Problems

A question, for example a value to find or a classification to make.

Ideas 1–147 of 147.

Name	Kind	Subject
Trisecting the angle	Problem	Geometry
Doubling the cube	Problem	Geometry
Buffon's needle problem	Problem	Probability theory and stochastic processes
Squaring the circle	Problem	Geometry
Coupon collector's problem	Problem	Probability theory and stochastic processes
Monty Hall problem	Problem	Probability theory and stochastic processes
Gambler's ruin	Problem	Probability theory and stochastic processes
Hilbert's twentieth problem	Problem	Calculus of variations and optimal control; optimization
Mayer and Lagrange problems	Problem	Calculus of variations and optimal control; optimization
Non-negative least squares	Problem	Numerical analysis
Post's problem	Problem	Mathematical logic and foundations
Kirkman's schoolgirl problem	Problem	Combinatorics
Gelfand's problem on the index	Problem	Global analysis, analysis on manifolds
Gauss circle problem	Problem	Number theory
Stefan problem	Problem	Partial differential equations
Thomson problem	Problem	Convex and discrete geometry
Ten martini problem	Problem	Operator theory
Levi problem	Problem	Several complex variables and analytic spaces
Conjugacy problem	Problem	Group theory and generalizations
Erdős distinct distances problem	Problem	Convex and discrete geometry
First Cousin problem	Problem	Several complex variables and analytic spaces
Matrix Riemann–Hilbert problem	Problem	Functions of a complex variable
Invariant subspace problem	Problem	Operator theory
Neumann problem	Problem	Potential theory
n-body problem	Problem	Mechanics of particles and systems
Yamabe problem	Problem	Differential geometry
Isoperimetric problem of the calculus of variations	Problem	Calculus of variations and optimal control; optimization
Variational inequality	Problem	Operator theory
Serre's problem on projective modules	Problem	Commutative algebra
Hilbert's twenty-first problem	Problem	Ordinary differential equations
Waring's problem	Problem	Number theory
Topology optimization	Problem	Mechanics of deformable solids
Word problem for an algebra	Problem	General algebraic systems
Hilbert's third problem	Problem	Convex and discrete geometry
Hauptvermutung	Problem	Manifolds and cell complexes
Dirichlet problem	Problem	Potential theory
Catenary problem	Problem	Calculus of variations and optimal control; optimization
Bolza problem	Problem	Calculus of variations and optimal control; optimization
Gauss variational problem	Problem	Potential theory
Tammes problem	Problem	Convex and discrete geometry
Tautochrone problem	Problem	Integral equations
Tarski's finite basis problem	Problem	General algebraic systems
Minimal surface of revolution	Problem	Calculus of variations and optimal control; optimization
Word problem for free algebras of a variety	Problem	General algebraic systems
Kurosh problem	Problem	Associative rings and algebras
Hilbert's sixteenth problem	Problem	Algebraic geometry
Schottky problem	Problem	Algebraic geometry
Kadison–Singer problem	Problem	Functional analysis
Euler's elastica	Problem	Calculus of variations and optimal control; optimization
Ulam's stability problem	Problem	Difference and functional equations
Moment problem	Problem	Integral transforms, operational calculus
Kelvin problem	Problem	Calculus of variations and optimal control; optimization
Inverse spectral problem	Problem	Ordinary differential equations
Suslin's problem	Problem	Mathematical logic and foundations
Second Cousin problem	Problem	Several complex variables and analytic spaces
Linear-quadratic-Gaussian control	Problem	Systems theory; control
Moser's worm problem	Problem	Convex and discrete geometry
Plateau's problem	Problem	Calculus of variations and optimal control; optimization
Merton's portfolio problem	Problem	Game theory, economics, finance, and other social and behavioral sciences
Fermi–Pasta–Ulam–Tsingou problem	Problem	Dynamical systems and ergodic theory
Behrens–Fisher problem	Problem	Statistics
Unit distance problem	Problem	Convex and discrete geometry
Whitehead problem	Problem	Group theory and generalizations
Problem of Apollonius	Problem	Geometry
Dido's problem	Problem	Calculus of variations and optimal control; optimization
Fourier restriction problem	Problem	Harmonic analysis on Euclidean spaces
Smale's problems on dynamics	Problem	Dynamical systems and ergodic theory
Hausdorff moment problem	Problem	Integral transforms, operational calculus
Matrix completion	Problem	Linear and multilinear algebra; matrix theory
Hadamard's maximal determinant problem	Problem	Linear and multilinear algebra; matrix theory
Riemann problem	Problem	Partial differential equations
Goddard problem	Problem	Calculus of variations and optimal control; optimization
Obstacle problem	Problem	Partial differential equations
Tomographic reconstruction	Problem	Integral transforms, operational calculus
Linear-quadratic regulator	Problem	Calculus of variations and optimal control; optimization
Illumination problem	Problem	Convex and discrete geometry
Hilbert's seventeenth problem	Problem	Field theory and polynomials
Three-body problem	Problem	Mechanics of particles and systems
Triangulation conjecture	Problem	Manifolds and cell complexes
Banach measure problem	Problem	Measure and integration
Optimal transport and the Monge problem	Problem	Calculus of variations and optimal control; optimization
Zermelo's navigation problem	Problem	Calculus of variations and optimal control; optimization
Zarankiewicz problem	Problem	Combinatorics
Class number problem	Problem	Number theory
Homicidal chauffeur problem	Problem	Calculus of variations and optimal control; optimization
Pompeiu problem	Problem	Partial differential equations
Hilbert's fourteenth problem	Problem	Commutative algebra
Danzer set	Problem	Convex and discrete geometry
Group isomorphism problem	Problem	Group theory and generalizations
Busemann–Petty problem	Problem	Convex and discrete geometry
Congruent number problem	Problem	Number theory
Minkowski problem	Problem	Convex and discrete geometry
Bernstein's problem	Problem	Differential geometry
Hilbert's fifth problem	Problem	Topological groups, Lie groups
Hilbert's program	Problem	Mathematical logic and foundations
Word problem for groups	Problem	Group theory and generalizations
Happy ending problem	Problem	Convex and discrete geometry
dbar-Neumann problem	Problem	Several complex variables and analytic spaces
Kuratowski's closure-complement problem	Problem	General topology
Signorini problem	Problem	Mechanics of deformable solids
Hilbert's nineteenth problem	Problem	Partial differential equations
Poincaré problem	Problem	Several complex variables and analytic spaces
Calderón problem	Problem	Partial differential equations
Tarski's high school algebra problem	Problem	General algebraic systems
Dedekind's problem	Problem	Order, lattices, ordered algebraic structures
Riemann–Hilbert problem	Problem	Functions of a complex variable
Hilbert's eighteenth problem	Problem	Convex and discrete geometry
Secretary problem	Problem	Probability theory and stochastic processes
Steklov eigenvalue problem	Problem	Partial differential equations
Lebesgue's universal covering problem	Problem	Convex and discrete geometry
Hamburger moment problem	Problem	Integral transforms, operational calculus
Newton's minimal resistance problem	Problem	Calculus of variations and optimal control; optimization
No-three-in-line problem	Problem	Convex and discrete geometry
Measure problem of Lebesgue	Problem	Measure and integration
Complex structure on the six-sphere	Problem	Several complex variables and analytic spaces
Smale's fourteenth problem	Problem	Dynamical systems and ergodic theory
Unknotting problem	Problem	Manifolds and cell complexes
Finite lattice representation problem	Problem	Order, lattices, ordered algebraic structures
Lüroth problem	Problem	Algebraic geometry
Congruence lattice problem	Problem	Order, lattices, ordered algebraic structures
Hilbert's thirteenth problem	Problem	Real functions
Hilbert's fifteenth problem	Problem	Algebraic geometry
Shape optimization	Problem	Calculus of variations and optimal control; optimization
Euler's thirty-six officers problem	Problem	Combinatorics
Kakeya needle problem	Problem	Measure and integration
Matrix multiplication exponent	Problem	Computer science
Hearing the shape of a drum	Problem	Global analysis, analysis on manifolds
Hilbert's fourth problem	Problem	Geometry
Sub-Riemannian geodesic problem	Problem	Differential geometry
Equilibrium problem with an external field	Problem	Potential theory
Heilbronn triangle problem	Problem	Convex and discrete geometry
Burnside problem	Problem	Group theory and generalizations
Stieltjes moment problem	Problem	Integral transforms, operational calculus
Hilbert's twenty-third problem	Problem	Calculus of variations and optimal control; optimization
Trigonometric moment problem	Problem	Harmonic analysis on Euclidean spaces
Inverse Galois problem	Problem	Field theory and polynomials
Discrete Dirichlet problem	Problem	Potential theory
Integer factorization	Problem	Number theory
Free boundary problem	Problem	Partial differential equations
Time-optimal control	Problem	Calculus of variations and optimal control; optimization
Hadwiger–Nelson problem	Problem	Combinatorics
Connes embedding problem	Problem	Functional analysis
Change detection	Problem	Statistics
Normal Moore space problem	Problem	General topology
Kervaire invariant problem	Problem	Algebraic topology
Cauchy's functional equation	Problem	Difference and functional equations
Brachistochrone problem	Problem	Calculus of variations and optimal control; optimization