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Description of an issue
problem statement is a description of an issue to be addressed, or a condition to be improved upon. It identifies the gap between the current problem
Problem_statement
Seven mathematical problems with a US$1 million prize for each solution
satisfiability problem. Most mathematicians and computer scientists expect that P ≠ NP; however, it remains unproven. The official statement of the problem was given
Millennium_Prize_Problems
2026 scientific priority controversy
problem with a smooth external force. However, approximately 12 hours before OpenAI's announcement, mathematician Tristan Buckmaster made a statement
Navier–Stokes priority controversy
Navier–Stokes_priority_controversy
Problem used to illustrate synchronization issues and techniques for resolving them
In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues
Dining_philosophers_problem
Classic problem in graph theory
mainland portions of the city—Altstadt and Vorstadt—by seven bridges. The problem was to devise a walk through the city that would cross each of those bridges
Seven_Bridges_of_Königsberg
Philosophical thought experiment about utility
In philosophy, Pascal's mugging is a thought experiment demonstrating a problem in expected utility maximization. A rational agent should choose actions
Pascal's_mugging
Mathematical method for optimizing material layout under given conditions
(\rho ),\rho )\leq 0{\text{ with }}j=1,...,m.\end{aligned}}} The problem statement includes the following: An objective function F ( u ( ρ ) , ρ ) {\displaystyle
Topology_optimization
Paradox in probability theory
different assumptions can lead to different outcomes (because the problem statement was not well enough defined to allow a single straightforward interpretation
Boy_or_girl_paradox
value modulo a sufficiently large integer. In the rational reconstruction problem, one is given as input a value n ≡ r / s ( mod m ) {\displaystyle n\equiv
Rational reconstruction (mathematics)
Rational_reconstruction_(mathematics)
Combinatorial optimization problem
distances multiplied by the corresponding flows. The problem statement resembles that of the assignment problem, except that the cost function is expressed in
Quadratic_assignment_problem
Problem in computer science
mathematically definable but not computable. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually
Halting_problem
Yes-or-no question that cannot ever be solved by a computer
consequence of the undecidability of the halting problem. This weaker form differs from the standard statement of the incompleteness theorem by asserting that
Undecidable_problem
Very general problem in computer science
hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. It is a generalization of problems including factoring
Hidden_subgroup_problem
Philosophical problem articulated by David Hume
The is–ought problem is the question of whether moral statements about what ought to be can be inferred from objective statements about what is. It was
Is–ought_problem
Deterministic quantum algorithm
computer. Simon's problem is an example of a problem that yields an oracle separation between BQP and BPP. In the Deutsch–Jozsa problem, we are given a
Deutsch–Jozsa_algorithm
Mathematical algorithm
+ by = gcd(a, b). The problem that can supposedly be solved by the Kuṭṭaka method was not formulated by Aryabhaṭa as a problem of solving the linear Diophantine
Kuṭṭaka
Mathematical problem in number theory
Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with
Archimedes's_cattle_problem
Optimization algorithm
real-valued function. The Frank–Wolfe algorithm solves the optimization problem Minimize f ( x ) {\displaystyle f(\mathbf {x} )} subject to x ∈ D {\displaystyle
Frank–Wolfe_algorithm
Quantum algorithm
The Bernstein–Vazirani algorithm, which solves the Bernstein–Vazirani problem, is a quantum algorithm invented by Ethan Bernstein and Umesh Vazirani in
Bernstein–Vazirani_algorithm
Unsolved problem in extremal graph theory
subgraphs of a given size? More unsolved problems in mathematics The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible
Zarankiewicz_problem
project charter The project owner, sponsors, and stakeholders The problem statement The project goals and objectives The project requirements A bill of
Scope_statement
Control flow construct for executing code repeatedly
called infinite loops. The problem of determining whether a program contains an infinite loop is known as the halting problem. A conditional loop (also
Loop_(statement)
Problem in computer science
quantum computing, the hidden shift problem is a type of oracle-based problem. Various versions of this problem have quantum algorithms which can run
Hidden_shift_problem
Method for finding kth smallest value
{\displaystyle k} th order statistic. Selection includes as special cases the problems of finding the minimum, median, and maximum element in the collection.
Selection_algorithm
Problem of determining whether polynomials are identical
In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally
Polynomial_identity_testing
Problem in quantum information science
Hamiltonian simulation (also referred to as quantum simulation) is a problem in quantum information science that attempts to find the computational complexity
Hamiltonian_simulation
Millennium Prize Problem
first person providing a solution for one of the four specific statements of the problem as given by Charles Fefferman. On 8 September 2026, artificial
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
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
Can all boundary value problems be solved
variation problems in more than 1 dimension (for example, minimal surface problems or minimal curvature problems) The original problem statement in its entirety
Hilbert's_twentieth_problem
Problem in continuous-time finance
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to
Merton's_portfolio_problem
Type of numerical analysis
algorithm. Conversely, Best and Chakravarti studied the problem as an active set identification problem, and proposed a primal algorithm. These two algorithms
Isotonic_regression
Planned operator–machine interaction
assessing matters from the target audience's viewpoint, defining a problem statement, ideating potential solutions, prototyping wireframes, and testing
User_interface_design
founded on problems that are believed to be intractable. The higher residuosity problem (also called the nth-residuosity problem) is one such problem. This
Higher_residuosity_problem
Mathematical problem of making a structure rigid
In the mathematics of structural rigidity, grid bracing is a problem of adding cross bracing to a rectangular grid to make it into a rigid structure.
Grid_bracing
Unsolved problem in computer science
fixed-size Sudoku, the problem is in P, as the answer can be found by table lookup.) The precise statement of the P versus NP problem was introduced in 1971
P_versus_NP_problem
Mathematics optimization problem
Clearly the first method is more efficient. With this information, the problem statement can be refined as "how to determine the optimal parenthesization of
Matrix_chain_multiplication
Representation learning method
to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to
Sparse_dictionary_learning
The majority problem, or density classification task, is the problem of finding one-dimensional cellular automaton rules that accurately perform majority
Majority_problem
Function used in optimal control theory
a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that
Hamiltonian_(control_theory)
Process of achieving a goal by overcoming obstacles
philosophy of science Problem-posing education – Method of teaching coined by Paulo Freire Problem statement – Description of an issue Problem structuring methods –
Problem_solving
Mathematics problem
The Hundred Fowls Problem is a problem first discussed in the fifth century CE Chinese mathematics text Zhang Qiujian suanjing (The Mathematical Classic
Hundred_Fowls_Problem
Free software project
unit tests to verify that the submitted implementations solve the problem statement A framework for running and timing the implementations A website to
The Computer Language Benchmarks Game
The_Computer_Language_Benchmarks_Game
theoretical computer science, the monochromatic triangle problem is an algorithmic problem on graphs, in which the goal is to partition the edges of
Monochromatic_triangle
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
Millennium Prize Problem
existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Abstract mathematics problem
don't know, as the problem statement says nothing about this. Hence, like the previous solution, this solution states that the problem is underspecified
Ross–Littlewood_paradox
Software concurrency problem
computer science, the sleeping barber problem is a classic inter-process communication and synchronization problem that illustrates the complexities that
Sleeping_barber_problem
Automated recognition of patterns and regularities in data
whether a given email is "spam"). Pattern recognition is a more general problem that encompasses other types of output as well. Other examples are regression
Pattern_recognition
Post-secondary academic institution in Singapore
typically receive a problem statement from their lecturers at the start of each day before exploring the solutions to the problem in a group of three
Republic_Polytechnic
On Schubert's enumerative calculus
string theory. The entirety of the original problem statement, in English translation, is as follows: The problem consists in this: To establish rigorously
Hilbert's_fifteenth_problem
Computer science problem
The firing squad synchronization problem is a problem in computer science and cellular automata in which the goal is to design a cellular automaton that
Firing squad synchronization problem
Firing_squad_synchronization_problem
Problem of determining if a Boolean formula could be made true
computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT)
Boolean satisfiability problem
Boolean_satisfiability_problem
several years. The difficulties described above translate into the following problem: Find an efficient (high-performance and fault tolerant) method to enforce
Global_serializability
Any type of calculation
encoded into a Turing machine: ("Paul loves me twice as much as Joe"). Problem statements that appear to be well-defined, but for which it can be proved that
Computation
Minimum-cost tree with exactly k vertices
The k-minimum spanning tree problem, studied in theoretical computer science, asks for a tree of minimum cost that has exactly k vertices and forms a
K-minimum_spanning_tree
Fastest curve descent without friction
I shall publicly declare him worthy of praise Bernoulli wrote the problem statement as: Given two points A and B in a vertical plane, what is the curve
Brachistochrone_curve
Construction of an angle equal to one third a given angle
a classical problem of straightedge and compass construction of ancient Greek mathematics. In 1837, Pierre Wantzel proved that the problem, as stated,
Angle_trisection
Method of describing good design practices
the context description, the problem statement, a longer part of text with examples and explanations, a solution statement, a sketch and further references
Pattern_language
Limitative results in mathematical logic
criteria is false. The main problem in fleshing out the proof just described is that it seems at first that to construct a statement p that is equivalent to
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
IETF working group
recovery and with smaller changes in RFC 8025 and RFC 8066). The problem statement document is RFC 4919. IPv6 over Bluetooth Low Energy using 6LoWPAN
6LoWPAN
Resolved problem in plane geometry
Hermann Rothe, and Roland Weitzenböck. A generalization of this problem statement was answered in the negative in 1997 by Marek R. Rychlik. An equichordal
Equichordal_point_problem
Statement which ends execution of a function and resumes in the main code
from the same sort of problems that arise for the GOTO statement. Conversely, it can be argued that using the return statement is worthwhile when the
Return_statement
Search problem in quantum mechanics
hidden linear function problem, is a search problem that generalizes the Bernstein–Vazirani problem. In the Bernstein–Vazirani problem, the hidden function
Hidden linear function problem
Hidden_linear_function_problem
NP-complete graph problem
NP-complete decision problem that involves finding a given graph as an induced subgraph of a larger graph. Formally, the problem takes as input two graphs
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
{\displaystyle r[k]=\sum _{n=-\infty }^{\infty }h[n]s[k-n]} The blind equalization problem can now be formulated as follows; Given the received signal r [ k ] {\displaystyle
Blind_equalization
Physics problem related to laws of motion and gravity
three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles. The mathematical statement of the
Three-body_problem
Problem in computer programming
a problem in programming of parser generators in which an optional else clause in an if–then(–else) statement can make nested conditional statements ambiguous
Dangling_else
Logic puzzle
product X·Y, and the observer O knows nothing more than the original problem statement. All three parties keep the same information but interpret it differently
Sum_and_Product_Puzzle
Problem discovery
used for problem finding in literature including problem discovery, problem formulation, problem identification, problem construction, and problem posing
Problem_finding
Annual computer programming event
puzzle. The exception is the final star, which is awarded without any problem statement to those that have collected all other stars. As a result, the statistics
Advent_of_Code
Eight disciplines of team-oriented problem solving method
design. The relationships between 8D and FMEA are outlined below: The problem statements and descriptions are sometimes linked between both documents. An 8D
Eight disciplines problem solving
Eight_disciplines_problem_solving
On mathematics of sums of prime powers
The Waring–Goldbach problem is a problem in additive number theory, concerning the representation of integers as sums of powers of prime numbers. It is
Waring–Goldbach_problem
Philosophical problem about why neural processes give rise to inner experience at all
In 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
Algorithmic problem in order theory
Betweenness is an algorithmic problem in order theory about ordering a collection of items subject to constraints that some items must be placed between
Betweenness_problem
Educational concept
provide a problem statement followed by a step-by-step demonstration of how to solve it. Worked examples are often contrasted with open-ended problem solving
Expertise_reversal_effect
Promotes work on calculus of variations
much a specific "problem" as an encouragement towards further development of the calculus of variations. His statement of the problem is a summary of the
Hilbert's twenty-third problem
Hilbert's_twenty-third_problem
Probability puzzle
Pigeons repeatedly exposed to the problem rapidly learn to always switch, unlike humans. Most statements of the problem, notably the one in Parade, do not
Monty_Hall_problem
On uniformization of analytic relations
relations by means of automorphic functions. The entirety of the original problem statement is as follows: As Poincaré was the first to prove, it is always possible
Hilbert's twenty-second problem
Hilbert's_twenty-second_problem
Falsification of building safety records
scandal dubbed in Japanese media as the "structural calculation forgery problem" (構造計算書偽造問題, kōzō keisansho gizō mondai). Hidetsugu Aneha, Moriyoshi Kimura
2005 Japanese architectural forgery scandal
2005_Japanese_architectural_forgery_scandal
UNESCO statements about issues of race
has published several statements about issues of race. The statements include: Statement on race (Paris, July 1950) Statement on the nature of race and
UNESCO_statements_on_race
minimizes/maximizes Objective. The formal mathematical (standard form) statement of the design optimization problem is minimize f ( x ) s u b j e c t t o h i ( x ) = 0
Design_optimization
Impossible task in computing
mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert
Entscheidungsproblem
Problem of sorting pairs of numbers by their sum
Unsolved problem in computer science Is there an X + Y {\displaystyle X+Y} sorting algorithm faster than O ( n 2 log n ) {\displaystyle O(n^{2}\log
X_+_Y_sorting
the Skorokhod problem is the problem of solving a stochastic differential equation with a reflecting boundary condition. The problem is named after Anatoliy
Skorokhod_problem
Distinction between what is and what ought to be
fundamental epistemological distinction between: Statements of fact (positive or descriptive statements), which are based upon reason and observation, and
Fact–value_distinction
some of the major problems in philosophy. A statement is a conditional statement with a false antecedent. For example, the statement "If Joseph Swan had
List of philosophical problems
List_of_philosophical_problems
In graph theory and computer science, the graph sandwich problem is a problem of finding a graph that belongs to a particular family of graphs and is "sandwiched"
Graph_sandwich_problem
Group brainstorming technique
the supervisor. Once the topic of the session is narrowed down to a problem statement, this is announced and written on top of the Idea Form. This is a
6-3-5_Brainwriting
Problem asking the probability that the sun will rise tomorrow
be used to evaluate the plausibility of the statement, "The sun will rise tomorrow." The sunrise problem was first introduced publicly in 1763 by Richard
Sunrise_problem
Assertion about the feelings, beliefs, values etc. of the person speaking
the statement on the defensive. In a dispute, use of a phrase that begins with "I want" may encourage the parties to engage in positional problem solving
I-message
Equality of areas of a sliced disk
Scientist. Upton, L. J. (1967), "Problem 660", Mathematics Magazine, 40 (3): 163, JSTOR 2688484. Problem statement{{citation}}: CS1 maint: postscript
Pizza_theorem
Open problem on 3x+1 and x/2 functions
Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers
Collatz_conjecture
Political document written by the Students for a Democratic Society
was written to reflect their view that all problems in every area were linked to each other. The statement expressed SDS's willingness to work with groups
Port_Huron_Statement
When are solutions in the calculus of variations analytic
with analytic coefficients, Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential
Hilbert's_nineteenth_problem
Dublin Statement on Water and Sustainable Development, also known as the Dublin Principles, was a meeting of experts on water related problems that took
Dublin_Statement
Improvements in an organization to eliminate non-conformities or undesirable situations
corrections to a problem with no identified systemic root cause. When multiple investigations end in no corrective action, a new problem statement with expanded
Corrective and preventive action
Corrective_and_preventive_action
23 mathematical problems stated in 1900
closely related unsolved problems exist. Some of Hilbert's statements were not precise enough to specify a particular problem, but were suggestive enough
Hilbert's_problems
Physical law for entropy and heat
empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder
Second_law_of_thermodynamics
Equations of motion for viscous fluids
stated that the solution to the problem, a counterexample that refers to statements C and D of the problem statement, was developed by its researchers
Navier–Stokes_equations
18 mathematical problems stated in 1998
that he chosen the problems using three criteria: simple statement that is preferably precise, personal acquaintance with the problem and belief that solution
Smale's_problems
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