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In science and mathematics, not yet solved problem
In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective
Open_problem
List of links to unsolved problems in mathematics, prizes and research Open Problem Garden AIM Problem Lists Unsolved Problem of the Week Archive. MathPro
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
number of important questions remain open in the area of physics beyond the Standard Model, such as the strong CP problem, determining the absolute mass of
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
articles contain lists of problems. This includes unsolved problems, which may refer to several notable conjectures or open problems in various academic fields:
Lists_of_problems
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More
P_versus_NP_problem
23 mathematical problems stated in 1900
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several
Hilbert's_problems
Book published in 2016
Open Problems in Mathematics is a book, edited by John Forbes Nash Jr. and Michael Th. Rassias, published in 2016 by Springer (ISBN 978-3-319-32160-8)
Open_Problems_in_Mathematics
List of unsolved computational problems
NP? NC = P problem NP = co-NP problem P = BPP problem P = PSPACE problem L = NL problem PH = PSPACE problem L = P problem L = RL problem Unique games
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Class in computational complexity theory
Unsolved problem in computer science N C = ? P {\displaystyle {\mathsf {NC}}{\overset {?}{=}}{\mathsf {P}}} More unsolved problems in computer science
NC_(complexity)
Philosophical concept
In the philosophy of mind, the hard problem of consciousness (or simply the hard problem) is to explain how and why organisms have qualia, phenomenal consciousness
Hard_problem_of_consciousness
Conformance of AI to intended objectives
median voters, which increases political legitimacy. AI alignment is an open problem for modern AI systems and is a research field within AI. Aligning AI
AI_alignment
Unsolved geometry question on moving a sofa through a 90° angle
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
Moving_sofa_problem
Seven mathematical problems with a US$1 million prize for each solution
to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch
Millennium_Prize_Problems
Mathematics problem
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own
100_prisoners_problem
Problem of determining if a Boolean formula could be made true
NP problem - one of the most important open problems in the theory of computing. Nevertheless, heuristic SAT-algorithms are able to solve problem instances
Boolean satisfiability problem
Boolean_satisfiability_problem
Probability puzzle
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal
Monty_Hall_problem
Open problem on 3x+1 and x/2 functions
mathematics". However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results. Consider
Collatz_conjecture
Unanswered question in the study of consciousness
binding problem is the problem of how objects, background, and abstract or emotional features are combined into a single experience. The binding problem refers
Binding_problem
Russian mathematician (born 1966)
proved the soul conjecture in Riemannian geometry, which had been an open problem for the previous 20 years. In 2002 and 2003, he developed new techniques
Grigori_Perelman
Complexity class
theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete
NP-completeness
Problem in discrete geometry
3 points are collinear and no 4 points are cocircular, then it is an open problem. Currently the best result is g gen ( n ) ≥ Ω ( n ) {\displaystyle
Erdős distinct distances problem
Erdős_distinct_distances_problem
Conceptual issue in the philosophy of mind
actions. The problem divides into several distinct sub-problems, including the problem of causal exclusion, the problem of anomalism, and the problem of externalism
Problem_of_mental_causation
Physics problem related to laws of motion and gravity
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses
Three-body_problem
This page lists notable open problems related to fair division - a field in the intersection of mathematics, computer science, political science and economics
List of unsolved problems in fair division
List_of_unsolved_problems_in_fair_division
Unsolved problem about inscribing a square in a Jordan curve
Unsolved problem in mathematics Does every Jordan curve have an inscribed square? More unsolved problems in mathematics The inscribed square problem, also
Inscribed_square_problem
Mathematical problem involving optimal stopping theory
known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also
Secretary_problem
Unsolved mathematical problem
The mean value problem is an open problem in the mathematical field of complex analysis first posed by Stephen Smale in 1981. The problem asks: For a given
Mean_value_problem
American mathematician and Nobel Laureate (1928–2015)
resolved Hilbert's nineteenth problem on regularity in the calculus of variations, which had been a well-known open problem for almost 60 years. In 1959
John_Forbes_Nash_Jr.
Unsolved problem in mathematics Which finite groups are BI-groups? More unsolved problems in mathematics Babai's problem is a problem in algebraic graph
Babai's_problem
Problem in theoretical computer science
accepts one of the two strings and rejects the other string. It is an open problem how large such an automaton must be, in the worst case, as a function
Separating_words_problem
Mathematical problem in operations research
In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal
Cutting_stock_problem
Mathematical term in group theory
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
Grigorchuk_group
McMullen problem is an open problem in discrete geometry named after Peter McMullen. In 1972, David G. Larman wrote about the following problem: Determine
McMullen_problem
Hungarian mathematician (1913–1996)
necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. He taught
Paul_Erdős
Points with no three in a line
intriguing open problems in additive combinatorics and Ramsey theory for over 20 years, highlighted, for instance, by blog posts on this problem from Fields
Cap_set
Inherent difficulty of computational problems
computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task
Computational complexity theory
Computational_complexity_theory
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
Hermite's problem is an open problem in mathematics posed by Charles Hermite in 1848. He asked for a way of expressing real numbers as sequences of natural
Hermite's_problem
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
List_of_conjectures
in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of
List of unsolved problems in statistics
List_of_unsolved_problems_in_statistics
Problem in computer science
for the same problem. In its general form, it is equivalent to the hidden subgroup problem for the dihedral group. It is a major open problem to understand
Hidden_shift_problem
case n = 2, it is an open problem whether matrix mortality is decidable, but several special cases have been solved: the problem is decidable for sets
Matrix_mortality_problem
Problem caused by profanity filters on the Internet
The Scunthorpe problem is the unintentional blocking of online content by a spam filter, search engine or wordfilter because the text contains a string
Scunthorpe_problem
Conjecture in knot theory relating quantum invariants and hyperbolic geometry
branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry of
Volume_conjecture
Optimization problem in computer science
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
Lattice_problem
Proposition in mathematics that is unproven
considered by many to be the most important open problem in the field. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute
Conjecture
Planar maps require at most four colors
Hedetniemi, Stephen T. (eds.), Graph Theory: Favorite Conjectures and Open Problems, II, Problem Books in Mathematics, Springer International Publishing, pp. 115–133
Four_color_theorem
Area of discrete mathematics
theorem. Relatedly, Earth–Moon problem is known for the nowadays open problem on extension of the planar map coloring problem, solved by the four-color theorem
Graph_theory
Unsolved problem in mathematics
Maass forms, the conjecture's counterpart for Maass forms is still an open problem, as the Deligne method which solves the holomorphic case does not work
Ramanujan–Petersson conjecture
Ramanujan–Petersson_conjecture
Unsolved problem in graph theory
More unsolved problems in mathematics In mathematics, the Oberwolfach problem is an open problem that may be formulated either as a problem of scheduling
Oberwolfach_problem
Informal fallacy
the proposition can be called unproven, undecided, inconclusive, an open problem or a conjecture. The term was likely coined by philosopher John Locke
Argument_from_ignorance
On dissections between polyhedra
The third of Hilbert's problems presented in 1900 was the first to be solved. The problem asks the following: Given any two polyhedra of equal volume,
Hilbert's_third_problem
Even integers as sums of two primes
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural
Goldbach's_conjecture
expansion problem asks whether a greedy algorithm for finding Egyptian fractions with odd denominators always succeeds. It is an open problem. An Egyptian
Odd_greedy_expansion
Rewriting system and type of formal grammar
rules, setting a new benchmark in L-system inference. There are many open problems involving studies of L-systems. For example: Characterisation of all
L-system
Topics referred to by the same term
equation for which a solution is sought Unknown, the ongoing answer to an open problem Unknown (video game) or Amnesia: The Dark Descent, a 2010 video game
Unknown
open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Many of the problems posed
List of problems in loop theory and quasigroup theory
List_of_problems_in_loop_theory_and_quasigroup_theory
Problem in computer science
In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program
Halting_problem
Recursive integer sequence
= 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
Catalan_number
Problem in number theory
problems in mathematics In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes
Sums_of_three_cubes
Method to solve optimization problems
algorithm? More unsolved problems in computer science There are several open problems in the theory of linear programming, the solution of which would represent
Linear_programming
Problem in computer science
complexity in the Turing machine model is open, as of 1997. The main difficulty is that, in order to solve the problem, the square-roots should be computed
Square-root_sum_problem
Optimization problem
Open-shop scheduling or open-shop scheduling problem (OSSP) is an optimization problem in computer science and operations research. It is a variant of
Open-shop_scheduling
Mathematical problem
problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that
Coin_problem
Unproved conjecture in mathematics
curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
1979 conjecture in combinatorics
family? More unsolved problems in mathematics The union-closed sets conjecture, also known as Frankl’s conjecture, is an open problem in combinatorics posed
Union-closed_sets_conjecture
Standard model in theoretical computer science
interesting open problem in computational complexity theory is the P vs. NP problem. Roughly, this problem is to determine whether a given problem can be solved
Arithmetic_circuit_complexity
Thought experiment
philosophy and mathematics, Newcomb's problem, also known as Newcomb's paradox, is a thought experiment posing a decision problem in which a player must decide
Newcomb's_problem
Algorithm that arranges lists in order
(i.e. taking into account machine-specific details) is still an open research problem, with solutions only known for very small arrays (fewer than 20
Sorting_algorithm
with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Problems posed here
Problems_in_Latin_squares
Unsolved problem in number theory
In mathematics, the Casas-Alvero conjecture is an open problem about polynomials which have factors in common with their derivatives, proposed by Eduardo
Casas-Alvero_conjecture
American sci-fi television series
3 Body Problem is an American science fiction television series created by David Benioff, D. B. Weiss, and Alexander Woo. It is the third adaptation of
3_Body_Problem_(TV_series)
Quantum field theory
Unsolved problem in physics Yang–Mills theory and the mass gap. Quantum particles described by the theory have mass but the classical waves of the field
Yang–Mills_theory
Computer hardware technology that uses quantum mechanics
the dihedral hidden subgroup problem, which would break many lattice-based cryptosystems, is a well-studied open problem. It has been shown that applying
Quantum_computing
Classification of computer problems
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
Geometric_complexity_theory
Concept in theoretical computer science
used to systematically solve many open problems in mathematics. However, current results on the busy beaver problem suggest that this will not be practical
Busy_beaver
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
Hyperfinite equivalence relation
Hyperfinite_equivalence_relation
Topics referred to by the same term
Open question may refer to: Open-ended question, a question that cannot be answered with a "yes" or "no" response Open problem, or open question, a known
Open_question
Concept in commutative algebra
but the positive characteristic case is (as of 2024) still a major open problem. Essentially all Noetherian rings that occur naturally in algebraic geometry
Excellent_ring
non-profit research organization Epoch AI in November 2024. The first such open problem—of the "moderately interesting" rank—to be solved was in hypergraph theory:
FrontierMath
American artificial intelligence company
2025. Castelvecchi, Davide (July 24, 2025). "DeepMind and OpenAI models solve maths problems at level of top students". Nature. 644 (8075): 20. Bibcode:2025Natur
OpenAI
Algebraic structure
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
Moufang_loop
Fairness notion in fair item allocation
exist is widely regarded as the central open problem in the theory of fair item allocation. Unsolved problem in computer science Does there exist an envy-free
Envy-freeness_up_to_any_item
Mathematicians in 1966 (Moscow) The Kolchin Catenary Conjecture is a fundamental open problem in differential algebra related to dimension theory. "Let Σ {\displaystyle
Kolchin's_problems
and output, but whether they can be solved in polynomial time is an open problem. A Boolean function takes as input an assignment of truth values to its
Monotone_dualization
Issue in artificial intelligence and categorical algebra
frame) remains unchanged. The frame problem occurs even in very simple domains. A scenario with a door, which can be open or closed, and a light, which can
Frame_problem
Dynamical system involving reflection
triangular table. It is a special case of dynamical billiards. A major open problem in this area concerns the existence of periodic billiards paths: does
Triangular_billiards
is a list of notable unsolved problems in astronomy. Problems may be theoretical or experimental. Theoretical problems result from inability of current
List of unsolved problems in astronomy
List_of_unsolved_problems_in_astronomy
Fifteen problems in mathematical physic
mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain
Simon_problems
Geometric problems involving the partition of a figure
circle-squaring problem, the pieces are typically required to be well-behaved. For instance, they may be restricted to being the closures of disjoint open sets.
Dissection_problem
On minimizing crossings in bicliques
Closing the gap between this lower bound and the upper bound remains an open problem. If edges are required to be drawn as straight line segments, rather
Turán's_brick_factory_problem
Problem that is difficult or impossible to solve
In planning and policy, a wicked problem is a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements
Wicked_problem
Physical phenomenon
an open problem for the 2012 International Young Physicists' Tournament (IYPT). In 2013, science presenter Steve Mould brought the chain problem to widespread
Chain_fountain
Class of problems
(PTAS) for the problem. By providing a provably polynomial-time ε-approximation algorithm, they resolved a long-standing open problem in optimal control
Kinodynamic_planning
Complexity class
hashing. 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
PPP_(complexity)
Number that is not a ratio of integers
most famous open problems in number theory" (PDF). Waldschmidt, Michel (2022). "Transcendental Number Theory: recent results and open problems". Michel Waldschmidt
Irrational_number
Class of mathematical games
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
Graph_coloring_game
On existence of a strongly regular graph
Biggs, and its existence noted as an open problem by others before Conway. Conway himself had worked on the problem as early as 1975, but offered the prize
Conway's_99-graph_problem
Mathematical problem set on a chessboard
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution
Eight_queens_puzzle
Unique extension of pure states in Hilbert spaces
Richard Kadison and Isadore Singer. The problem was subsequently shown to be equivalent to numerous open problems in pure mathematics, applied mathematics
Kadison–Singer_problem
OPEN PROBLEM
OPEN PROBLEM
Boy/Male
English French
Open.
Boy/Male
English French
Open.
Boy/Male
American, British, English, French
Open; Variant of Darrel Open
Male
Swedish
Norwegian and Swedish form of Old Norse Óðinn, ODEN means "poetry, song" and "eager, frenzied, raging."
Boy/Male
English French
Open.
Boy/Male
Hindu, Indian
Open
Female
English
English short form of Latin Penelope, PEN means "weaver of cunning."
Male
Welsh
Variant form of Welsh Owen, possibly OUEN means "born of yew."
Boy/Male
English French
Open.
Boy/Male
Welsh
Son of Owen.
Boy/Male
French
Open.
Boy/Male
English
Open.
Female
Thai/Siamese
Thai name PEN-CHAN means "full moon."
Surname or Lastname
English
English : variant of Penn.Dutch : metonymic occupational name for a clerk or penman, from Dutch pen ‘pen’.Cambodian : unexplained.
Male
English
 Anglicized form of Irish Gaelic Eóghan, OWEN means "born of yew." Compare with another form of Owen.
Boy/Male
English French American
Open.
Male
Welsh
 Modern Welsh form of Old Welsh Owain, OWEN means "born of yew." Compare with another form of Owen.
Boy/Male
English French
Open.
Boy/Male
English French
Open.
Boy/Male
Celtic Welsh
Son of Owen.
OPEN PROBLEM
OPEN PROBLEM
Boy/Male
Tamil
Ramabhakta | ரமாஂபாகதாÂ
Devoted to Rama, Lord Hanuman
Surname or Lastname
English
English : variant spelling of Vise.
Surname or Lastname
English
English : habitational name from Arrow in Warwickshire or Arrowe in Cheshire. The first takes its name from the Arrow river, a Celtic or pre-Celtic term meaning ‘stream’; the second, recorded c. 1245 as Arwe, is from Old Norse erg ‘shieling’.Perhaps in some cases a translation of French La Flèche (‘the arrow’).
Surname or Lastname
German
German : reduced form of Widmer.German : occupational name from Middle High German wimmer ‘wine maker’.German : nickname from Middle High German wim(m)er ‘knotty growth on a tree trunk’.German : variant of Weimer 2.English : from the Old English personal name Winemǣr, a compound of wine ‘friend’ + mǣr ‘famous’.
Boy/Male
Shakespearean
Love's Labours Lost' A clown.
Girl/Female
Irish
meaning light; most beautiful woman.
Boy/Male
American, Australian, British, Celtic, Chinese, English
Hilltop; Variant of Brent
Boy/Male
Hindu
Sorrow less, Free of sorrow
Girl/Female
Indian, Sanskrit
Sacred God
Boy/Male
Tamil
Thought, Devotion, Another name of the Sun, Lord Shiva
OPEN PROBLEM
OPEN PROBLEM
OPEN PROBLEM
OPEN PROBLEM
OPEN PROBLEM
a.
Not concealed or secret; not hidden or disguised; exposed to view or to knowledge; revealed; apparent; as, open schemes or plans; open shame or guilt.
a.
Open.
v. t.
To enter upon; to begin; as, to open a discussion; to open fire upon an enemy; to open trade, or correspondence; to open a case in court, or a meeting.
a.
Free of access; not shut up; not closed; affording unobstructed ingress or egress; not impeding or preventing passage; not locked up or covered over; -- applied to passageways; as, an open door, window, road, etc.; also, to inclosed structures or objects; as, open houses, boxes, baskets, bottles, etc.; also, to means of communication or approach by water or land; as, an open harbor or roadstead.
v. t.
To loosen or make less compact; as, to open matted cotton by separating the fibers.
a.
Not drawn together, closed, or contracted; extended; expanded; as, an open hand; open arms; an open flower; an open prospect.
n.
Open or unobstructed space; clear land, without trees or obstructions; open ocean; open water.
a.
Produced by an open string; as, an open tone.
v. t.
To make or set open; to render free of access; to unclose; to unbar; to unlock; to remove any fastening or covering from; as, to open a door; to open a box; to open a room; to open a letter.
a.
Free; disengaged; unappropriated; as, to keep a day open for any purpose; to be open for an engagement.
a.
Having the mouth open; gaping; hence, greedy; clamorous.
a.
Not settled or adjusted; not decided or determined; not closed or withdrawn from consideration; as, an open account; an open question; to keep an offer or opportunity open.
a.
Taking place in the open air; outdoor; as, an open-air game or meeting.
a.
Free or cleared of obstruction to progress or to view; accessible; as, an open tract; the open sea.
a.
Free to be used, enjoyed, visited, or the like; not private; public; unrestricted in use; as, an open library, museum, court, or other assembly; liable to the approach, trespass, or attack of any one; unprotected; exposed.
a.
Uttered with a relatively wide opening of the articulating organs; -- said of vowels; as, the an far is open as compared with the a in say.
a.
Not of a quality to prevent communication, as by closing water ways, blocking roads, etc.; hence, not frosty or inclement; mild; -- used of the weather or the climate; as, an open season; an open winter.
v. t. & i.
To open.
a.
With eyes widely open; watchful; vigilant.
v. t.
To spread; to expand; as, to open the hand.