle m=2,3} and 4 {\displaystyle 4} , and it is an open problem to find a general combinatorial interpretation. Sergey Fomin and Nathan

important topic is the study of slice knots and ribbon knots. A notorious open problem asks whether every slice knot is also ribbon. Since a knot can be considered

condition holds for everyday quantum fields. Extending these results is an open problem. The strong energy condition is obeyed by all normal/Newtonian matter

possible extensions of a given number field is a difficult and partially open problem. Abelian extensions—that is, extensions L of K such that the Galois group

bipartite cubic polyhedral graph is Hamiltonian. Barnette's conjecture, the Open Problem Garden, retrieved 2009-10-12. Holton, D. A.; McKay, B. D. (1988), "The

conclusions. When and by whom the vandalism was done nevertheless remains an open problem. Greece portal Christianity portal Conversion of non-Islamic places of

\pi (x)=y} . PPP contains PPAD as a subclass (strict containment is an open problem). This is because End-of-the-Line, which defines PPAD, admits a straightforward

ED-12( ) and RTCA DO-178( ) AC 00-71 Best Practices for Management of Open Problem Reports (OPRs) AC 00-72 Best Practices for Airborne Electronic Hardware

unimpressed by the young actuary, but Wilder went on to solve a difficult open problem that Moore had posed to his class. Moore suggested Wilder write up the

of the disphenoid tetrahedral honeycomb. The complete list remains an open problem. If one relaxes the requirement that the tetrahedra be all the same shape

between this bound and 3 {\displaystyle {\sqrt {3}}} , it has been an open problem whether smooth embeddings, without self-intersection, exist. In 2023

about Fermat numbers for large n. In fact, each of the following is an open problem: Is Fn composite for all n > 4? Are there infinitely many Fermat primes

polynomially proportional to the number of steps. This was a long-standing open problem, due to size explosion, the existence of lambda terms which grow exponentially

construction of moduli spaces of Calabi-Yau varieties is an important open problem, and only special cases such as moduli spaces of K3 surfaces or Abelian

permanents of positive-semidefinite matrices related to the corresponding open problem in computer science) by combining tools proper to quantum optics and

a general rigidly foldable solution exists based on sink folds is an open problem.[citation needed] In 1998, I. Yaschenko constructed a 3D folding with

near-quadratic bound on the number of discrete changes is an important open problem. The Delaunay triangulation seems like a natural candidate, but a tight

sound type system for ML-style polymorphic references, an important open problem at the time. Moreover, he formalized a variant of the module system of

99% of atoms to reach BEC. Achieving continuous BEC has been a major open problem of experimental BEC research, driven by the same motivations as continuous

equivalent, but whether the partition principle implies AC is the oldest open problem in set theory, and the equivalences of the other statements are similarly

the theory of equidistribution he solved (with Harald Niederreiter) an open problem of Donald Knuth's book The Art of Computer Programming, by showing that

existence of gravity waves of maximum height on deep water, a previously open problem in mathematical hydrodynamics which dated back to the 19th century. He

one, or possibly two extra electrons. To prove this rigorously is an open problem. A similar question can be asked concerning molecules. Lieb proved a

conjecture was the proof of existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the Navier–Stokes equations

taking into account the collection of multiple message digests is an open problem. Selection of larger element sizes and stronger hash functions, such

as real reductive Lie groups (discussed below), remains an important open problem in representation theory. It has been solved for many particular groups

second law of entanglement manipulation has been identified as a major open problem in quantum information science. Quantum teleportation Unextendible product

formal unconditional location verification via quantum effects remains an open problem. The study of position-based quantum cryptography also has connections

analyst himself projects such content onto his patient; then he has an own open problem and has to go to his own analyst if he is not yet able to help himself

the infinite (separable) factor of type I. For many years it was an open problem to find a type II factor whose fundamental group was not the group of

"On a spatial analogue of Kuratowski's theorem on planar graphs — An open problem", in Horowiecki, M.; Kennedy, J. W.; Sysło, M. M. (eds.), Graph Theory:

a Lambek grammar is context-free, is much more difficult. It was an open problem for nearly thirty years, from the early 1960s until about 1991 when it

(n)} -state 2DFA? More unsolved problems in computer science It is an open problem whether every 2NFA can be converted to a 2DFA with only a polynomial

brief chronicle of the Levi (Hartog's inverse) problem, coherence and open problem". Notices of the International Congress of Chinese Mathematicians. 7

EXPSPACE-hard, although decidability itself has had the status of a longstanding open problem. In 2015, a proof of decidability was published in the journal Theoretical

calculated, the derivation of the moment generating function remains an open problem. Despite the simple formula for the probability density function, numerical

O notation). Bounding the final error term more precisely remains an open problem, known as Dirichlet's divisor problem. Several common games or recreations

the existence of infinitely many twin primes, a basic and notorious open problem. As proved by Schinzel and Sierpiński it is equivalent to the following:

turned out to be negative for n ≥ 5. More generally, it was a major open problem whether braid groups were linear. In 1990, Ruth Lawrence described a

type-checking straightforward. Joe Wells (1994) settled an "embarrassing open problem" by proving that type checking is undecidable for a Curry-style variant

differential geometry are often used. The classification of TPMS is an open problem. TPMS often come in families that can be continuously deformed into each

bounded below by logφ n, but whether this is also the upper bound is an open problem. The s-value (or rank) of a node is the distance from that node to the

(matroids that can be partitioned into disjoint circuits). It is an open problem whether the family of algebraic matroids is self-dual. If V is a vector

p + 2 {\displaystyle p+2} stages. In general, however, it remains an open problem what the precise minimum number of stages s {\displaystyle s} is for

Open problem on 3x+1 and x/2 functions

The incorporation of these corrections in the K-theory framework is an open problem. For more on this problem, click here. Kalb–Ramond field Ramond, P. (1971-05-15)

of the positive mass theorem in higher dimensions was left as a major open problem in Schoen and Yau's 1979 work. In 1988, they settled the problem in arbitrary

original work of Marcus, Spielman and Srivastava to r-lifts. It is still an open problem whether there are infinitely many d {\displaystyle d} -regular (non-bipartite)

of order N = 12 is still open.[citation needed] Another longstanding open problem is whether there exist finite projective planes of prime order which

and it is optimal if it simulates all other proof systems. It is an open problem whether such proof systems exist: Problem (Optimality) Does there exist

equivalence relation. While this is still an open problem, some partial results are known. Another open problem in the area is whether a countable increasing

conjecture for divisors (algebraic cycles of codimension 1) is a major open problem. For example, let f : X → C be a morphism from a smooth projective surface

the truth or falsehood of this bound for this particular case was an open problem, called "Noether's gap". It was finally solved independently by Fleischmann

falling below their advertised security ratings for some keys remains an open problem and is computationally infeasible. They believe that these probabilities

discrete values and it is associated to the electron magnetic moment. One open problem in solid-state physics before the arrival of quantum mechanics was to

indices of the chosen block. The case of ω × ω × ω Chomp is a notable open problem; a $100 reward has been offered for finding a winning first move. More

strong irrationality condition (a Diophantine condition), thus solving an open problem since Fatou conjectured his theorem on the Classification of Fatou components

(deterministic) polynomial algorithms for graph isomorphism is still an open problem in computational complexity theory, in 1977 László Babai reported that

"Rosetta stone" for connecting disparate fields of mathematics. It is an open problem to determine the exact growth rate of rk(N). The best known general bounds

discovery of an extremal unimodular lattice in 72 dimensions settled a long open problem. 1995 – Friedrich Wilhelm Prize 2002 – Merckle Research Prize 2003 –

that takes into account the complexity of human societies remains an open problem. Researchers currently have very little ability to identify internal

Bowers Uniform polytope ACW (May 24, 2012), "Convex uniform 5-polytopes", Open Problem Garden, archived from the original on October 5, 2016, retrieved 2016-10-04

strong irrationality condition (a Diophantine condition), thus solving an open problem since Fatou conjectured his theorem on the Classification of Fatou components

perform mutable operations. How to make this interaction smooth remains an open problem. In some cases, it is possible to have principled partial solutions.

dimensions higher than 2 is an open problem. Efficient kinetic convex hull in dimensions higher than 2 is also an open problem. Kinetic diameter Kinetic minimum

trees (the Harary-Schwenk-Scott conjecture from 1972) was a longstanding open problem until 2017, when a non-reconstructible tree of maximum degree 3 was found

human mobility whilst remaining mathematically tractable remains an open problem due to the large range of factors that influence it. Some typical models

This is one of the Clay Institute Millennium problems and it remains an open problem. Such states for Yang–Mills theory should be physical states, named glueballs

implementation of the former in a strongly-normalizing language as an open problem. In combination with an existing language implementation, meta-circular

1016/0012-365X(71)90027-6, MR 0291010 Weisstein, Eric W., "Barnette's Conjecture", MathWorld Barnette's Conjecture in the Open Problem Garden, Robert Samal, 2007.

call options on an asset with stochastic volatility is considered an open problem in financial economics.[citation needed] Home bias in trade puzzle: The

Thus, a Mersenne prime cannot also be a Wieferich prime. A notable open problem is to determine whether or not all Mersenne numbers of prime index are

positions is difficult (for a general parallel manipulator, this is an open problem). This implies that the workspaces of the parallel manipulators are,

strings. In 1979, together with Ofer Gabber, Galil solved the previously open problem of constructing a family of expander graphs with an explicit expansion

{\displaystyle C_{b}} is normal in base b {\displaystyle b} for any b. It is an open problem whether C k {\displaystyle C_{k}} is normal in bases b ≠ k {\displaystyle

group Out(Fn) satisfies the Tits alternative, settling a long-standing open problem. In a 1997 paper Bestvina and Brady developed a version of discrete Morse

objective function. Many solutions have been proposed, but it is still an open problem. Even the state-of-the-art architecture, BigGAN (2019), could not avoid

Retrieved 15 October 2015. Frankl's union-closed sets conjecture, the Open Problem Garden. http://blog.livedoor.jp/bbgmgt/archives/2935820.html

the complete bipartite graph with equal partite sets. The most famous open problem about list edge-coloring is probably the list coloring conjecture. ch

that the one he had in mind didn't work, and issued the question as an open problem. Together with Miguel Navascués and Stefano Pironio, Antonio Acín had

Kummer–Vandiver conjecture Field Algebraic number theory Conjectured by Ernst Kummer Conjectured in 1849 Open problem Yes

2015 Zuckerman and his student Eshan Chattopadhyay solved an important open problem in the area by giving the first explicit construction of two-source extractors

"Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)". Open Problem Garden. "Revista Pesquisa Fapesp" (PDF). Archived from the original (PDF)

one-way functions. Although the existence of one-way functions is still an open problem, many candidate one-way functions are based on hard problems such as

turned out to be much more difficult, and the question became a famous open problem in formal language theory for over two decades. For years, there was

certain type. Her result is called the Ragsdale conjecture; it was an open problem for 90 years until counterexamples were derived by Oleg Viro (1979) and

computations, number theory, and knot theory. In 1963, he solved an open problem in knot theory by proving that there are non-invertible knots. At the

{\displaystyle X+Y} sorting. Whether a faster algorithm exists is an open problem, posed by Elwyn Berlekamp prior to 1975. A variant of the problem sorts

found gaps in many of them. The Jacobian conjecture is (as of 2016) an open problem, and more incomplete proofs are regularly announced. Hyman Bass, Edwin

their existence implies P ≠ NP, which is widely believed but a famously open problem. The existence of cryptographically secure pseudorandom generators is

necessary and sufficient. Characterizing knot groups in dimension four is an open problem. For the trefoil knot, a Wirtinger presentation can be shown to be π

1112/jlms/s1-21.2.98 Šámal, Robert (11 June 2007), Barnette's conjecture, the Open Problem Garden, retrieved 24 Feb 2011 Ding, Guoli; Marshall, Emily (2018), "Minimal

identities are somewhat more difficult (Kunen 1996). Phillips' problem is an open problem in the theory presented by J. D. Phillips at Loops '03 in Prague. It

dimensions higher than 2 is an open problem. Efficient kinetic convex hull in dimensions higher than 2 is also an open problem. Kinetic width Kinetic minimum

manifolds of non-positive sectional curvature Cartan–Hadamard conjecture, an open problem in Riemannian geometry and geometric measure theory concerning the generalization

it is amenable. Amenable groups are unitarizable; the converse is an open problem. Countable discrete amenable groups obey the Ornstein isomorphism theorem

cryptographic obfuscation and many other applications), solving a long-standing open problem Homomorphic Encryption. Halevi is one of the leading researchers on homomorphic

function j was conjectured by Daniel Bertrand in 1997, and remains an open problem. Writing q = e2πiτ for the square of the nome and j(τ) = J(q), the conjecture

of spinors in supergravity and string theory is a particularly subtle open problem, which was recently addressed in references. It turns out that the standard

manifolds of non-positive sectional curvature Cartan–Hadamard conjecture, an open problem in Riemannian geometry and geometric measure theory concerning the generalization

exact number (and possible syzygies among the various invariants) is an open problem. Curvature invariant, for more about curvature invariants in (semi)-Riemannian

does not disprove the polynomial Hirsch conjecture, which remains an open problem. Ziegler (1994), p. 84. Dantzig (1963), pp. 160 and 168. E.g. see Naddef

"On a spatial analogue of Kuratowski's Theorem on planar graphs – an open problem", in Horowiecki, M.; Kennedy, J. W.; Sysło, M. M. (eds.), Graph Theory:

resolution, although providing a rigorous proof remained an outstanding open problem for much of the 19th century. Even though Cramer had cited Maclaurin

S2CID 16237685 DeVos, Matthew (March 7, 2007), "4-flow conjecture", Open Problem Garden Wikimedia Commons has media related to Snarks (graph theory).

one exception, the spaces with exactly thirty points. This case was an open problem for many years, until it was resolved in 2010 by Betten and Betten. "Jean

\choose B}{N-K \choose K-B} \over {N \choose K}} It is a hard (and often open) problem to calculate the minimum number of tickets one needs to purchase to

over any fixed finite field has complexity n (Kambites, 2007). A major open problem in finite semigroup theory is the decidability of complexity: is there

quantum models, and quantum field theoretical arguments. Although it is an open problem to establish rigorously the renormalization group picture or the conformal

the American Mathematical Society. In 2009, he solved a 55-year-old open problem posed in 1954 by Friedrich Hirzebruch, which asks "which linear combinations

to have too many partially completed orders at any time. This was an open problem until 2007, when an efficient algorithm based on dynamic programming

only in 1980. Envy-free division for four or more partners had been an open problem until the 1990s, when three procedures for general pieces and a procedure

Anurag Anshu and Chinmay Nirkhe) on proving the NLTS conjecture, a famous open problem in quantum information theory. Breuckmann was born in Duisburg and grew

maximum clique, it also implies that W[1] ≠ FPT. It is an important open problem in this area whether this implication can be reversed: does W[1] ≠ FPT

0x12345678) { ... } requires the theorem prover to invert SHA256, which is an open problem. pathcrawler-online.com is a restricted version of the current PathCrawler

much the same as the theory of 4 dimensional smooth manifolds. A major open problem in the theory of smooth 4-manifolds is to classify the simply connected

was added to Painlevé's list by Gambier (1910). It was a controversial open problem for many years to show that these 6 equations really were irreducible

Dean, Nathaniel; Latka, Brenda J. (1995), "Squaring the tournament—an open problem", Proceedings of the Twenty-Sixth Southeastern International Conference

when n = 9, and for 2 matrices when n = 15. In the case n = 2, it is an open problem whether matrix mortality is decidable, but several special cases have

many additional hardness results have been shown. Yet, it is still an open problem to determine whether any faster algorithms exist. Kozen, D. (1977). Lower

University of New York. In 1974, he proposed the Entropy Conjecture, an open problem in dynamical systems, which was proved by Yosef Yomdin for C ∞ {\displaystyle

example, when the 1st edition came out, Fermat's Last Theorem was still an open problem. By the 3rd edition, it has been solved by Andrew Wiles. Other revised

drawing area for completions of the nested triangle graph remains an open problem. Unsolved problem in mathematics What is the minimum bounding box area

the Voronoi cell of the lattice, and discrete Gaussian sampling. An open problem is whether algorithms for solving exact SVP exist running in single exponential

Algorithms, Springer, p. 969, ISBN 9780387307701, Another long-standing open problem is whether there is a polynomial-time algorithm to compute the treewidth

squares: Denne speaks at Jordan Ellenberg's blog Grant Sanderson, This open problem taught me what topology is, 3Blue1Brown, YouTube – a video showing a

C_{5}} , a pentagon. Since the original paper of Shannon (1956) it was an open problem to determine the value of Θ ( C 5 ) {\displaystyle \Theta (C_{5})} .

entropy considerations (rather than only the energy theorem), he solved an open problem in the theory of shock waves in an essay "Sur l'impossibilité des ondes

L(G_{1})\cup L(G_{2})} ⁠ can be constructed S → start(G1) | start(G2) It is an open problem to give a concrete example of a context-free language which cannot be

p-adic setting, and using the p-adic logarithm function, remains an open problem. It is known that proving algebraic independence of linearly independent

is true or false, even in the case of two variables. This is a major open problem in the theory of polynomials. When f : R n → R m {\displaystyle f:\mathbb

{\displaystyle TWA\subsetneq DPA} or these classes are incomparable, which is an open problem P A ⊊ R E G {\displaystyle PA\subsetneq REG} , i.e. tree-walking automata

" Here, he essentially settled in dimensions 5 and higher, the basic open problem regarding these geometric objects, though he did not push his results

conjecture on logarithmic coefficients published in 1983 is still an open problem. I.M. Milin devoted many years of his scientific life for active research

(n)} -state 2DFA? More unsolved problems in computer science It is an open problem whether all 2NFAs can be converted to 2DFAs with polynomially many states

generated for any variety X of dimension n over a number field. It is an open problem whether all Chow groups are finitely generated for every variety over

package by this Perverse sheaf for higher codimension strata is still an open problem. Markus Banagl (M. Banagl, 2010; M. Banagl, et al., 2014) addressed the

physicist Paul A.M. Dirac in 1931. The detection of magnetic monopoles is an open problem in experimental physics. In some theoretical models, magnetic monopoles

something else. The origin of symbolic communication remains a controversial open problem, obscured by the lack of a fossil record. However, it has been speculated

counterexample. The optimal solution of the counterexample is still an open problem. Witsenhausen, Hans. "A counterexample in stochastic optimum control

counterexample. The optimal solution of the counterexample is still an open problem. Witsenhausen, Hans. "A counterexample in stochastic optimum control

brief chronicle of the Levi (Hartog's inverse) problem, coherence and open problem". Notices of the International Congress of Chinese Mathematicians. 7

problem of positron-electron annihilation in the milky-way galaxy, a still-open problem in high-energy astrophysics. His more recent work concerns gamma-ray

}).} The existence of a local data structure for this problem is an open problem. Agarwal, Pankaj; Guibas, Leonidas J.; Hershberger, John; Eric Veach

Özaydin, and later by Volovikov and Sarkaria. It was a long-standing open problem, whether the statement of the topological Tverberg theorem also holds

Open Problem Garden. The 4-flow conjecture, Open Problem Garden. The 5-flow conjecture, Open Problem Garden. Conjectures of François Jaeger, Open Problem

suggested in 1969 by Norman L. Biggs, and its existence noted as an open problem by others before Conway. Conway himself had worked on the problem as

phenomenon with the rising chain was already described in 2011 as an open problem for the 2012 International Young Physicists' Tournament (IYPT) and subsequently

Mark Haiman (2001), by proving the n! conjecture. It is still a central open problem in algebraic combinatorics to find a combinatorial formula for the qt-Kostka

Khachiyan et al. (2008) resolved the complexity of the longstanding open problem of generating all vertices of polyhedra. Boros et al. (2008) uses a network

O(n^{2})} events, developing a more efficient data structure remains an open problem. Agarwal et al. developed a data structure that maintains the MST for

using calibrated trifocal tensors have been studied, but remains an open problem for uncalibrated trifocal tensors. The classical case is 6 point correspondences

equivalence of arrows grouped in different ways. These limitations remain an open problem, and extensions such as Generalized Arrows and N-ary FRP explore these

Kawarabayashi (2009). Lewis & Yannakakis (1980). "Jorgensen's Conjecture", Open Problem Garden, retrieved 2016-11-13. Kawarabayashi et al. (2012). Eppstein (2000);

Sociological Association. Generative model Doreian, Patrick (2006). "Some Open Problem Sets for Generalized Blockmodeling". In Batagelj, Vladimir (ed.). Data

superstring theories too in attempts to create realistic models. One open problem is the completion of the Bargmann–Wigner programme for the isometry group

see [Fine and Smith, 1983] and especially [Simons, 1987]. It is an open problem to adapt them into the OntoClean framework. Being dependent is indicated

noise. A more rigorous theoretical explanation of 1/f noise remains an open problem. When H g {\displaystyle H_{g}} is complex, pseudo-time-reversal symmetry

& Toft (1994), 11.6 Length of Hajós proofs, pp. 184–185, state as an open problem the question of determining the smallest number of steps needed to construct

Tzafriri (1977), p. 95, say that this question was "a long standing open problem going back to Banach's book" (Banach (1932)), but the question does not

Unsolved Problems in Number Theory. Problem Books in Mathematics. Springer New York. ISBN 978-0-387-26677-0. Retrieved 2024-07-20. Open Problem Garden

Journal of Graph Theory, 18 (2): 119–129, doi:10.1002/jgt.3190180203, MR 1258244 Graphs with a forbidden induced tree are chi-bounded, Open Problem Garden

(2014). "Introduction to Ryser's Conjecture" (PDF). "Ryser's conjecture | Open Problem Garden". www.openproblemgarden.org. Retrieved 2020-07-14. Tuza (1983)

traced back to the first principles of Special Relativity. It answers the open problem on how the temperature of a body is transformed in a moving inertial

first used by Peter G. Casazza. This question was not only an important open problem in frame theory but was found to be equivalent to the famous and long-open

time. The faithfulness of the Burau representation when n = 4 is an open problem. The Burau representation appears as a summand of the Jones representation

the graph (i-SSPPR) is a PSPACE-easy but ♯P-hard problem. It was an open problem to bridge this gap, but since then both the directed and undirected versions

is always either a sausage or a cluster, and never a pizza. It is an open problem whether this holds true for all dimensions. This result only concerns

irrationalzehlen". Monatshefte für Mathematik. 71 (3): 263–269. doi:10.1007/BF01298332. S2CID 122754182. Article in the Open Problem Garden no. 4, 551–562.

(1978) Little (1974), Vazirani (1988) Pólya (1913), Reich (1971) See open problem (4) at Shtetl Optimized: Introducing some British people to P vs. NP

"On a spatial analogue of Kuratowski's Theorem on planar graphs – an open problem", in Horowiecki, M.; Kennedy, J. W.; Sysło, M. M. (eds.), Graph Theory:

{\displaystyle \chi } -boundedness", Combinatorica, arXiv:2201.08814, doi:10.1007/s00493-023-00054-3, S2CID 246476859 Chi-bounded, Open Problem Garden

K} that are consistent with P {\displaystyle P} ; Williams solved an open problem by developing a new representation for finite bases that allowed for

related to homomorphisms. For example, Sidorenko's conjecture is a major open problem in extremal graph theory, which asserts that for any graph G {\displaystyle

group Out(Fn) satisfies the Tits alternative, settling a long-standing open problem. In 1984, Handel won a Sloan Research Fellowship. In 2014, he became

nowhere and thus the cycle-following strategy cannot be applied. It is an open problem whether in this case the winning probability tends to zero with growing

already known, by consequence of the Gelfond–Schneider theorem). An open problem in number theory settled by the conjecture is the question of whether

number theory Conjectured by Morris Newman Conjectured in 25 March 1960 Open problem Yes Known cases Prime powers except powers of 2 or powers of 3, plus

triangulation decision problem is NP-complete, since this depends on the known open problem whether the sum of radicals may be computed in polynomial time. However

Dean, Nathaniel; Latka, Brenda J. (1995), "Squaring the tournament—an open problem", Proceedings of the Twenty-Sixth Southeastern International Conference

Stalling's theorem yielded a positive solution to the long-standing open problem about characterizing finitely generated groups of cohomological dimension

There is also a connection to the Hadwiger conjecture, an important open problem in combinatorics concerning the relationship between chromatic number

generators in NC0 (even with sub-linear stretch) was a long-standing open problem until 2006.) It is possible that this construction could be broken with

dimension 1. The picture is less clear in higher dimensions. A central open problem is the Green–Griffiths–Lang conjecture: if X is a complex projective

rationalization). Computing the homotopy groups of spheres is a central open problem in homotopy theory. However, the rational homotopy groups of spheres

rationalization). Computing the homotopy groups of spheres is a central open problem in homotopy theory. However, the rational homotopy groups of spheres

free personnel, and "gifts" from the Casas Fuertes. Corruption was an open problem in the administration as well. Rafael Nsue Nchama was dismissed in 1966

P=NP. tchow (February 19, 2009), "Shannon capacity of the seven-cycle", Open Problem Garden. Alon, Noga; Lubetzky, Eyal (2006), "The Shannon capacity of a

between two trees with a given number of nodes is known, but it remains an open problem whether the rotation distance between two arbitrary trees can be found

and algorithms for approximate sequence matching. He also solved the open problem of computing string edit distance or biological sequence alignments in

coNP, which is generally conjectured to be false, but is still a major open problem in complexity theory. This lack of connections with NP is a major motivation

intermediate growth in a 1984 article. This result answered a long-standing open problem posed by John Milnor in 1968 about the existence of finitely generated

Terence Tao. In his blog post, Tao refers to it as "perhaps, my favorite open problem" and gives a simplified proof of the exponential bound on cap sets, namely

Rationale for Accepting Masking MC/DC in Certification Projects 2001 CAST-7 Open Problem Report (OPR) Management for Certification 2001 CAST-8 Use of the C++

effect of this friction in some cases. He went on to solve a famous open problem concerning the motion of pairs of bodies. There followed a long series

doi:10.1145/2783434. MR 3424197. S2CID 15668961. "Another Annoying Open Problem". 19 November 2011. Lee, James R. (2017). "Fusible HSTs and the Randomized

bases of the rigidity matroid of the complete graph) is an important open problem. Graver, Jack E. (1991), "Rigidity matroids", SIAM Journal on Discrete

several applications, as for instance in the Ambrosio's proof of an open problem posed by Di Perna and Lions concerning the well-posedness of the continuity

integrality gap is a constant Ω(1). Finding the exact integrality gap is an open problem. In the bin covering problem, there are n items with different sizes

number or max leaf number all have bounded treewidth, however it is an open problem to determine the complexity of the metric dimension problem even on graphs

would settle the P versus NP problem, considered the most important open problem in computer science and one of the Millennium Prize Problems. An example

resulting massive spin connection, free of ghosts and tachyons, remains an open problem. Standard-Model Extension Riemann–Cartan geometry Antimatter tests of

deterministic algorithm with a polynomial worst-case complexity is still an open problem. Like distinct-degree factorization algorithm, Rabin's algorithm is based

quantum systems. Proving the quantum analog of the PCP theorem is an open problem. Hamiltonian simulation Density matrix renormalization group Matrix product

algorithm, or whether a non-constant ratio is necessary, remains an open problem. The maximum acyclic subgraph problem has an easy approximation algorithm

touching skew straight lines in 3-dimensional space that solves a known open problem. A model checking algorithm for a rather powerful logic with an operator

commonly used notion of cycle in hypergraph —the tight cycle— it remains an open problem whether the complete k {\displaystyle k} -uniform hypergraph K n ( k

bounds for the complexity of a k {\displaystyle k} -level remains a major open problem in discrete geometry. The best upper bound known is O ( n k 1 / 3 ) {\displaystyle

that, at every step, the edge lengths are rational numbers; it is an open problem whether every planar graph has a drawing with this property. It is possible

geometry and topology attributed to Heinz Hopf. The Hopf conjecture is an open problem in global Riemannian geometry. It goes back to questions of Heinz Hopf

equivalent to 1-consistency. The former was an answer to the long-standing open problem regarding the metamathematical meaning of 1-conservativity. Within the

not result in a word-representable graph, which solved a long-standing open problem. A graph is p-representable if it can be represented by a word avoiding

finite bound on toughness might imply Hamiltonicity remains an important open problem in graph theory. A simpler proof both of Fleischner's theorem, and of

as Michael's Conjecture. This conjecture is perhaps the most famous open problem in the theory of topological algebras. An increasing family means that

unless P=NP. Closing the gap between the 2 and the 3/2 is a long-standing open problem. Verschae and Wiese presented a different 2-factor approximation algorithm

dictionary or from an online resource such as WordNet. Word-sense induction – open problem of natural-language processing, which concerns the automatic identification

case d = 2 {\displaystyle d=2} or m = 2 {\displaystyle m=2} is still an open problem, known as Morrey's conjecture. Under certain growth condition of the

remains open. DeVos, Matthew (October 22, 2007), "Unfriendly partitions", Open problem garden Shelah, Saharon; Milner, E. C. (1990), "Graphs with no unfriendly

elements can be represented as V(R) for R von Neumann regular is an open problem. Dobbertin, Hans (1983), "Refinement monoids, Vaught monoids, and Boolean

tolerant control systems provides a positive answer to a previously open problem. By a constructive proof it is established that under mild conditions

general domains, the asymptotic expansion of the escape time remains an open problem. So does the problem of computing the escape time near a cusp point in

343 of the English translation). The necessity of the condition was an open problem until 1993, when it was proved by Kilpeläinen & Malý (1994). (Maz'ya

top-down vs. bottom-up controversy, which has been addressed as a major open problem of attention, a computational model has succeeded in illustrating the

path of size at least cn, where c > 0 is a constant, is a long-standing open problem. It is only known that every complete geometric graph on n vertices contains

30..187A, doi:10.1070/SM1976v030n02ABEH002267, MR 0460162 Weisstein, Eric W., "Earth-Moon Problem", MathWorld "Earth-Moon Problem", Open Problem Garden

subdivision. The complexity of barrier resilience for unit disk barriers is an open problem. It may be solved by a fixed-parameter tractable algorithm whose time

wave family is selected. For most mathematical systems this remains an open problem. It is common that for some parameter values, the periodic travelling

Seymour. "Perceptrons." (1969). "Time vs. memory for best matching - an open problem" p. 222–225 Uma Ramamurthy; Sidney K. D'Mello; Stan Franklin. "Realizing

designed to support verification analysis of its networks which had been an open problem of DEVS formalism for 30 years. In addition, it was also designated to

time algorithm for solving any linear program (the latter is a famous open problem). Megiddo's algorithms can be executed using a tableau, just like the

In the late 1980s, Dahleh solved the L1 optimal control problem — an open problem at the time that addresses robustness in the presence of persistent disturbances

difficult and expensive. The connection to the electricity grid is still an open problem, a suitable solution to deliver the generated electrical energy needs

existence of a common refinement of two triangulations. This was an open problem, for manifolds, to 1961. 1910 L. E. J. Brouwer Brouwer's theorem on invariance

maintaining the convex hull of moving points in dimensions higher than 2 is an open problem. Kinetic convex hull can be used to solve the following related problems:

to effectively decide whether a vector is entropic or not) remains an open problem. Analogous questions for von Neumann entropy in quantum information theory

⁠18/11⁠n (approximately 1.07n and 1.64n,) but the exact value remains an open problem. In 1979, Bill Gates and Christos Papadimitriou gave an upper bound of

atomic commitment and consensus, for which he helped close the then open problem of the weakest failure detector for consensus with any number of faults

the algorithm can be made deterministic.: Sec.5  They mention as an open problem, whether there is a deterministic polytime (1-1/e)-approximation algorithm

foundational work. This work was the first to satisfactorily address the then open problem on robust stability and performance problems for constant real parameter

graphs of finite 3- or 4-dimensional point sets are connected is an open problem. The maximum number of flips required to transform a triangulation into

elliptic curves which led to their famous conjecture. It is in general an open problem whether the rank of all elliptic curves over a fixed field K is bounded

of forbidden minors for the existence of planar emulators remains an open problem. Hliněný (2010), p. 1 Hliněný (2010), Proposition 1, p. 2 Hliněný (2010)

Bodlaender's paper, the computational complexity was left as "an interesting open problem". Only in 2020 it was proved that the game is PSPACE-Complete. Acyclic

Romanian Nation", lest the Legionaries "find another solution to the open problem". In his later memoirs, Horia Sima noted that these manifestos received

Danner's history as a stamp collector to try to lure him out in the open. Problem is, one of Danner's men, Shockley (David Cass), knows who Hutch is,

predicts there are infinitely many of these. Field Number theory Conjectured by G. H. Hardy John Edensor Littlewood Conjectured in 1923 Open problem yes

generalising the computation of Godement (1957) for SL(2,R), was left as an open problem by Flensted-Jensen (1978). An explicit product formula for b(λ) was known

-flattenable graphs, for dimension d > 3 {\displaystyle d>3} , is an open problem. For any dimension d {\displaystyle d} , K d + 2 {\displaystyle K_{d+2}}

spherical fusion categories of a given rank. This is related to the other open problem of determining whether or not it is true that every fusion category admits

instead of twelve membranes. If this is an optimal construction remains an open problem. Theorem. E M 9 ( e n d o , e x o , f e n d o , f e x o ) = R E {\displaystyle

Some of her publications focused on these which include The woman, an open problem (1974), Matriarchy and the power of women (1978), The female of man (1982)

studying phylogenetic networks. The technique yields a solution to an open problem regarding tree containment, the exact and asymptotic counting of the

Kaplan was part of the team that solved the einstein problem, a major open problem in tiling theory and Euclidean geometry. The problem is to find an "aperiodic

computing Betti numbers, using a simplex tree most efficiently remains an open problem, however, current algorithms for this task on sparse simplicial complexes

nets refers to the number of common nets for the same set of polyhedra. Open problem 25.31 in Geometric Folding Algorithm by Rourke and Demaine reads: "Can

known as friendship graphs). Kotzig's conjecture was first listed as an open problem by Bondy & Murty in 1976, attributed to Kotzig and dated to 1974. Kotzig's

work on proving the no low-energy trivial state conjecture, a famous open problem in quantum information theory." 2024 Frank Schindler, "For numerous conceptual

partition (and is also related to solving energy games) It is a major open problem in computer science whether there exists a polynomial time algorithm

numbers, for general values of k {\displaystyle k} , was stated as an open problem by Alan J. Hoffman in 1967. As with any variety of algebras, the central

( log ⁡ n ) {\displaystyle \Omega (\log n)} . Indeed, it has been an open problem since 1981 to close the gap between the O ( log 2 ⁡ n ) {\displaystyle

depends on the interpretation of quantum mechanics, which is still an open problem in physics. Some authors reach different conclusions for this effect

not fit the data. He leaves finding a better-fitting function as an open problem. A multi-attribute utility (MAU) function maps a bundle with two or more

existence of an EJR rule that satisfies House monotonicity, which is another open problem). Stronger variants of these properties, where groups of voters may have