List of unsolved problems in mathematics

Lists of unsolved problems in mathematics

Millennium Prize Problems

• P versus NP
• Hodge conjecture
• Riemann hypothesis
• Yang–Mills existence and mass gap
• Navier–Stokes existence and smoothness
• Birch and Swinnerton-Dyer conjecture

Unsolved problems

[Algebra]

• Homological conjectures in commutative algebra
• Finite lattice representation problem
• Hilbert's sixteenth problem
• Hilbert's fifteenth problem
• Hadamard conjecture
• Jacobson's conjecture
• Crouzeix's conjecture
• Existence of perfect cuboids and associated cuboid conjectures
• Zauner's conjecture: existence of SIC-POVMs in all dimensions
• Wild Problem: Classification of pairs of n×n matrices under simultaneous conjugation and problems containing it such as a lot of classification problems
• Köthe conjecture
• Birch–Tate conjecture
• Serre's conjecture II
• Bombieri–Lang conjecture
• Farrell–Jones conjecture
• Bost conjecture
• Rota's basis conjecture
• Uniformity conjecture
• Kaplansky's conjectures
• Kummer–Vandiver conjecture
• Serre's multiplicity conjectures
• Pierce–Birkhoff conjecture
• Eilenberg–Ganea conjecture
• Green's conjecture
• Grothendieck–Katz p-curvature conjecture
• Sendov's conjecture
• Zariski–Lipman conjecture
• The Dneister Notebook collects several hundred unresolved problems in algebra, particularly ring theory and modulus theory.
• The Erlagol Notebook collects unresolved problems in algebra and model theory.

  Analysis">Mathematical analysis">Analysis

• The four exponentials conjecture on the transcendence of at least one of four exponentials of combinations of irrationals
• Lehmer's conjecture on the Mahler measure of non-cyclotomic polynomials
• The Pompeiu problem on the topology of domains for which some nonzero function has integrals that vanish over every congruent copy
• Schanuel's conjecture on the transcendence degree of exponentials of linearly independent irrationals
• Are , Pi| + e, − e, e, /e, ^e, ^{Square root of 2|}, , e², ln , 2^e, e^e, Catalan's constant, or Khinchin's constant rational, algebraic irrational, or transcendental? What is the irrationality measure of each of these numbers?
• Vitushkin's conjecture
• Invariant subspace problem
• Kung–Traub conjecture
• Regularity of solutions of Vlasov–Maxwell equations
• Regularity of solutions of Euler equations
• Convergence of Flint Hills series

  [Combinatorics]

• Frankl's union-closed sets conjecture: for any family of sets closed under sums there exists an element belonging to half or more of the sets
• The lonely runner conjecture: if runners with pairwise distinct speeds run round a track of unit length, will every runner be "lonely" at some time?
• Singmaster's conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle?
• Finding a function to model n-step self-avoiding walks.
• The 1/3–2/3 conjecture: does every finite partially ordered set that is not totally ordered contain two elements x and y such that the probability that x appears before y in a random linear extension is between 1/3 and 2/3?
• Give a combinatorial interpretation of the Kronecker coefficients.
• Open questions concerning Latin squares
• The values of the Dedekind numbers for.
• The values of the Ramsey numbers, particularly
• The values of the Van der Waerden numbers

  [Dynamical system]s

• Collatz conjecture
• Lyapunov's second method for stability – For what classes of ODEs, describing dynamical systems, does the Lyapunov’s second method formulated in the classical and canonically generalized forms define the necessary and sufficient conditions for the stability of motion?
• Furstenberg conjecture – Is every invariant and ergodic measure for the action on the circle either Lebesgue or atomic?
• Margulis conjecture – Measure classification for diagonalizable actions in higher-rank groups
• MLC conjecture – Is the Mandelbrot set locally connected?
• Weinstein conjecture – Does a regular compact contact type level set of a Hamiltonian on a symplectic manifold carry at least one periodic orbit of the Hamiltonian flow?
• Arnold–Givental conjecture and Arnold conjecture – relating symplectic geometry to Morse theory
• Eremenko's conjecture that every component of the escaping set of an entire transcendental function is unbounded
• Is every reversible cellular automaton in three or more dimensions locally reversible?
• Birkhoff conjecture: if a billiard table is strictly convex and integrable, is its boundary necessarily an ellipse?
• Many problems concerning an outer billiard, for example showing that outer billiards relative to almost every convex polygon have unbounded orbits.
• Quantum unique ergodicity conjecture
• Berry–Tabor conjecture
• Painlevé conjecture

  Games and puzzles

Combinatorial games">Combinatorial game theory">Combinatorial games

• Sudoku:
• * What is the maximum number of givens for a minimal puzzle?
• * How many puzzles have exactly one solution?
• * How many puzzles with exactly one solution are minimal?
• Tic-tac-toe variants:
• *Given a width of tic-tac-toe board, what is the smallest dimension such that X is guaranteed a winning strategy?
• What is the Turing completeness status of all unique elementary cellular automata?

  Games with imperfect information">Game theory">Games with imperfect information

• Rendezvous problem

  [Geometry]

[Algebraic geometry]

• Abundance conjecture
• Bass conjecture
• Deligne conjecture
• Dixmier conjecture
• Fröberg conjecture
• Fujita conjecture
• Hartshorne conjectures
• The Jacobian conjecture
• Manin conjecture
• Maulik–Nekrasov–Okounkov–Pandharipande conjecture on an equivalence between Gromov–Witten theory and Donaldson–Thomas theory
• Nakai conjecture
• Resolution of singularities in characteristic
• Standard conjectures on algebraic cycles
• Section conjecture
• Tate conjecture
• Termination of flips
• Virasoro conjecture
• Weight-monodromy conjecture
• Zariski multiplicity conjecture

  [Differential geometry]

• The filling area conjecture, that a hemisphere has the minimum area among shortcut-free surfaces in Euclidean space whose boundary forms a closed curve of given length
• The Hopf conjectures relating the curvature and Euler characteristic of higher-dimensional Riemannian manifolds
• The spherical Bernstein's problem, a possible generalization of the original Bernstein's problem
• Cartan–Hadamard conjecture: Can the classical isoperimetric inequality for subsets of Euclidean space be extended to spaces of nonpositive curvature, known as Cartan–Hadamard manifolds?
• Carathéodory conjecture
• Chern's conjecture
• Chern's conjecture for hypersurfaces in spheres
• Yau's conjecture
• Yau's conjecture on the first eigenvalue
• Closed curve problem: Find necessary and sufficient conditions that determine when, given two periodic functions with the same period, the integral curve is closed.

  [Discrete geometry]

• Solving the happy ending problem for arbitrary
• Finding matching upper and lower bounds for k-sets and halving lines
• The Hadwiger conjecture on covering n-dimensional convex bodies with at most 2ⁿ smaller copies
• Find lower and upper bounds for Borsuk's problem on the number of smaller-diameter subsets needed to cover a bounded n-dimensional set.
• The Kobon triangle problem on triangles in line arrangements
• The McMullen problem on projectively transforming sets of points into convex position
• Tripod packing
• Ulam's packing conjecture about the identity of the worst-packing convex solid
• Sphere packing problems, including the density of the densest packing in dimensions other than 1, 2, 3, 8 and 24, and its asymptotic behavior for high dimensions.
• What is the asymptotic growth rate of wasted space for packing unit squares into a half-integer square?
• Kissing number problem for dimensions other than 1, 2, 3, 4, 8 and 24
• How many unit distances can be determined by a set of points in the Euclidean plane?

  [Euclidean geometry]

• Bellman's lost in a forest problem – find the shortest route that is guaranteed to reach the boundary of a given shape, starting at an unknown point of the shape with unknown orientation
• Borromean rings — are there three unknotted space curves, not all three circles, which cannot be arranged to form this link?
• Danzer's problem and Conway's dead fly problem – do Danzer sets of bounded density or bounded separation exist?
• Dissection into orthoschemes – is it possible for simplices of every dimension?
• The – does there exist a two-dimensional shape that forms the prototile for an aperiodic tiling, but not for any periodic tiling?
• The Erdős–Oler conjecture that when is a triangular number, packing circles in an equilateral triangle requires a triangle of the same size as packing circles
• Falconer's conjecture that sets of Hausdorff dimension greater than in must have a distance set of nonzero Lebesgue measure
• Inscribed square problem, also known as Toeplitz' conjecture – does every Jordan curve have an inscribed square?
• The Kakeya conjecture – do -dimensional sets that contain a unit line segment in every direction necessarily have Hausdorff dimension and Minkowski dimension equal to ?
• The Kelvin problem on minimum-surface-area partitions of space into equal-volume cells, and the optimality of the Weaire–Phelan structure as a solution to the Kelvin problem
• Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one
• Moser's worm problem – what is the smallest area of a shape that can cover every unit-length curve in the plane?
• The moving sofa problem – what is the largest area of a shape that can be maneuvered through a unit-width L-shaped corridor?
• Shephard's problem – does every convex polyhedron have a net, or simple edge-unfolding?
• The Thomson problem – what is the minimum energy configuration of mutually-repelling particles on a unit sphere?
• Uniform 5-polytopes – find and classify the complete set of these shapes
• Covering problem of Rado – if the union of finitely many axis-parallel squares has unit area, how small can the largest area covered by a disjoint subset of squares be?
• Atiyah conjecture on configurations

  [Graph theory]

Paths and cycles in graphs

• Barnette's conjecture that every cubic bipartite three-connected planar graph has a Hamiltonian cycle
• Chvátal's toughness conjecture, that there is a number such that every -tough graph is Hamiltonian
• The cycle double cover conjecture that every bridgeless graph has a family of cycles that includes each edge twice
• The Erdős–Gyárfás conjecture on cycles with power-of-two lengths in cubic graphs
• The linear arboricity conjecture on decomposing graphs into disjoint unions of paths according to their maximum degree
• The Lovász conjecture on Hamiltonian paths in symmetric graphs
• The Oberwolfach problem on which 2-regular graphs have the property that a complete graph on the same number of vertices can be decomposed into edge-disjoint copies of the given graph.

  Graph coloring and labeling

• Cereceda's conjecture on the diameter of the space of colorings of degenerate graphs
• The Erdős–Faber–Lovász conjecture on coloring unions of cliques
• The Gyárfás–Sumner conjecture on χ-boundedness of graphs with a forbidden induced tree
• The Hadwiger conjecture relating coloring to clique minors
• The Hadwiger–Nelson problem on the chromatic number of unit distance graphs
• Jaeger's Petersen-coloring conjecture that every bridgeless cubic graph has a cycle-continuous mapping to the Petersen graph
• The list coloring conjecture that, for every graph, the list chromatic index equals the chromatic index
• The total coloring conjecture of Behzad and Vizing that the total chromatic number is at most two plus the maximum degree

  Graph drawing

• The Albertson conjecture that the crossing number can be lower-bounded by the crossing number of a complete graph with the same chromatic number
• The Blankenship–Oporowski conjecture on the book thickness of subdivisions
• Conway's thrackle conjecture
• Harborth's conjecture that every planar graph can be drawn with integer edge lengths
• Negami's conjecture on projective-plane embeddings of graphs with planar covers
• The strong Papadimitriou–Ratajczak conjecture that every polyhedral graph has a convex greedy embedding
• Turán's brick factory problem – Is there a drawing of any complete bipartite graph with fewer crossings than the number given by Zarankiewicz?
• Universal point sets of subquadratic size for planar graphs

  Word-representation of graphs

• Characterise word-representable planar graphs
• Characterise word-representable near-triangulations containing the complete graph K₄
• Classify graphs with representation number 3, that is, graphs that can be represented using 3 copies of each letter, but cannot be represented using 2 copies of each letter
• Is the line graph of a non-word-representable graph always non-word-representable?
• Are there any graphs on n vertices whose representation requires more than floor copies of each letter?
• Is it true that out of all bipartite graphs crown graphs require longest word-representants?
• Characterise word-representable graphs in terms of forbidden subgraphs.
• Which problems on graphs can be translated to words representing them and solved on words ?

  Miscellaneous graph theory

• Conway's 99-graph problem: does there exist a strongly regular graph with parameters ?
• The Erdős–Hajnal conjecture on large cliques or independent sets in graphs with a forbidden induced subgraph
• The GNRS conjecture on whether minor-closed graph families have embeddings with bounded distortion
• Graham's pebbling conjecture on the pebbling number of Cartesian products of graphs
• The implicit graph conjecture on the existence of implicit representations for slowly-growing hereditary families of graphs
• Jørgensen's conjecture that every 6-vertex-connected K₆-minor-free graph is an apex graph
• Meyniel's conjecture that cop number is
• Does a Moore graph with girth 5 and degree 57 exist?
• What is the largest possible pathwidth of an -vertex cubic graph?
• The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted subgraphs.
• The second neighborhood problem: does every oriented graph contain a vertex for which there are at least as many other vertices at distance two as at distance one?
• Sumner's conjecture: does every -vertex tournament contain as a subgraph every -vertex oriented tree?
• Tutte's conjectures that every bridgeless graph has a nowhere-zero 5-flow and every Petersen-minor-free bridgeless graph has a nowhere-zero 4-flow
• Vizing's conjecture on the domination number of cartesian products of graphs

  [Group theory]

• Is every finitely presented periodic group finite?
• The inverse Galois problem: is every finite group the Galois group of a Galois extension of the rationals?
• For which positive integers m, n is the free Burnside group finite? In particular, is finite?
• Is every group surjunctive?
• Andrews–Curtis conjecture
• Herzog–Schönheim conjecture
• Does generalized moonshine exist?
• Are there an infinite number of Leinster groups?
• Guralnick–Thompson conjecture
• Problems in loop theory and quasigroup theory consider generalizations of groups
• The Kourovka Notebook is a collection of unsolved problems in group theory, first published in 1965 and updated many times since.

  [Model theory] and [formal language]s

• Vaught's conjecture
• The Cherlin–Zilber conjecture: A simple group whose first-order theory is stable in is a simple algebraic group over an algebraically closed field.
• The Main Gap conjecture, e.g. for uncountable first order theories, for AECs, and for -saturated models of a countable theory.
• Determine the structure of Keisler's order
• The stable field conjecture: every infinite field with a stable first-order theory is separably closed.
• Is the theory of the field of Laurent series over decidable? of the field of polynomials over ?
• Is the Borel monadic theory of the real order decidable? Is the monadic theory of well-ordering consistently decidable?
• The Stable Forking Conjecture for simple theories
• For which number fields does Hilbert's tenth problem hold?
• Assume K is the class of models of a countable first order theory omitting countably many types. If K has a model of cardinality does it have a model of cardinality continuum?
• Shelah's eventual categoricity conjecture: For every cardinal there exists a cardinal such that If an AEC K with LS<= is categorical in a cardinal above then it is categorical in all cardinals above.
• Shelah's categoricity conjecture for : If a sentence is categorical above the Hanf number then it is categorical in all cardinals above the Hanf number.
• Is there a logic L which satisfies both the Beth property and Δ-interpolation, is compact but does not satisfy the interpolation property?
• If the class of atomic models of a complete first order theory is categorical in the, is it categorical in every cardinal?
• Is every infinite, minimal field of characteristic zero algebraically closed?
• Kueker's conjecture
• Does there exist an o-minimal first order theory with a trans-exponential function?
• Does a finitely presented homogeneous structure for a finite relational language have finitely many reducts?
• Do the Henson graphs have the finite model property?
• The universality problem for C-free graphs: For which finite sets C of graphs does the class of C-free countable graphs have a universal member under strong embeddings?
• The universality spectrum problem: Is there a first-order theory whose universality spectrum is minimum?
• Generalized star height problem

  [Number theory]

General

• Grand Riemann hypothesis
• *Generalized Riemann hypothesis
• **Riemann hypothesis
• n conjecture
• * abc conjecture
• * Szpiro's conjecture
• Hilbert's ninth problem
• Hilbert's eleventh problem
• Hilbert's twelfth problem
• Carmichael's totient function conjecture
• Erdős–Straus conjecture
• Erdős–Ulam problem
• Pillai's conjecture
• Hall's conjecture
• Lindelöf hypothesis and its consequence, the density hypothesis for zeroes of the Riemann zeta function
• Montgomery's pair correlation conjecture
• Hilbert–Pólya conjecture
• Grimm's conjecture
• Leopoldt's conjecture
• Scholz conjecture
• Do any odd perfect numbers exist?
• Are there infinitely many perfect numbers?
• Do quasiperfect numbers exist?
• Do any odd weird numbers exist?
• Do any Lychrel numbers exist?
• Is 10 a solitary number?
• Catalan–Dickson conjecture on aliquot sequences
• Do any Taxicab exist for n > 1?
• Brocard's problem: existence of integers,, such that n! + 1 = m² other than n = 4, 5, 7
• Beilinson conjecture
• Littlewood conjecture
• Vojta's conjecture
• Goormaghtigh conjecture
• Congruent number problem
• Lehmer's totient problem: if φ divides n − 1, must n be prime?
• Are there infinitely many amicable numbers?
• Are there any pairs of amicable numbers which have opposite parity?
• Are there any pairs of relatively prime amicable numbers?
• Are there infinitely many betrothed numbers?
• Are there any pairs of betrothed numbers which have same parity?
• The Gauss circle problem – how far can the number of integer points in a circle centered at the origin be from the area of the circle?
• Piltz divisor problem, especially Dirichlet's divisor problem
• Exponent pair conjecture
• Is π a normal number ?
• Casas-Alvero conjecture
• Sato–Tate conjecture
• Find value of De Bruijn–Newman constant
• Which integers can be written as the sum of three perfect cubes?
• Erdős–Moser problem: is 1¹ + 2¹ = 3¹ the only solution to the Erdős–Moser equation?
• Is there a covering system with odd distinct moduli?
• The uniqueness conjecture for Markov numbers
• Keating–Snaith conjecture concerning the asymptotics of an integral involving the Riemann zeta function

  [Additive number theory]

• Beal's conjecture
• Fermat–Catalan conjecture
• Goldbach's conjecture
• The values of g and G in Waring's problem
• Lander, Parkin, and Selfridge conjecture
• Gilbreath's conjecture
• Erdős conjecture on arithmetic progressions
• Erdős–Turán conjecture on additive bases
• Pollock octahedral numbers conjecture
• Skolem problem
• Determine growth rate of r_k
• Minimum overlap problem
• Do the Ulam numbers have a positive density?

  [Algebraic number theory]

• Are there infinitely many real quadratic number fields with unique factorization ?
• Characterize all algebraic number fields that have some power basis.
• Stark conjectures
• Kummer–Vandiver conjecture
• Greenberg's conjectures

  [Computational number theory]

• Integer factorization: Can integer factorization be done in polynomial time?

  [Prime number]s

• Brocard's Conjecture
• Catalan's Mersenne conjecture
• Agoh–Giuga conjecture
• Dubner's conjecture
• The Gaussian moat problem: is it possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded?
• New Mersenne conjecture
• Erdős–Mollin–Walsh conjecture
• Are there infinitely many prime quadruplets?
• Are there infinitely many cousin primes?
• Are there infinitely many sexy primes?
• Are there infinitely many Mersenne primes ; equivalently, infinitely many even perfect numbers?
• Are there infinitely many Wagstaff primes?
• Are there infinitely many Sophie Germain primes?
• Are there infinitely many Pierpont primes?
• Are there infinitely many regular primes, and if so is their relative density ?
• For any given integer b which is not a perfect power and not of the form −4k⁴ for integer k, are there infinitely many repunit primes to base b?
• Are there infinitely many Cullen primes?
• Are there infinitely many Woodall primes?
• Are there infinitely many Carol primes?
• Are there infinitely many Kynea primes?
• Are there infinitely many palindromic primes to every base?
• Are there infinitely many Fibonacci primes?
• Are there infinitely many Lucas primes?
• Are there infinitely many Pell primes?
• Are there infinitely many Newman–Shanks–Williams primes?
• Are all Mersenne numbers of prime index square-free?
• Are there infinitely many Wieferich primes?
• Are there any Wieferich primes in base 47?
• Are there any composite c satisfying 2^{c − 1} ≡ 1 ?
• For any given integer a > 0, are there infinitely many primes p such that a^{p − 1} ≡ 1 ?
• Can a prime p satisfy 2^{p − 1} ≡ 1 and 3^{p − 1} ≡ 1 simultaneously?
• Are there infinitely many Wilson primes?
• Are there infinitely many Wolstenholme primes?
• Are there any Wall–Sun–Sun primes?
• For any given integer a > 0, are there infinitely many Lucas–Wieferich primes associated with the pair ?
• Is every Fermat number 2²ⁿ + 1 composite for ?
• Are all Fermat numbers square-free?
• For any given integer a which is not a square and does not equal to −1, are there infinitely many primes with a as a primitive root?
• Artin's conjecture on primitive roots
• Is 78,557 the lowest Sierpiński number ?
• Is 509,203 the lowest Riesel number?
• Fortune's conjecture
• Landau's problems
• Feit–Thompson conjecture
• Does every prime number appear in the Euclid–Mullin sequence?
• Does the converse of Wolstenholme's theorem hold for all natural numbers?
• Elliott–Halberstam conjecture
• Problems associated to Linnik's theorem
• Find the smallest Skewes' number

  [Set theory]

• The problem of finding the ultimate core model, one that contains all large cardinals.
• If ℵ_ω is a strong limit cardinal, then 2^ℵ_ω < ℵ_ω1. The best bound, ℵ_ω4, was obtained by Shelah using his pcf theory.
• Woodin's Ω-hypothesis.
• Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal?
• Does the Generalized Continuum Hypothesis below a strongly compact cardinal imply the Generalized Continuum Hypothesis everywhere?
• Does there exist a Jónsson algebra on ℵ_ω?
• Without assuming the axiom of choice, can a nontrivial elementary embedding V→V exist?
• Does the Generalized Continuum Hypothesis entail Diamondsuit| for every singular cardinal ?
• Does the Generalized Continuum Hypothesis imply the existence of an ℵ₂-Suslin tree?
• Is OCA consistent with ?
• Assume ZF and that whenever there is a surjection from onto, there is an injection from into. Does the Axiom of Choice hold?

  [Topology]

• Baum–Connes conjecture
• Borel conjecture
• Hilbert–Smith conjecture
• Mazur's conjectures
• Novikov conjecture
• Unknotting problem
• Volume conjecture
• Whitehead conjecture
• Zeeman conjecture

  Problems solved since 1995

• Deciding whether the Conway knot is a slice knot
• Ringel's conjecture on graceful labeling of trees
• Connes embedding problem
• Duffin-Schaeffer conjecture
• Hedetniemi's conjecture on the chromatic number of tensor products of graphs
• Erdős sumset conjecture
• McMullen's g-conjecture on the possible numbers of faces of different dimensions in a simplicial sphere
• Yau's conjecture
• Pentagonal tiling
• Erdős–Burr conjecture
• Boolean Pythagorean triples problem
• Babai's problem
• Main conjecture in Vinogradov's mean-value theorem
• Erdős discrepancy problem
• Umbral moonshine conjecture
• Alspach's conjecture
• Anderson conjecture
• Gaussian correlation inequality
• Goldbach's weak conjecture
• Kadison–Singer problem
• Virtual Haken conjecture
• Hsiang–Lawson's conjecture
• Willmore conjecture
• Beck's 3-permutations conjecture
• Ehrenpreis conjecture
• Hanna Neumann conjecture
• Bloch–Kato conjecture
• Erdős distinct distances problem
• Density theorem
• Hirsch conjecture
• Sidon set problem
• Atiyah conjecture
• Kauffman–Harary conjecture
• Surface subgroup conjecture
• Scheinerman's conjecture
• Cobordism hypothesis
• Full classification of finite simple groups
• Geometrization conjecture, proven by Grigori Perelman in a series of preprints in 2002–2003.
• Serre's modularity conjecture
• Heterogeneous tiling conjecture
• Normal scalar curvature conjecture and the Böttcher–Wenzel conjecture
• Erdős–Menger conjecture
• Road coloring conjecture
• Spherical space form conjecture
• The angel problem
• Nirenberg–Treves conjecture
• Lax conjecture
• The Langlands–Shelstad fundamental lemma
• Tameness conjecture and Ahlfors measure conjecture
• Robertson–Seymour theorem
• Stanley–Wilf conjecture
• Green–Tao theorem
• Ending lamination theorem
• Carpenter's rule problem
• Cameron–Erdős conjecture
• Milnor conjecture
• Kemnitz's conjecture
• Nagata's conjecture
• Kirillov's conjecture
• Poincaré conjecture
• Strong perfect graph conjecture
• Kouchnirenko’s conjecture
• Vaught conjecture
• Double bubble conjecture
• Catalan's conjecture
• n! conjecture
• Kato's conjecture
• Deligne's conjecture on 1-motives
• Modularity theorem
• Erdős–Stewart conjecture
• Berry–Robbins problem
• Erdős–Graham problem
• Honeycomb conjecture
• Gradient conjecture
• Bogomolov conjecture
• Lafforgue's theorem
• Kepler conjecture
• Dodecahedral conjecture
• Ganea conjecture
• Torsion conjecture
• Harary's conjecture
• Fermat's Last Theorem

  Books discussing problems solved since 1995

• Books discussing unsolved problems

• The Sverdlovsk Notebook is a collection of unsolved problems in semigroup theory.
• Formulation of unresloved problems for infinite Abelian groups are depicted in the book
• The list of unresolved problems for Combinatorial Geometry are depicted in the book.
• Several dozens of unresolved problems for Combinatorial Geometry are depicted in the book.
• Many unresolved problems for Graph theory are depicted in the article.
• The list of several unresolved problems converning Maler Conjecture are depicted in the book.