World Famous Unsolved Mysteries Pdf

1. Famous Unsolved Mysteries
2. Famous Unsolved Deaths

The world is full of unsolved and greatest mysteries, some that invoke the supernatural. According to the Mesoamerican Long Count Calendar, made famous by the ancient Mayan people, December 2012 marks the ending of the current baktun cycle. 46 thoughts on “World’s 20 Greatest Mysteries”. Bermuda Triangle. The Bermuda Triangle is one of the great unsolved mysteries of the world, a section of ocean in the western North Atlantic where ships and aircrafts have disappeared under deeply suspicious circumstances. Included in this list is the infamous “Flight 19”, a group of 5 bombers who went on a routine training exercise in 1945.

Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, yet many mathematical problems, both major and minor, still remain unsolved.^[1] These unsolved problems occur in multiple domains, including physics, computer science, algebra, analysis, combinatorics, algebraic, discrete and Euclidean geometries, graph, group, model, number, set and Ramsey theories, dynamical systems, partial differential equations, and more. Some problems may belong to more than one discipline of mathematics and be studied using techniques from different areas. Prizes are often awarded for the solution to a long-standing problem, and lists of unsolved problems (such as the list of Millennium Prize Problems) receive considerable attention.

Download Unsolved Mysteries ebook PDF or Read Online books in PDF, EPUB. Format: PDF, Kindle Download: 503 Read: 392. Download eBook. A collection of classic mysteries from around the world including those that are enigmatic, ancient riddles or oddities in the skies. Including current theories and famous examples'--Provided. Unsolved mysteries of the world Download unsolved mysteries of the world or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get unsolved mysteries of the world book now. List of links to unsolved problems in mathematics, prizes and research; Open Problem Garden The collection of open problems in mathematics build on the principle of user editable ('wiki') site; AIM Problem Lists; Unsolved Problem of the Week Archive. MathPro Press. Ball, John M. 'Some Open Problems in Elasticity' (PDF). Constantin, Peter. UNSOLVED MYSTERIES - ROOM TWO 3 NOMOLI: GUARDS OF THE SKY STONES Unknown objects from Sierra Leone in Western Africa In West Africa there are many various cultures. Myths, fairy tales and legends are very important in people’s lives and in their religions.

Nazhika to hour converters. These remedies include suggested dress to be worn during the dasa period, devata bhajanam, morning prayers to be chanted along with specific instructions to be followed while chanting, if any.

• 1Lists of unsolved problems in mathematics
• 2Unsolved problems
  • 2.9Games and puzzles
  • 2.10Graph theory
  • 2.13Number theory
• 6Further reading

Lists of unsolved problems in mathematics

Over the course of time, several lists of unsolved mathematical problems have appeared.

Millennium Prize Problems

Of the original seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000, six have yet to be solved as of 2019:^[7]

The seventh problem, the Poincaré conjecture, has been solved.^[13] The smooth four-dimensional Poincaré conjecture—that is, whether a four-dimensional topological sphere can have two or more inequivalent smooth structures—is still unsolved.^[14]

Unsolved problems

Famous Unsolved Mysteries

Algebra

• 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
• The Dneister Notebook (Dnestrovskaya Tetrad) collects several hundred unresolved problems in algebra, particularly ring theory and modulus theory.^[15]
• The Erlagol Notebook (Erlagolskaya Tetrad) collects unresolved problems in algebra and model theory.^[16]

Algebraic geometry

• Hartshorne conjectures^[17]
• The Jacobian conjecture
• Maulik–Nekrasov–Okounkov–Pandharipande conjecture on an equivalence between Gromov–Witten theory and Donaldson–Thomas theory^[18]
• Resolution of singularities in characteristic ${\displaystyle p}$
• Standard conjectures on algebraic cycles
• Zariski multiplicity conjecture^[19]

Analysis

• The four exponentials conjecture on the transcendence of at least one of four exponentials of combinations of irrationals^[20]
• Lehmer's conjecture on the Mahler measure of non-cyclotomic polynomials^[21]
• The Pompeiu problem on the topology of domains for which some nonzero function has integrals that vanish over every congruent copy^[22]
• Schanuel's conjecture on the transcendence degree of exponentials of linearly independent irrationals^[20]
• Are ${\displaystyle \gamma }$ (the Euler–Mascheroni constant), π + e, π − e, πe, π/e, π^e, π^√2, π^π, e^π2, lnπ, 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?^[23][24][25]
• Kung–Traub conjecture^[26]

Combinatorics

• Frankl's union-closed sets conjecture: for any family of sets closed under sums there exists an element (of the underlying space) belonging to half or more of the sets^[27]
• The lonely runner conjecture: if ${\displaystyle k+1}$ runners with pairwise distinct speeds run round a track of unit length, will every runner be 'lonely' (that is, be at least a distance ${\displaystyle 1/(k+1)}$ from each other runner) at some time?^[28]
• Singmaster's conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle?^[29]
• Finding a function to model n-step self-avoiding walks.^[30]
• 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?^[31]
• Give a combinatorial interpretation of the Kronecker coefficients.^[32]
• Open questions concerning Latin squares

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^[33]
• The Hopf conjectures relating the curvature and Euler characteristic of higher-dimensional Riemannian manifolds^[34]
• The spherical Bernstein's problem, a possible generalization of the original Bernstein's problem
• Closed curve problem: Find (explicit) necessary and sufficient conditions that determine when, given two periodic functions with the same period, the integral curve is closed.^[35]

Discrete geometry

• Solving the happy ending problem for arbitrary ${\displaystyle n}$^[36]
• Finding matching upper and lower bounds for k-sets and halving lines^[37]
• The Hadwiger conjecture on covering n-dimensional convex bodies with at most 2ⁿ smaller copies^[38]
• The Kobon triangle problem on triangles in line arrangements^[39]
• The McMullen problem on projectively transforming sets of points into convex position^[40]
• Tripod packing^[41]
• Ulam's packing conjecture about the identity of the worst-packing convex solid^[42]
• 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?^[43]
• Kissing number problem for dimensions other than 1, 2, 3, 4, 8 and 24^[44]
• How many unit distances can be determined by a set of n points in the Euclidean plane?^[45]

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^[46]
• Danzer's problem and Conway's dead fly problem – do Danzer sets of bounded density or bounded separation exist?^[47]
• Dissection into orthoschemes – is it possible for simplices of every dimension?^[48]
• The einstein problem – does there exist a two-dimensional shape that forms the prototile for an aperiodic tiling, but not for any periodic tiling?^[49]
• The Erdős–Oler conjecture that when ${\displaystyle n}$ is a triangular number, packing ${\displaystyle n-1}$ circles in an equilateral triangle requires a triangle of the same size as packing ${\displaystyle n}$ circles^[50]
• Falconer's conjecture that sets of Hausdorff dimension greater than ${\displaystyle d/2}$ in ${\displaystyle {\mathbb{R}}^d}$ must have a distance set of nonzero Lebesgue measure^[51]
• Inscribed square problem, also known as Toeplitz' conjecture – does every Jordan curve have an inscribed square?^[52]
• The Kakeya conjecture – do ${\displaystyle n}$-dimensional sets that contain a unit line segment in every direction necessarily have Hausdorff dimension and Minkowski dimension equal to ${\displaystyle n}$?^[53]
• 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^[54]
• Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one^[55]
• Moser's worm problem – what is the smallest area of a shape that can cover every unit-length curve in the plane?^[56]
• The moving sofa problem – what is the largest area of a shape that can be maneuvered through a unit-width L-shaped corridor?^[57]
• Shephard's problem (a.k.a. Dürer's conjecture) – does every convex polyhedron have a net?^[58]
• The Thomson problem – what is the minimum energy configuration of ${\displaystyle n}$ mutually-repelling particles on a unit sphere?^[59]
• Uniform 5-polytopes – find and classify the complete set of these shapes^[60]
• 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?^[61]

Dynamical systems

• Collatz conjecture (3n + 1 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 (asymptotical) stability of motion?
• Furstenberg conjecture – Is every invariant and ergodic measure for the ${\displaystyle \times 2,\times 3}$ 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 typelevel 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?^[62]
• Birkhoff conjecture: if a billiard table is strictly convex and integrable, is its boundary necessarily an ellipse?^[63]
• 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^[64]

Games and puzzles

Combinatorial games

• Sudoku:
  • What is the maximum number of givens for a minimal puzzle?^[65]
  • How many puzzles have exactly one solution?^[65]
  • How many minimal puzzles have exactly one solution?^[65]
• 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?^[66]
• What is the Turing completeness status of all unique elementary cellular automata?

Games with imperfect information

Graph theory

Paths and cycles in graphs

• Barnette's conjecture that every cubic bipartite three-connected planar graph has a Hamiltonian cycle^[67]
• Chvátal's toughness conjecture, that there is a number t such that every t-tough graph is Hamiltonian^[68]
• The cycle double cover conjecture that every bridgeless graph has a family of cycles that includes each edge twice^[69]
• The Erdős–Gyárfás conjecture on cycles with power-of-two lengths in cubic graphs^[70]
• The linear arboricity conjecture on decomposing graphs into disjoint unions of paths according to their maximum degree^[71]
• The Lovász conjecture on Hamiltonian paths in symmetric graphs^[72]
• 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.^[73]

Graph coloring and labeling

• The Erdős–Faber–Lovász conjecture on coloring unions of cliques^[74]
• The Gyárfás–Sumner conjecture on χ-boundedness of graphs with a forbidden induced tree^[75]
• The Hadwiger conjecture relating coloring to clique minors^[76]
• The Hadwiger–Nelson problem on the chromatic number of unit distance graphs^[77]
• Jaeger's Petersen-coloring conjecture that every bridgeless cubic graph has a cycle-continuous mapping to the Petersen graph^[78]
• The list coloring conjecture that, for every graph, the list chromatic index equals the chromatic index^[79]
• The Ringel–Kotzig conjecture on graceful labeling of trees^[80]
• The total coloring conjecture of Behzad and Vizing that the total chromatic number is at most two plus the maximum degree^[81]

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^[82]
• The Blankenship–Oporowski conjecture on the book thickness of subdivisions^[83]
• Conway's thrackle conjecture^[84]
• Harborth's conjecture that every planar graph can be drawn with integer edge lengths^[85]
• Negami's conjecture on projective-plane embeddings of graphs with planar covers^[86]
• The strong Papadimitriou–Ratajczak conjecture that every polyhedral graph has a convex greedy embedding^[87]
• Turán's brick factory problem – Is there a drawing of any complete bipartite graph with fewer crossings than the number given by Zarankiewicz?^[88]
• Universal point sets of subquadratic size for planar graphs^[89]

Miscellaneous graph theory

• Conway's 99-graph problem: does there exist a strongly regular graph with parameters (99,14,1,2)?^[90]
• The Erdős–Hajnal conjecture on large cliques or independent sets in graphs with a forbidden induced subgraph^[91]
• The GNRS conjecture on whether minor-closed graph families have ${\displaystyle {\ell }_1}$ embeddings with bounded distortion^[92]
• The implicit graph conjecture on the existence of implicit representations for slowly-growing hereditary families of graphs^[93]
• Jørgensen's conjecture that every 6-vertex-connected K₆-minor-free graph is an apex graph^[94]
• Meyniel's conjecture that cop number is ${\displaystyle O(\sqrt{n})}$^[95]
• Does a Moore graph with girth 5 and degree 57 exist?^[96]
• What is the largest possible pathwidth of an n-vertex cubic graph?^[97]
• The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted subgraphs.^[98][99]
• 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?^[100]
• Sumner's conjecture: does every ${\displaystyle (2n-2)}$-vertex tournament contain as a subgraph every ${\displaystyle n}$-vertex oriented tree?^[101]
• 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^[102]
• Vizing's conjecture on the domination number of cartesian products of graphs^[103]

Group theory

• Is every finitely presentedperiodic 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 groupB(m,n) finite? In particular, is B(2, 5) finite?
• Is every group surjunctive?
• Does generalized moonshine exist?
• Are there an infinite number of Leinster groups?
• Guralnick–Thompson conjecture^[104]
• 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.^[105]
• The Sverdlovsk Notebook is a collection of unsolved problems in semigroup theory.^[106][107]

Model theory and formal languages

• The Cherlin–Zilber conjecture: A simple group whose first-order theory is stable in ${\displaystyle {\mathrm{\aleph }}_0}$ 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 ${\displaystyle {\mathrm{\aleph }}_1}$-saturated models of a countable theory.^[108]
• Determine the structure of Keisler's order^[109][110]
• 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 ${\displaystyle {\mathbb{Z}}_p}$decidable? of the field of polynomials over ${\displaystyle \mathbb{C}}$?
• (BMTO) Is the Borel monadic theory of the real order decidable? (MTWO) Is the monadic theory of well-ordering consistently decidable?^[111]
• The Stable Forking Conjecture for simple theories^[112]
• 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 ${\displaystyle {\mathrm{\aleph }}_{{\omega }_1}}$ does it have a model of cardinality continuum?^[113]
• Shelah's eventual categoricity conjecture: For every cardinal ${\displaystyle \lambda }$ there exists a cardinal ${\displaystyle \mu (\lambda )}$ such that If an AEC K with LS(K)<= ${\displaystyle \lambda }$ is categorical in a cardinal above ${\displaystyle \mu (\lambda )}$ then it is categorical in all cardinals above ${\displaystyle \mu (\lambda )}$.^[108][114]
• Shelah's categoricity conjecture for ${\displaystyle L_{{\omega }_1,\omega }}$: If a sentence is categorical above the Hanf number then it is categorical in all cardinals above the Hanf number.^[108]
• Is there a logic L which satisfies both the Beth property and Δ-interpolation, is compact but does not satisfy the interpolation property?^[115]
• If the class of atomic models of a complete first order theory is categorical in the ${\displaystyle {\mathrm{\aleph }}_n}$, is it categorical in every cardinal?^[116][117]
• Is every infinite, minimal field of characteristic zero algebraically closed? (Here, 'minimal' means that every definable subset of the structure is finite or co-finite.)
• Kueker's conjecture^[118]
• Does there exist an o-minimal first order theory with a trans-exponential (rapid growth) 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?^[119]
• The universality spectrum problem: Is there a first-order theory whose universality spectrum is minimum?^[120]

Number theory

General

• Grand Riemann hypothesis
  • Generalized Riemann hypothesis
• n conjecture
• Lindelöf hypothesis and its consequence, the density hypothesis for zeroes of the Riemann zeta function (see Bombieri–Vinogradov theorem)
• 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?
• Do any Taxicab(5, 2, n) exist for n > 1?
• Brocard's problem: existence of integers, (n,m), such that n! + 1 = m² other than n = 4, 5, 7
• Congruent number problem (a corollary to Birch and Swinnerton-Dyer conjecture, per Tunnell's theorem)
• Lehmer's totient problem: if φ(n) 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 primeamicable 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
• Is π a normal number (its digits are 'random')?^[121]
• Find value of De Bruijn–Newman constant
• Which integers can be written as the sum of three perfect cubes?^[122]
• Erdős–Moser problem: is 1¹ + 2¹ = 3¹ the only solution to the Erdős–Moser equation?
• Is there a covering system with odd distinct moduli?^[123]
• The uniqueness conjecture for Markov numbers^[124]
• Keating–Snaith conjecture concerning the asymptotics of an integral involving the Riemann zeta function^[125]

Additive number theory

• The values of g(k) and G(k) in Waring's problem
• Determine growth rate of r_k(N) (see Szemerédi's theorem)
• Do the Ulam numbers have a positive density?

Algebraic number theory

• Are there infinitely many real quadratic number fields with unique factorization (Class number problem)?
• Characterize all algebraic number fields that have some power basis.
• Stark conjectures (including Brumer–Stark conjecture)

Computational number theory

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

Prime numbers

• 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?
• Are there infinitely many prime quadruplets?
• Are there infinitely many cousin primes?
• Are there infinitely many sexy primes?
• Are there infinitely many Mersenne primes (Lenstra–Pomerance–Wagstaff conjecture); 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 ${\displaystyle e^{-1/2}}$?
• 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 (mod c²)?
• For any given integer a > 0, are there infinitely many primes p such that a^{p − 1} ≡ 1 (mod p²)?^[126]
• Can a prime p satisfy 2^{p − 1} ≡ 1 (mod p²) and 3^{p − 1} ≡ 1 (mod p²) simultaneously?^[127]
• 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 (a, −1)? (Specially, when a = 1, this is the Fibonacci-Wieferich primes, and when a = 2, this is the Pell-Wieferich primes)
• Is every Fermat number 2²ⁿ + 1 composite for ${\displaystyle n>4}$?
• 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?
• Is 78,557 the lowest Sierpiński number (so-called Selfridge's conjecture)?
• Is 509,203 the lowest Riesel number?
• Fortune's conjecture (that no Fortunate number is composite)
• Does every prime number appear in the Euclid–Mullin sequence?
• Does the converse of Wolstenholme's theorem hold for all natural numbers?
• Problems associated to Linnik's theorem
• Find the smallest Skewes' number

Partial differential equations

• Regularity of solutions of Vlasov–Maxwell equations
• Regularity of solutions of Euler equations

Ramsey theory

• The values of the Ramsey numbers, particularly ${\displaystyle R(5,5)}$
• The values of the Van der Waerden numbers

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 (see Singular cardinals hypothesis). The best bound, ℵ_ω4, was obtained by Shelah using his pcf theory.
• Woodin'sΩ-hypothesis.
• Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal?
• (Woodin) 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 embeddingV→V exist?
• Does the Generalized Continuum Hypothesis entail ${\displaystyle \mathrm{♢}(E_{\mathrm{cf}(\lambda )}^{{\lambda }^{+}})}$ for every singular cardinal${\displaystyle \lambda }$?
• Does the Generalized Continuum Hypothesis imply the existence of an ℵ₂-Suslin tree?
• Is OCA (Open coloring axiom) consistent with ${\displaystyle 2^{{\mathrm{\aleph }}_0}>{\mathrm{\aleph }}_2}$?
• Assume ZF and that whenever there is a surjection from ${\displaystyle A}$ onto ${\displaystyle B}$ there is an injection from ${\displaystyle B}$ into ${\displaystyle A}$. Does the Axiom of Choice hold?^[128]

Topology

• Mazur's conjectures^[129]

Problems solved since 1995

• Duffin-Schaeffer conjecture (Dimitris Koukoulopoulos, James Maynard, 2019)
• Hedetniemi's conjecture on the chromatic number of tensor products of graphs (Yaroslav Shitov, 2019)^[130]
• Erdős sumset conjecture (Joel Moreira, Florian Richter, Donald Robertson, 2018)^[131]
• McMullen's g-conjecture on the possible numbers of faces of different dimensions in a simplicial sphere (also Grünbaum conjecture, several conjectures of Kühnel)(Karim Adiprasito, 2018)^[132][133]
• Pentagonal tiling (Michaël Rao, 2017)^[134]
• Erdős–Burr conjecture (Choongbum Lee, 2017)^[135]
• Boolean Pythagorean triples problem (Marijn Heule, Oliver Kullmann, Victor Marek, 2016)^[136][137]
• It was shown that the problem of theoretical determination of the presence or absence of a gap in the spectrum in the general case is algorithmically unsolvable (2015)^[138].
• Babai's problem (Problem 3.3 in 'Spectra of Cayley graphs') (Alireza Abdollahi, Maysam Zallaghi, 2015)^[139]
• Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian Demeter, Larry Guth, 2015)^[140]
• Erdős discrepancy problem (Terence Tao, 2015)^[141]
• Umbral moonshine conjecture (John F. R. Duncan, Michael J. Griffin, Ken Ono, 2015)^[142]
• Anderson conjecture (Cheeger, Naber, 2014)^[143]
• Gaussian correlation inequality (Thomas Royen, 2014)^[144]
• Goldbach's weak conjecture (Harald Helfgott, 2013)^{[145][146][147]}
• Kadison–Singer problem (Adam Marcus, Daniel Spielman and Nikhil Srivastava, 2013)^[148][149] (and the Feichtinger's conjecture, Anderson’s paving conjectures, Weaver’s discrepancy theoretic ${\displaystyle K{S}_r}$ and conjectures, Bourgain-Tzafriri conjecture and ${\displaystyle R_{ϵ}}$-conjecture)
• Virtual Haken conjecture (Agol, Groves, Manning, 2012)^[150] (and by work of Wise also virtually fibered conjecture)
• Hsiang–Lawson's conjecture (Brendle, 2012)^[151]
• Willmore conjecture (Fernando Codá Marques and André Neves, 2012)^[152]
• Beck's 3-permutations conjecture (Newman, Nikolov, 2011)^[153]
• Ehrenpreis conjecture (Kahn, Markovic, 2011)^[154]
• Hanna Neumann conjecture (Mineyev, 2011)^[155]
• Bloch–Kato conjecture (Voevodsky, 2011)^[156] (and Quillen–Lichtenbaum conjecture and by work of Geisser and Levine (2001) also Beilinson–Lichtenbaum conjecture^{[157][158][159]})
• Erdős distinct distances problem (Larry Guth, Netz Hawk Katz, 2011)^[160]
• Density theorem (Namazi, Souto, 2010)^[161]
• Hirsch conjecture (Francisco Santos Leal, 2010)^[162][163]
• Sidon set problem (J. Cilleruelo, I. Ruzsa and C. Vinuesa, 2010)^[164]
• Atiyah conjecture (Austin, 2009)^[165]
• Kauffman–Harary conjecture (Matmann, Solis, 2009)^[166]
• Surface subgroup conjecture (Kahn, Markovic, 2009)^[167]
• Scheinerman's conjecture (Jeremie Chalopin and Daniel Gonçalves, 2009)^[168]
• Cobordism hypothesis (Jacob Lurie, 2008)^[169]
• Full classification of finite simple groups (Harada, Solomon, 2008)
• Geometrization conjecture, proven by Grigori Perelman^[170] in a series of preprints in 2002-2003^[171].
• Serre's modularity conjecture (Chandrashekhar Khare and Jean-Pierre Wintenberger, 2008)^{[172][173][174]}
• Heterogeneous tiling conjecture (squaring the plane) (Frederick V. Henle and James M. Henle, 2008)^[175]
• Normal scalar curvature conjecture and the Böttcher–Wenzel conjecture (Lu, 2007)^[176]
• Erdős–Menger conjecture (Aharoni, Berger 2007)^[177]
• Road coloring conjecture (Avraham Trahtman, 2007)^[178]
• The angel problem (Various independent proofs, 2006)^{[179][180][181][182]}
• Nirenberg–Treves conjecture (Nils Dencker, 2005)^[183][184]
• Lax conjecture (Lewis, Parrilo, Ramana, 2005)^[185]
• The Langlands–Shelstad fundamental lemma (Ngô Bảo Châu and Gérard Laumon, 2004)^[186]
• Tameness conjecture and Ahlfors measure conjecture (Ian Agol, 2004)^[187]
• Robertson–Seymour theorem (Robertson, Seymour, 2004)^[188]
• Stanley–Wilf conjecture (Gábor Tardos and Adam Marcus, 2004)^[189] (and also Alon–Friedgut conjecture)
• Green–Tao theorem (Ben J. Green and Terence Tao, 2004)^[190]
• Ending lamination theorem (Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky, 2004)^[191]
• Carpenter's rule problem (Connelly, Demaine, Rote, 2003)^[192]
• Cameron–Erdős conjecture (Ben J. Green, 2003, Alexander Sapozhenko, 2003)^[193][194]
• Milnor conjecture (Vladimir Voevodsky, 2003)^[195]
• Kemnitz's conjecture (Reiher, 2003, di Fiore, 2003)^[196]
• Nagata's conjecture (Shestakov, Umirbaev, 2003)^[197]
• Kirillov's conjecture (Baruch, 2003)^[198]
• Poincaré conjecture (Grigori Perelman, 2002)^[170]
• Strong perfect graph conjecture (Maria Chudnovsky, Neil Robertson, Paul Seymour and Robin Thomas, 2002)^[199]
• Kouchnirenko’s conjecture (Haas, 2002)^[200]
• Vaught conjecture (Knight, 2002)^[201]
• Double bubble conjecture (Hutchings, Morgan, Ritoré, Ros, 2002)^[202]
• Catalan's conjecture (Preda Mihăilescu, 2002)^[203]
• n! conjecture (Haiman, 2001)^[204] (and also Macdonald positivity conjecture)
• Kato's conjecture (Auscher, Hofmann, Lacey, McIntosh and Tchamitchian, 2001)^[205]
• Deligne's conjecture on 1-motives (Luca Barbieri-Viale, Andreas Rosenschon, Morihiko Saito, 2001)^[206]
• Modularity theorem (Breuil, Conrad, Diamond and Taylor, 2001)^[207]
• Erdős–Stewart conjecture (Florian Luca, 2001)^[208]
• Berry–Robbins problem (Atiyah, 2000)^[209]
• Erdős–Graham problem (Croot, 2000)^[210]
• Honeycomb conjecture (Thomas Hales, 1999)^[211]
• Gradient conjecture (Krzysztof Kurdyka, Tadeusz Mostowski, Adam Parusinski, 1999)^[212]
• Bogomolov conjecture (Emmanuel Ullmo, 1998, Shou-Wu Zhang, 1998)^[213][214]
• Lafforgue's theorem (Laurent Lafforgue, 1998)^[215]
• Kepler conjecture (Ferguson, Hales, 1998)^[216]
• Dodecahedral conjecture (Hales, McLaughlin, 1998)^[217]
• Ganea conjecture (Iwase, 1997)^[218]
• Torsion conjecture (Merel, 1996)^[219]
• Harary's conjecture (Chen, 1996)^[220]
• Fermat's Last Theorem (Andrew Wiles and Richard Taylor, 1995)^[221][222]

See also

References

1. ^Eves, An Introduction to the History of Mathematics 6th Edition, Thomson, 1990, ISBN978-0-03-029558-4.
2. ^Thiele, Rüdiger (2005), 'On Hilbert and his twenty-four problems', in Van Brummelen, Glen (ed.), Mathematics and the historian's craft. The Kenneth O. May Lectures, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 21, pp. 243–295, ISBN978-0-387-25284-1
3. ^Guy, Richard (1994), Unsolved Problems in Number Theory (2nd ed.), Springer, p. vii, ISBN978-1-4899-3585-4, archived from the original on 2019-03-23, retrieved 2016-09-22.
4. ^Shimura, G. (1989). 'Yutaka Taniyama and his time'. Bulletin of the London Mathematical Society. 21 (2): 186–196. doi:10.1112/blms/21.2.186. Archived from the original on 2016-01-25. Retrieved 2015-01-15.
5. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-02-08. Retrieved 2016-01-22.CS1 maint: Archived copy as title (link)
6. ^'THREE DIMENSIONAL MANIFOLDS, KLEINIAN GROUPS AND HYPERBOLIC GEOMETRY'(PDF). Archived(PDF) from the original on 2016-04-10. Retrieved 2016-02-09.
7. ^ ^ab'Millennium Problems'. Archived from the original on 2017-06-06. Retrieved 2015-01-20.
8. ^'Fields Medal awarded to Artur Avila'. Centre national de la recherche scientifique. 2014-08-13. Archived from the original on 2018-07-10. Retrieved 2018-07-07.
9. ^Bellos, Alex (2014-08-13). 'Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained'. The Guardian. Archived from the original on 2016-10-21. Retrieved 2018-07-07.
10. ^Abe, Jair Minoro; Tanaka, Shotaro (2001). Unsolved Problems on Mathematics for the 21st Century. IOS Press. ISBN978-9051994902.
11. ^'DARPA invests in math'. CNN. 2008-10-14. Archived from the original on 2009-03-04. Retrieved 2013-01-14.
12. ^'Broad Agency Announcement (BAA 07-68) for Defense Sciences Office (DSO)'. DARPA. 2007-09-10. Archived from the original on 2012-10-01. Retrieved 2013-06-25.
13. ^'Poincaré Conjecture'. Clay Mathematics Institute. Archived from the original on 2013-12-15.
14. ^'Smooth 4-dimensional Poincare conjecture'. Archived from the original on 2018-01-25. Retrieved 2019-08-06.
15. ^Dnestrovskaya notebook(PDF) (in Russian), The Russian Academy of Sciences, 1993
    'Dneister Notebook: Unsolved Problems in the Theory of Rings and Modules'(PDF), University of Saskatchewan, retrieved 2019-08-15
16. ^Erlagol notebook(PDF) (in Russian), The Novosibirsk State University, 2018
17. ^Barlet, Daniel; Peternell, Thomas; Schneider, Michael (1990). 'On two conjectures of Hartshorne's'. Mathematische Annalen. 286 (1–3): 13–25. doi:10.1007/BF01453563.
18. ^Maulik, Davesh; Nekrasov, Nikita; Okounov, Andrei; Pandharipande, Rahul (2004-06-05), Gromov–Witten theory and Donaldson–Thomas theory, I, arXiv:math/0312059
19. ^Zariski, Oscar (1971). 'Some open questions in the theory of singularities'. Bulletin of the American Mathematical Society. 77 (4): 481–491. doi:10.1090/S0002-9904-1971-12729-5. MR0277533.
20. ^ ^abWaldschmidt, Michel (2013), Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables, Springer, pp. 14, 16, ISBN9783662115695
21. ^Smyth, Chris (2008), 'The Mahler measure of algebraic numbers: a survey', in McKee, James; Smyth, Chris (eds.), Number Theory and Polynomials, London Mathematical Society Lecture Note Series, 352, Cambridge University Press, pp. 322–349, ISBN978-0-521-71467-9
22. ^Berenstein, Carlos A. (2001) [1994], 'Pompeiu problem', in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN978-1-55608-010-4
23. ^For background on the numbers that are the focus of this problem, see articles by Eric W. Weisstein, on pi ([1]Archived 2014-12-06 at the Wayback Machine), e ([2]Archived 2014-11-21 at the Wayback Machine), Khinchin's Constant ([3]Archived 2014-11-05 at the Wayback Machine), irrational numbers ([4]Archived 2015-03-27 at the Wayback Machine), transcendental numbers ([5]Archived 2014-11-13 at the Wayback Machine), and irrationality measures ([6]Archived 2015-04-21 at the Wayback Machine) at Wolfram MathWorld, all articles accessed 15 December 2014.
24. ^Michel Waldschmidt, 2008, 'An introduction to irrationality and transcendence methods,' at The University of Arizona The Southwest Center for Arithmetic Geometry 2008 Arizona Winter School, March 15–19, 2008 (Special Functions and Transcendence), see [7]Archived 2014-12-16 at the Wayback Machine, accessed 15 December 2014.
25. ^John Albert, posting date unknown, 'Some unsolved problems in number theory' [from Victor Klee & Stan Wagon, 'Old and New Unsolved Problems in Plane Geometry and Number Theory'], in University of Oklahoma Math 4513 course materials, see [8]Archived 2014-01-17 at the Wayback Machine, accessed 15 December 2014.
26. ^Kung, H. T.; Traub, Joseph Frederick (1974), 'Optimal order of one-point and multipoint iteration', Journal of the ACM, 21 (4): 643–651, doi:10.1145/321850.321860
27. ^Bruhn, Henning; Schaudt, Oliver (2015), 'The journey of the union-closed sets conjecture'(PDF), Graphs and Combinatorics, 31 (6): 2043–2074, arXiv:1309.3297, doi:10.1007/s00373-014-1515-0, MR3417215, archived(PDF) from the original on 2017-08-08, retrieved 2017-07-18
28. ^Tao, Terence (2017), 'Some remarks on the lonely runner conjecture', arXiv:1701.02048 [math.CO]
29. ^Singmaster, D. (1971), 'Research Problems: How often does an integer occur as a binomial coefficient?', American Mathematical Monthly, 78 (4): 385–386, doi:10.2307/2316907, JSTOR2316907, MR1536288.
30. ^Liśkiewicz, Maciej; Ogihara, Mitsunori; Toda, Seinosuke (2003-07-28). 'The complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and hypercubes'. Theoretical Computer Science. 304 (1): 129–156. doi:10.1016/S0304-3975(03)00080-X.
31. ^Brightwell, Graham R.; Felsner, Stefan; Trotter, William T. (1995), 'Balancing pairs and the cross product conjecture', Order, 12 (4): 327–349, CiteSeerX10.1.1.38.7841, doi:10.1007/BF01110378, MR1368815.
32. ^Murnaghan, F. D. (1938), 'The Analysis of the Direct Product of Irreducible Representations of the Symmetric Groups', American Journal of Mathematics, 60 (1): 44–65, doi:10.2307/2371542, JSTOR2371542, MR1507301, PMC1076971, PMID16577800
33. ^Katz, Mikhail G. (2007), Systolic geometry and topology, Mathematical Surveys and Monographs, 137, American Mathematical Society, Providence, RI, p. 57, doi:10.1090/surv/137, ISBN978-0-8218-4177-8, MR2292367
34. ^Rosenberg, Steven (1997), The Laplacian on a Riemannian Manifold: An introduction to analysis on manifolds, London Mathematical Society Student Texts, 31, Cambridge: Cambridge University Press, pp. 62–63, doi:10.1017/CBO9780511623783, ISBN978-0-521-46300-3, MR1462892
35. ^Barros, Manuel (1997), 'General Helices and a Theorem of Lancret', Proceedings of the American Mathematical Society, 125 (5): 1503–1509, doi:10.1090/S0002-9939-97-03692-7, JSTOR2162098
36. ^Morris, Walter D.; Soltan, Valeriu (2000), 'The Erdős-Szekeres problem on points in convex position—a survey', Bull. Amer. Math. Soc., 37 (4): 437–458, doi:10.1090/S0273-0979-00-00877-6, MR1779413; Suk, Andrew (2016), 'On the Erdős–Szekeres convex polygon problem', J. Amer. Math. Soc., 30 (4): 1047–1053, arXiv:1604.08657, doi:10.1090/jams/869
37. ^Dey, Tamal K. (1998), 'Improved bounds for planar k-sets and related problems', Discrete Comput. Geom., 19 (3): 373–382, doi:10.1007/PL00009354, MR1608878; Tóth, Gábor (2001), 'Point sets with many k-sets', Discrete Comput. Geom., 26 (2): 187–194, doi:10.1007/s004540010022, MR1843435.
38. ^Boltjansky, V.; Gohberg, I. (1985), '11. Hadwiger's Conjecture', Results and Problems in Combinatorial Geometry, Cambridge University Press, pp. 44–46.
39. ^Weisstein, Eric W.'Kobon Triangle'. MathWorld.
40. ^Matoušek, Jiří (2002), Lectures on discrete geometry, Graduate Texts in Mathematics, 212, Springer-Verlag, New York, p. 206, doi:10.1007/978-1-4613-0039-7, ISBN978-0-387-95373-1, MR1899299
41. ^Aronov, Boris; Dujmović, Vida; Morin, Pat; Ooms, Aurélien; Schultz Xavier da Silveira, Luís Fernando (2019), 'More Turán-type theorems for triangles in convex point sets', Electronic Journal of Combinatorics, 26 (1): P1.8, arXiv:1706.10193, Bibcode:2017arXiv170610193A, archived from the original on 2019-02-18, retrieved 2019-02-18
42. ^Gardner, Martin (1995), New Mathematical Diversions (Revised Edition), Washington: Mathematical Association of America, p. 251
43. ^Brass, Peter; Moser, William; Pach, János (2005), Research Problems in Discrete Geometry, New York: Springer, p. 45, ISBN978-0387-23815-9, MR2163782
44. ^Conway, John H.; Neil J.A. Sloane (1999), Sphere Packings, Lattices and Groups (3rd ed.), New York: Springer-Verlag, pp. 21–22, ISBN978-0-387-98585-5
45. ^Brass, Peter; Moser, William; Pach, János (2005), '5.1 The Maximum Number of Unit Distances in the Plane', Research problems in discrete geometry, Springer, New York, pp. 183–190, ISBN978-0-387-23815-9, MR2163782
46. ^Finch, S. R.; Wetzel, J. E. (2004), 'Lost in a forest', American Mathematical Monthly, 11 (8): 645–654, doi:10.2307/4145038, JSTOR4145038, MR2091541
47. ^Solomon, Yaar; Weiss, Barak (2016), 'Dense forests and Danzer sets', Annales Scientifiques de l'École Normale Supérieure, 49 (5): 1053–1074, arXiv:1406.3807, doi:10.24033/asens.2303, MR3581810; Conway, John H., Five $1,000 Problems (Update 2017)(PDF), On-Line Encyclopedia of Integer Sequences, archived(PDF) from the original on 2019-02-13, retrieved 2019-02-12
48. ^Brandts, Jan; Korotov, Sergey; Křížek, Michal; Šolc, Jakub (2009), 'On nonobtuse simplicial partitions'(PDF), SIAM Review, 51 (2): 317–335, Bibcode:2009SIAMR.51.317B, doi:10.1137/060669073, MR2505583, archived(PDF) from the original on 2018-11-04, retrieved 2018-11-22. See in particular Conjecture 23, p. 327.
49. ^Socolar, Joshua E. S.; Taylor, Joan M. (2012), 'Forcing nonperiodicity with a single tile', The Mathematical Intelligencer, 34 (1): 18–28, arXiv:1009.1419, doi:10.1007/s00283-011-9255-y, MR2902144
50. ^Melissen, Hans (1993), 'Densest packings of congruent circles in an equilateral triangle', American Mathematical Monthly, 100 (10): 916–925, doi:10.2307/2324212, JSTOR2324212, MR1252928
51. ^Arutyunyants, G.; Iosevich, A. (2004), 'Falconer conjecture, spherical averages and discrete analogs', in Pach, János (ed.), Towards a Theory of Geometric Graphs, Contemp. Math., 342, Amer. Math. Soc., Providence, RI, pp. 15–24, doi:10.1090/conm/342/06127, ISBN9780821834848, MR2065249
52. ^Matschke, Benjamin (2014), 'A survey on the square peg problem', Notices of the American Mathematical Society, 61 (4): 346–352, doi:10.1090/noti1100
53. ^Katz, Nets; Tao, Terence (2002), 'Recent progress on the Kakeya conjecture', Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), Publicacions Matemàtiques (Vol. Extra): 161–179, CiteSeerX10.1.1.241.5335, doi:10.5565/PUBLMAT_Esco02_07, MR1964819
54. ^Weaire, Denis, ed. (1997), The Kelvin Problem, CRC Press, p. 1, ISBN9780748406326
55. ^Brass, Peter; Moser, William; Pach, János (2005), Research problems in discrete geometry, New York: Springer, p. 457, ISBN9780387299297, MR2163782
56. ^Norwood, Rick; Poole, George; Laidacker, Michael (1992), 'The worm problem of Leo Moser', Discrete and Computational Geometry, 7 (2): 153–162, doi:10.1007/BF02187832, MR1139077
57. ^Wagner, Neal R. (1976), 'The Sofa Problem'(PDF), The American Mathematical Monthly, 83 (3): 188–189, doi:10.2307/2977022, JSTOR2977022, archived(PDF) from the original on 2015-04-20, retrieved 2014-05-14
58. ^Demaine, Erik D.; O'Rourke, Joseph (2007), 'Chapter 22. Edge Unfolding of Polyhedra', Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Cambridge University Press, pp. 306–338
59. ^Whyte, L. L. (1952), 'Unique arrangements of points on a sphere', The American Mathematical Monthly, 59 (9): 606–611, doi:10.2307/2306764, JSTOR2306764, MR0050303
60. ^ACW (May 24, 2012), 'Convex uniform 5-polytopes', Open Problem Garden, archived from the original on October 5, 2016, retrieved 2016-10-04.
61. ^Bereg, Sergey; Dumitrescu, Adrian; Jiang, Minghui (2010), 'On covering problems of Rado', Algorithmica, 57 (3): 538–561, doi:10.1007/s00453-009-9298-z, MR2609053
62. ^Kari, Jarkko (2009), 'Structure of reversible cellular automata', Unconventional Computation: 8th International Conference, UC 2009, Ponta Delgada, Portugal, September 7ÔÇô11, 2009, Proceedings, Lecture Notes in Computer Science, 5715, Springer, p. 6, Bibcode:2009LNCS.5715..6K, doi:10.1007/978-3-642-03745-0_5, ISBN978-3-642-03744-3
63. ^Kaloshin, Vadim; Sorrentino, Alfonso (2018). 'On the local Birkhoff conjecture for convex billiards'. Annals of Mathematics. 188 (1): 315–380. arXiv:1612.09194. doi:10.4007/annals.2018.188.1.6.
64. ^Sarnak, Peter (2011), 'Recent progress on the quantum unique ergodicity conjecture', Bulletin of the American Mathematical Society, 48 (2): 211–228, doi:10.1090/S0273-0979-2011-01323-4, MR2774090
65. ^ ^abchttp://english.log-it-ex.comArchived 2017-11-10 at the Wayback Machine Ten open questions about Sudoku (2012-01-21).
66. ^'Higher-Dimensional Tic-Tac-Toe'. PBS Infinite Series. YouTube. 2017-09-21. Archived from the original on 2017-10-11. Retrieved 2018-07-29.
67. ^Florek, Jan (2010), 'On Barnette's conjecture', Discrete Mathematics, 310 (10–11): 1531–1535, doi:10.1016/j.disc.2010.01.018, MR2601261.
68. ^Broersma, Hajo; Patel, Viresh; Pyatkin, Artem (2014), 'On toughness and Hamiltonicity of $2K_2$-free graphs', Journal of Graph Theory, 75 (3): 244–255, doi:10.1002/jgt.21734, MR3153119
69. ^Jaeger, F. (1985), 'A survey of the cycle double cover conjecture', Annals of Discrete Mathematics 27 – Cycles in Graphs, North-Holland Mathematics Studies, 27, pp. 1–12, doi:10.1016/S0304-0208(08)72993-1, ISBN9780444878038.
70. ^Heckman, Christopher Carl; Krakovski, Roi (2013), 'Erdös-Gyárfás conjecture for cubic planar graphs', Electronic Journal of Combinatorics, 20 (2), P7, archived from the original on 2016-10-06, retrieved 2016-09-22.
71. ^Akiyama, Jin; Exoo, Geoffrey; Harary, Frank (1981), 'Covering and packing in graphs. IV. Linear arboricity', Networks, 11 (1): 69–72, doi:10.1002/net.3230110108, MR0608921.
72. ^L. Babai, Automorphism groups, isomorphism, reconstructionArchived 2007-06-13 at the Wayback Machine, in Handbook of Combinatorics, Vol. 2, Elsevier, 1996, 1447–1540.
73. ^Lenz, Hanfried; Ringel, Gerhard (1991), 'A brief review on Egmont Köhler's mathematical work', Discrete Mathematics, 97 (1–3): 3–16, doi:10.1016/0012-365X(91)90416-Y, MR1140782
74. ^Chung, Fan; Graham, Ron (1998), Erdős on Graphs: His Legacy of Unsolved Problems, A K Peters, pp. 97–99.
75. ^Chudnovsky, Maria; Seymour, Paul (2014), 'Extending the Gyárfás-Sumner conjecture', Journal of Combinatorial Theory, Series B, 105: 11–16, doi:10.1016/j.jctb.2013.11.002, MR3171779
76. ^Toft, Bjarne (1996), 'A survey of Hadwiger's conjecture', Congressus Numerantium, 115: 249–283, MR1411244.
77. ^Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1991), Unsolved Problems in Geometry, Springer-Verlag, Problem G10.
78. ^Hägglund, Jonas; Steffen, Eckhard (2014), 'Petersen-colorings and some families of snarks', Ars Mathematica Contemporanea, 7 (1): 161–173, doi:10.26493/1855-3974.288.11a, MR3047618, archived from the original on 2016-10-03, retrieved 2016-09-30.
79. ^Jensen, Tommy R.; Toft, Bjarne (1995), '12.20 List-Edge-Chromatic Numbers', Graph Coloring Problems, New York: Wiley-Interscience, pp. 201–202, ISBN978-0-471-02865-9.
80. ^Huang, C.; Kotzig, A.; Rosa, A. (1982), 'Further results on tree labellings', Utilitas Mathematica, 21: 31–48, MR0668845.
81. ^Molloy, Michael; Reed, Bruce (1998), 'A bound on the total chromatic number', Combinatorica, 18 (2): 241–280, CiteSeerX10.1.1.24.6514, doi:10.1007/PL00009820, MR1656544.
82. ^Barát, János; Tóth, Géza (2010), 'Towards the Albertson Conjecture', Electronic Journal of Combinatorics, 17 (1): R73, arXiv:0909.0413, Bibcode:2009arXiv0909.0413B, archived from the original on 2012-02-24, retrieved 2016-10-04.
83. ^Wood, David (January 19, 2009), 'Book Thickness of Subdivisions', Open Problem Garden, archived from the original on September 16, 2013, retrieved 2013-02-05.
84. ^Fulek, R.; Pach, J. (2011), 'A computational approach to Conway's thrackle conjecture', Computational Geometry, 44 (6–7): 345–355, arXiv:1002.3904, doi:10.1007/978-3-642-18469-7_21, MR2785903.
85. ^Hartsfield, Nora; Ringel, Gerhard (2013), Pearls in Graph Theory: A Comprehensive Introduction, Dover Books on Mathematics, Courier Dover Publications, p. 247, ISBN978-0-486-31552-2, MR2047103, archived from the original on 2017-03-01, retrieved 2016-10-28.
86. ^Hliněný, Petr (2010), '20 years of Negami's planar cover conjecture'(PDF), Graphs and Combinatorics, 26 (4): 525–536, CiteSeerX10.1.1.605.4932, doi:10.1007/s00373-010-0934-9, MR2669457, archived(PDF) from the original on 2016-03-04, retrieved 2016-10-04.
87. ^Nöllenburg, Martin; Prutkin, Roman; Rutter, Ignaz (2016), 'On self-approaching and increasing-chord drawings of 3-connected planar graphs', Journal of Computational Geometry, 7 (1): 47–69, arXiv:1409.0315, doi:10.20382/jocg.v7i1a3, MR3463906
88. ^Pach, János; Sharir, Micha (2009), '5.1 Crossings—the Brick Factory Problem', Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures, Mathematical Surveys and Monographs, 152, American Mathematical Society, pp. 126–127.
89. ^Demaine, E.; O'Rourke, J. (2002–2012), 'Problem 45: Smallest Universal Set of Points for Planar Graphs', The Open Problems Project, archived from the original on 2012-08-14, retrieved 2013-03-19.
90. ^Conway, John H., Five $1,000 Problems (Update 2017)(PDF), Online Encyclopedia of Integer Sequences, archived(PDF) from the original on 2019-02-13, retrieved 2019-02-12
91. ^Chudnovsky, Maria (2014), 'The Erdös–Hajnal conjecture—a survey'(PDF), Journal of Graph Theory, 75 (2): 178–190, arXiv:1606.08827, doi:10.1002/jgt.21730, MR3150572, Zbl1280.05086, archived(PDF) from the original on 2016-03-04, retrieved 2016-09-22.
92. ^Gupta, Anupam; Newman, Ilan; Rabinovich, Yuri; Sinclair, Alistair (2004), 'Cuts, trees and ${\displaystyle {\ell }_1}$-embeddings of graphs', Combinatorica, 24 (2): 233–269, doi:10.1007/s00493-004-0015-x, MR2071334
93. ^Spinrad, Jeremy P. (2003), '2. Implicit graph representation', Efficient Graph Representations, pp. 17–30, ISBN978-0-8218-2815-1.
94. ^'Jorgensen's Conjecture', Open Problem Garden, archived from the original on 2016-11-14, retrieved 2016-11-13.
95. ^Baird, William; Bonato, Anthony (2012), 'Meyniel's conjecture on the cop number: a survey', Journal of Combinatorics, 3 (2): 225–238, arXiv:1308.3385, doi:10.4310/JOC.2012.v3.n2.a6, MR2980752
96. ^Ducey, Joshua E. (2017), 'On the critical group of the missing Moore graph', Discrete Mathematics, 340 (5): 1104–1109, arXiv:1509.00327, doi:10.1016/j.disc.2016.10.001, MR3612450
97. ^Fomin, Fedor V.; Høie, Kjartan (2006), 'Pathwidth of cubic graphs and exact algorithms', Information Processing Letters, 97 (5): 191–196, doi:10.1016/j.ipl.2005.10.012, MR2195217
98. ^Schwenk, Allen (2012), 'Some History on the Reconstruction Conjecture'(PDF), Joint Mathematics Meetings, archived(PDF) from the original on 2015-04-09, retrieved 2018-11-26
99. ^Ramachandran, S. (1981), 'On a new digraph reconstruction conjecture', Journal of Combinatorial Theory, Series B, 31 (2): 143–149, doi:10.1016/S0095-8956(81)80019-6, MR0630977
100. ^Seymour's 2nd Neighborhood ConjectureArchived 2019-01-11 at the Wayback Machine, Open Problems in Graph Theory and Combinatorics, Douglas B. West.
101. ^Kühn, Daniela; Mycroft, Richard; Osthus, Deryk (2011), 'A proof of Sumner's universal tournament conjecture for large tournaments', Proceedings of the London Mathematical Society, Third Series, 102 (4): 731–766, arXiv:1010.4430, doi:10.1112/plms/pdq035, MR2793448, Zbl1218.05034.
102. ^4-flow conjectureArchived 2018-11-26 at the Wayback Machine and 5-flow conjectureArchived 2018-11-26 at the Wayback Machine, Open Problem Garden
103. ^Brešar, Boštjan; Dorbec, Paul; Goddard, Wayne; Hartnell, Bert L.; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. (2012), 'Vizing's conjecture: a survey and recent results', Journal of Graph Theory, 69 (1): 46–76, CiteSeerX10.1.1.159.7029, doi:10.1002/jgt.20565, MR2864622.
104. ^Aschbacher, Michael (1990), 'On Conjectures of Guralnick and Thompson', Journal of Algebra, 135 (2): 277–343, doi:10.1016/0021-8693(90)90292-V
105. ^Khukhro, Evgeny I.; Mazurov, Victor D. (2019), Unsolved Problems in Group Theory. The Kourovka Notebook, arXiv:1401.0300v16
106. ^The Sverdlovsk Notebook: collects unsolved problems in semigroup theory, Ural State University, 1979
107. ^The Sverdlovsk Notebook: collects unsolved problems in semigroup theory, Ural State University, 1989
108. ^ ^abcShelah S, Classification Theory, North-Holland, 1990
109. ^Keisler, HJ (1967). 'Ultraproducts which are not saturated'. J. Symb. Log. 32 (1): 23–46. doi:10.2307/2271240. JSTOR2271240.
110. ^Malliaris M, Shelah S, 'A dividing line in simple unstable theories.' https://arxiv.org/abs/1208.2140Archived 2017-08-02 at the Wayback Machine
111. ^Gurevich, Yuri, 'Monadic Second-Order Theories,' in J. Barwise, S. Feferman, eds., Model-Theoretic Logics (New York: Springer-Verlag, 1985), 479–506.
112. ^Peretz, Assaf (2006). 'Geometry of forking in simple theories'. Journal of Symbolic Logic Volume. 71 (1): 347–359. arXiv:math/0412356. doi:10.2178/jsl/1140641179.
113. ^Shelah, Saharon (1999). 'Borel sets with large squares'. Fundamenta Mathematicae. 159 (1): 1–50. arXiv:math/9802134. Bibcode:1998math...2134S.
114. ^Shelah, Saharon (2009). Classification theory for abstract elementary classes. College Publications. ISBN978-1-904987-71-0.
115. ^Makowsky J, 'Compactness, embeddings and definability,' in Model-Theoretic Logics, eds Barwise and Feferman, Springer 1985 pps. 645–715.
116. ^Baldwin, John T. (July 24, 2009). Categoricity(PDF). American Mathematical Society. ISBN978-0-8218-4893-7. Archived(PDF) from the original on July 29, 2010. Retrieved February 20, 2014.
117. ^Shelah, Saharon (2009). 'Introduction to classification theory for abstract elementary classes'. arXiv:0903.3428. Bibcode:2009arXiv0903.3428S.
118. ^Hrushovski, Ehud (1989). 'Kueker's conjecture for stable theories'. Journal of Symbolic Logic. 54 (1): 207–220. doi:10.2307/2275025. JSTOR2275025.
119. ^Cherlin, G.; Shelah, S. (May 2007). 'Universal graphs with a forbidden subtree'. Journal of Combinatorial Theory, Series B. 97 (3): 293–333. arXiv:math/0512218. doi:10.1016/j.jctb.2006.05.008.
120. ^Džamonja, Mirna, 'Club guessing and the universal models.' On PCF, ed. M. Foreman, (Banff, Alberta, 2004).
121. ^'Are the Digits of Pi Random? Berkeley Lab Researcher May Hold Key'. Archived from the original on 2016-03-27. Retrieved 2016-03-18.
122. ^Bruhn, Henning; Schaudt, Oliver (2016). 'Newer sums of three cubes'. arXiv:1604.07746v1 [math.NT].
123. ^Guo, Song; Sun, Zhi-Wei (2005), 'On odd covering systems with distinct moduli', Advances in Applied Mathematics, 35 (2): 182–187, arXiv:math/0412217, doi:10.1016/j.aam.2005.01.004, MR2152886
124. ^Aigner, Martin (2013), Markov's theorem and 100 years of the uniqueness conjecture, Cham: Springer, doi:10.1007/978-3-319-00888-2, ISBN978-3-319-00887-5, MR3098784
125. ^Conrey, Brian, 'Lectures on the Riemann zeta function (book review)', Bulletin of the American Mathematical Society, 53 (3): 507–512, doi:10.1090/bull/1525
126. ^Ribenboim, P. (2006). Die Welt der Primzahlen. Springer-Lehrbuch (in German) (2nd ed.). Springer. pp. 242–243. doi:10.1007/978-3-642-18079-8. ISBN978-3-642-18078-1.
127. ^Dobson, J. B. (1 April 2017), 'On Lerch's formula for the Fermat quotient', p. 23, arXiv:1103.3907v6 [math.NT]
128. ^Banaschewski, Bernhard; Moore, Gregory H. (June 1990). 'The dual Cantor-Bernstein theorem and the partition principle'. Notre Dame Journal of Formal Logic. 31 (3): 375–381. doi:10.1305/ndjfl/1093635502.
129. ^Mazur, Barry (1992), 'The topology of rational points', Experimental Mathematics, 1 (1): 35–45, doi:10.1080/10586458.1992.10504244 (inactive 2019-08-20), archived from the original on 2019-04-07, retrieved 2019-04-07
130. ^Shitov, Yaroslav (May 2019). 'Counterexamples to Hedetniemi's conjecture'. arXiv:1905.02167.
131. ^Moreira, Joel; Richter, Florian K.; Robertson, Donald (2019). 'A proof of a sumset conjecture of Erdős'. Annals of Mathematics. 189 (2): 605–652. doi:10.4007/annals.2019.189.2.4.
132. ^Stanley, Richard P. (1994), 'A survey of Eulerian posets', in Bisztriczky, T.; McMullen, P.; Schneider, R.; Weiss, A. Ivić (eds.), Polytopes: abstract, convex and computational (Scarborough, ON, 1993), NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, 440, Dordrecht: Kluwer Academic Publishers, pp. 301–333, MR1322068. See in particular p. 316.
133. ^Kalai, Gil. 'Amazing: Karim Adiprasito proved the g-conjecture for spheres!'. Archived from the original on 2019-02-16. Retrieved 2019-02-15.
134. ^Wolchover, Natalie (July 11, 2017), 'Pentagon Tiling Proof Solves Century-Old Math Problem', Quanta Magazine, archived from the original on August 6, 2017, retrieved July 18, 2017
135. ^Lee, Choongbum (2017). 'Ramsey numbers of degenerate graphs'. Annals of Mathematics. 185 (3): 791–829. arXiv:1505.04773. doi:10.4007/annals.2017.185.3.2.
136. ^Lamb, Evelyn (26 May 2016). 'Two-hundred-terabyte maths proof is largest ever'. Nature. 534 (7605): 17–18. Bibcode:2016Natur.534..17L. doi:10.1038/nature.2016.19990. PMID27251254.
137. ^Heule, Marijn J. H.; Kullmann, Oliver; Marek, Victor W. (2016). 'Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer'. In Creignou, N.; Le Berre, D. (eds.). Theory and Applications of Satisfiability Testing – SAT 2016. Lecture Notes in Computer Science. 9710. Springer, [Cham]. pp. 228–245. arXiv:1605.00723. doi:10.1007/978-3-319-40970-2_15. ISBN978-3-319-40969-6. MR3534782.
138. ^Michael Wolf, Toby Cebitt, David Perez Garcia Unsolvable problem // In the world of science — 2018, № 12. — p. 46 — 59
139. ^Abdollahi A., Zallaghi M. (2015). 'Character sums for Cayley graphs'. Communications in Algebra. 43 (12): 5159–5167. doi:10.1080/00927872.2014.967398.
140. ^Bourgain, Jean; Ciprian, Demeter; Larry, Guth (2015). 'Proof of the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three'. Annals of Mathematics. 184 (2): 633–682. doi:10.4007/annals.2016.184.2.7. hdl:1721.1/115568.
141. ^Bruhn, Henning; Schaudt, Oliver (2015). 'The Erdos discrepancy problem'. arXiv:1509.05363v5 [math.CO].
142. ^Duncan, John F. R.; Griffin, Michael J.; Ono, Ken (1 December 2015). 'Proof of the umbral moonshine conjecture'. Research in the Mathematical Sciences. 2 (1): 26. doi:10.1186/s40687-015-0044-7.
143. ^Bruhn, Henning; Schaudt, Oliver (2014). 'Regularity of Einstein Manifolds and the Codimension 4 Conjecture'. arXiv:1406.6534v10 [math.DG].
144. ^'A Long-Sought Proof, Found and Almost Lost'. Quanta Magazine. Natalie Wolchover. March 28, 2017. Archived from the original on April 24, 2017. Retrieved May 2, 2017.
145. ^Helfgott, Harald A. (2013). 'Major arcs for Goldbach's theorem'. arXiv:1305.2897 [math.NT].
146. ^Helfgott, Harald A. (2012). 'Minor arcs for Goldbach's problem'. arXiv:1205.5252 [math.NT].
147. ^Helfgott, Harald A. (2013). 'The ternary Goldbach conjecture is true'. arXiv:1312.7748 [math.NT].
148. ^Casazza, Peter G.; Fickus, Matthew; Tremain, Janet C.; Weber, Eric (2006). 'The Kadison-Singer problem in mathematics and engineering: A detailed account'. In Han, Deguang; Jorgensen, Palle E. T.; Larson, David Royal (eds.). Large Deviations for Additive Functionals of Markov Chains: The 25th Great Plains Operator Theory Symposium, June 7–12, 2005, University of Central Florida, Florida. Contemporary Mathematics. 414. American Mathematical Society. pp. 299–355. doi:10.1090/conm/414/07820. ISBN978-0-8218-3923-2. Retrieved 24 April 2015.
149. ^Mackenzie, Dana. 'Kadison–Singer Problem Solved'(PDF). SIAM News (January/February 2014). Society for Industrial and Applied Mathematics. Archived(PDF) from the original on 23 October 2014. Retrieved 24 April 2015.
150. ^Bruhn, Henning; Schaudt, Oliver (2012). 'The virtual Haken conjecture'. arXiv:1204.2810v1 [math.GT].
151. ^Lee, Choongbum (2012). 'Embedded minimal tori in S^3 and the Lawson conjecture'. arXiv:1203.6597v2 [math.DG].
152. ^Marques, Fernando C.; Neves, André (2013). 'Min-max theory and the Willmore conjecture'. Annals of Mathematics. 179 (2): 683–782. arXiv:1202.6036. doi:10.4007/annals.2014.179.2.6.
153. ^Lee, Choongbum (2011). 'A counterexample to Beck's conjecture on the discrepancy of three permutations'. arXiv:1104.2922 [cs.DM].
154. ^Bruhn, Henning; Schaudt, Oliver (2011). 'The good pants homology and the Ehrenpreis conjecture'. arXiv:1101.1330v4 [math.GT].
155. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-10-07. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
156. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-27. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
157. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-10-07. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
158. ^'page 359'(PDF). Archived(PDF) from the original on 2016-03-27. Retrieved 2016-03-18.
159. ^'motivic cohomology – Milnor–Bloch–Kato conjecture implies the Beilinson-Lichtenbaum conjecture – MathOverflow'. Retrieved 2016-03-18.
160. ^Bruhn, Henning; Schaudt, Oliver (2010). 'On the Erdos distinct distance problem in the plane'. arXiv:1011.4105v3 [math.CO].
161. ^Namazi, Hossein; Souto, Juan (2012). 'Non-realizability and ending laminations: Proof of the density conjecture'. Acta Mathematica. 209 (2): 323–395. doi:10.1007/s11511-012-0088-0.
162. ^Santos, Franciscos (2012). 'A counterexample to the Hirsch conjecture'. Annals of Mathematics. 176 (1): 383–412. arXiv:1006.2814. doi:10.4007/annals.2012.176.1.7.
163. ^Ziegler, Günter M. (2012). 'Who solved the Hirsch conjecture?'. Documenta Mathematica. Extra Volume 'Optimization Stories': 75–85. Archived from the original on 2015-04-02. Retrieved 2015-03-25.
164. ^Cilleruelo, Javier (2010). 'Generalized Sidon sets'. Advances in Mathematics. 225 (5): 2786–2807. doi:10.1016/j.aim.2010.05.010.
165. ^Bruhn, Henning; Schaudt, Oliver (2009). 'Rational group ring elements with kernels having irrational dimension'. Proceedings of the London Mathematical Society. 107 (6): 1424–1448. arXiv:0909.2360v3. doi:10.1112/plms/pdt029.
166. ^Bruhn, Henning; Schaudt, Oliver (2009). 'A proof of the Kauffman-Harary Conjecture'. Algebr. Geom. Topol. 9 (4): 2027–2039. arXiv:0906.1612v2. doi:10.2140/agt.2009.9.2027.
167. ^Bruhn, Henning; Schaudt, Oliver (2009). 'Immersing almost geodesic surfaces in a closed hyperbolic three manifold'. arXiv:0910.5501v5 [math.GT].
168. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-03. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
169. ^Lurie, Jacob (2009). 'On the classification of topological field theories'. Current Developments in Mathematics. 2008: 129–280. doi:10.4310/cdm.2008.v2008.n1.a3.
170. ^ ^ab'Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman'(PDF) (Press release). Clay Mathematics Institute. March 18, 2010. Archived from the original on March 22, 2010. Retrieved November 13, 2015. The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman.
171. ^Bruhn, Henning; Schaudt, Oliver (2008). 'Completion of the Proof of the Geometrization Conjecture'. arXiv:0809.4040 [math.DG].
172. ^Khare, Chandrashekhar; Wintenberger, Jean-Pierre (2009), 'Serre's modularity conjecture (I)', Inventiones Mathematicae, 178 (3): 485–504, Bibcode:2009InMat.178.485K, CiteSeerX10.1.1.518.4611, doi:10.1007/s00222-009-0205-7
173. ^Khare, Chandrashekhar; Wintenberger, Jean-Pierre (2009), 'Serre's modularity conjecture (II)', Inventiones Mathematicae, 178 (3): 505–586, Bibcode:2009InMat.178.505K, CiteSeerX10.1.1.228.8022, doi:10.1007/s00222-009-0206-6
174. ^'2011 Cole Prize in Number Theory'(PDF). Notices of the AMS. 58 (4): 610–611. ISSN1088-9477. OCLC34550461. Archived(PDF) from the original on 2015-11-06. Retrieved 2015-11-12.
175. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-24. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
176. ^Lu, Zhiqin (2007). 'Proof of the normal scalar curvature conjecture'. arXiv:0711.3510 [math.DG].
177. ^Bruhn, Henning; Schaudt, Oliver (2005). 'Menger's theorem for infinite graphs'. arXiv:math/0509397.
178. ^Seigel-Itzkovich, Judy (2008-02-08). 'Russian immigrant solves math puzzle'. The Jerusalem Post. Retrieved 2015-11-12.
179. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-04. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
180. ^'Archived copy'(PDF). Archived from the original(PDF) on 2016-01-07. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
181. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-10-13. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
182. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-04. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
183. ^Dencker, Nils (2006), 'The resolution of the Nirenberg–Treves conjecture'(PDF), Annals of Mathematics, 163 (2): 405–444, doi:10.4007/annals.2006.163.405, archived(PDF) from the original on 2018-07-20, retrieved 2019-04-07
184. ^'Research Awards', Clay Mathematics Institute, archived from the original on 2019-04-07, retrieved 2019-04-07
185. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-04-06. Retrieved 2016-03-22.CS1 maint: Archived copy as title (link)
186. ^'Fields Medal – Ngô Bảo Châu'. International Congress of Mathematicians 2010. ICM. 19 August 2010. Archived from the original on 24 September 2015. Retrieved 2015-11-12. Ngô Bảo Châu is being awarded the 2010 Fields Medal for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods.
187. ^Bruhn, Henning; Schaudt, Oliver (2004). 'Tameness of hyperbolic 3-manifolds'. arXiv:math/0405568.
188. ^'Graph Theory'. Archived from the original on 2016-03-08. Retrieved 2016-03-18.
189. ^Chung, Fan; Greene, Curtis; Hutchinson, Joan (April 2015). 'Herbert S. Wilf (1931–2012)'(PDF). Notices of the AMS. 62 (4): 358. ISSN1088-9477. OCLC34550461. Archived(PDF) from the original on 2016-03-04. Retrieved 2015-11-13. The conjecture was finally given an exceptionally elegant proof by A. Marcus and G. Tardos in 2004.
190. ^'Bombieri and Tao Receive King Faisal Prize'(PDF). Notices of the AMS. 57 (5): 642–643. May 2010. ISSN1088-9477. OCLC34550461. Archived(PDF) from the original on 2016-03-04. Retrieved 2016-03-18. Working with Ben Green, he proved there are arbitrarily long arithmetic progressions of prime numbers—a result now known as the Green–Tao theorem.
191. ^Bruhn, Henning; Schaudt, Oliver (2004). 'The classification of Kleinian surface groups, II: The Ending Lamination Conjecture'. arXiv:math/0412006.
192. ^Connelly, Robert; Demaine, Erik D.; Rote, Günter (2003), 'Straightening polygonal arcs and convexifying polygonal cycles'(PDF), Discrete and Computational Geometry, 30 (2): 205–239, doi:10.1007/s00454-003-0006-7, MR1931840
193. ^Green, Ben (2004), 'The Cameron–Erdős conjecture', The Bulletin of the London Mathematical Society, 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR2083752
194. ^'News from 2007'. American Mathematical Society. AMS. 31 December 2007. Archived from the original on 17 November 2015. Retrieved 2015-11-13. The 2007 prize also recognizes Green for 'his many outstanding results including his resolution of the Cameron-Erdős conjecture..'
195. ^Voevodsky, Vladimir (2003). 'Reduced power operations in motivic cohomology'(PDF). Publications Mathématiques de l'IHÉS. 98: 1–57. arXiv:math/0107109. CiteSeerX10.1.1.170.4427. doi:10.1007/s10240-003-0009-z. Archived from the original on 2017-07-28. Retrieved 2016-03-18.
196. ^Savchev, Svetoslav (2005). 'Kemnitz' conjecture revisited'. Discrete Mathematics. 297 (1–3): 196–201. doi:10.1016/j.disc.2005.02.018.
197. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-08. Retrieved 2016-03-23.CS1 maint: Archived copy as title (link)
198. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-04-03. Retrieved 2016-03-20.CS1 maint: Archived copy as title (link)
199. ^Chudnovsky, Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2002). 'The strong perfect graph theorem'. arXiv:math/0212070.
200. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-10-07. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
201. ^Knight, R. W. (2002), The Vaught Conjecture: A Counterexample, manuscript
202. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-03-03. Retrieved 2016-03-22.CS1 maint: Archived copy as title (link)
203. ^Metsänkylä, Tauno (5 September 2003). 'Catalan's conjecture: another old diophantine problem solved'(PDF). Bulletin of the American Mathematical Society. 41 (1): 43–57. doi:10.1090/s0273-0979-03-00993-5. ISSN0273-0979. Archived(PDF) from the original on 4 March 2016. Retrieved 13 November 2015. The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihăilescu.
204. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-10-07. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
205. ^'Archived copy'(PDF). Archived from the original(PDF) on 2015-09-08. Retrieved 2016-03-18.CS1 maint: Archived copy as title (link)
206. ^Bruhn, Henning; Schaudt, Oliver (2001). 'Deligne's Conjecture on 1-Motives'. arXiv:math/0102150.
207. ^Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard (2001), 'On the modularity of elliptic curves over Q: wild 3-adic exercises', Journal of the American Mathematical Society, 14 (4): 843–939, doi:10.1090/S0894-0347-01-00370-8, ISSN0894-0347, MR1839918
208. ^Luca, Florian (2000). 'On a conjecture of Erdős and Stewart'(PDF). Mathematics of Computation. 70 (234): 893–897. doi:10.1090/s0025-5718-00-01178-9. Archived(PDF) from the original on 2016-04-02. Retrieved 2016-03-18.
209. ^'Archived copy'(PDF). Archived(PDF) from the original on 2016-04-02. Retrieved 2016-03-20.CS1 maint: Archived copy as title (link)
210. ^Croot, Ernest S., III (2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S., III (2003), 'On a coloring conjecture about unit fractions', Annals of Mathematics, 157 (2): 545–556, arXiv:math.NT/0311421, doi:10.4007/annals.2003.157.545
211. ^Bruhn, Henning; Schaudt, Oliver (1999). 'The Honeycomb Conjecture'. arXiv:math/9906042.
212. ^Bruhn, Henning; Schaudt, Oliver (1999). 'Proof of the gradient conjecture of R. Thom'. arXiv:math/9906212.
213. ^Ullmo, E (1998). 'Positivité et Discrétion des Points Algébriques des Courbes'. Annals of Mathematics. 147 (1): 167–179. arXiv:alg-geom/9606017. doi:10.2307/120987. JSTOR120987. Zbl0934.14013.
214. ^Zhang, S.-W. (1998). 'Equidistribution of small points on abelian varieties'. Annals of Mathematics. 147 (1): 159–165. doi:10.2307/120986. JSTOR120986.
215. ^Lafforgue, Laurent (1998), 'Chtoucas de Drinfeld et applications' [Drinfelʹd shtukas and applications], Documenta Mathematica (in French), II: 563–570, ISSN1431-0635, MR1648105, archived from the original on 2018-04-27, retrieved 2016-03-18
216. ^Bruhn, Henning; Schaudt, Oliver (2015). 'A formal proof of the Kepler conjecture'. arXiv:1501.02155 [math.MG].
217. ^Bruhn, Henning; Schaudt, Oliver (1998). 'A proof of the dodecahedral conjecture'. arXiv:math/9811079.
218. ^Norio Iwase (1 November 1998). 'Ganea's Conjecture on Lusternik-Schnirelmann Category'. ResearchGate.
219. ^Merel, Loïc (1996). ''Bornes pour la torsion des courbes elliptiques sur les corps de nombres' [Bounds for the torsion of elliptic curves over number fields]'. Inventiones Mathematicae. 124 (1): 437–449. Bibcode:1996InMat.124.437M. doi:10.1007/s002220050059. MR1369424.
220. ^Chen, Zhibo (1996). 'Harary's conjectures on integral sum graphs'. Discrete Mathematics. 160 (1–3): 241–244. doi:10.1016/0012-365X(95)00163-Q.
221. ^Wiles, Andrew (1995). 'Modular elliptic curves and Fermat's Last Theorem'(PDF). Annals of Mathematics. 141 (3): 443–551. CiteSeerX10.1.1.169.9076. doi:10.2307/2118559. JSTOR2118559. OCLC37032255. Archived(PDF) from the original on 2011-05-10. Retrieved 2016-03-06.
222. ^Taylor R, Wiles A (1995). 'Ring theoretic properties of certain Hecke algebras'. Annals of Mathematics. 141 (3): 553–572. CiteSeerX10.1.1.128.531. doi:10.2307/2118560. JSTOR2118560. OCLC37032255.

Further reading

Books discussing problems solved since 1995

• Singh, Simon (2002). Fermat's Last Theorem. Fourth Estate. ISBN978-1-84115-791-7.
• O'Shea, Donal (2007). The Poincaré Conjecture. Penguin. ISBN978-1-84614-012-9.
• Szpiro, George G. (2003). Kepler's Conjecture. Wiley. ISBN978-0-471-08601-7.
• Ronan, Mark (2006). Symmetry and the Monster. Oxford. ISBN978-0-19-280722-9.

Books discussing unsolved problems

• Chung, Fan; Graham, Ron (1999). Erdös on Graphs: His Legacy of Unsolved Problems. AK Peters. ISBN978-1-56881-111-6.
• Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1994). Unsolved Problems in Geometry. Springer. ISBN978-0-387-97506-1.
• Guy, Richard K. (2004). Unsolved Problems in Number Theory. Springer. ISBN978-0-387-20860-2.
• Klee, Victor; Wagon, Stan (1996). Old and New Unsolved Problems in Plane Geometry and Number Theory. The Mathematical Association of America. ISBN978-0-88385-315-3.
• du Sautoy, Marcus (2003). The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. Harper Collins. ISBN978-0-06-093558-0.
• Derbyshire, John (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Joseph Henry Press. ISBN978-0-309-08549-6.
• Devlin, Keith (2006). The Millennium Problems – The Seven Greatest Unsolved* Mathematical Puzzles Of Our Time. Barnes & Noble. ISBN978-0-7607-8659-8.
• Blondel, Vincent D.; Megrestski, Alexandre (2004). Unsolved problems in mathematical systems and control theory. Princeton University Press. ISBN978-0-691-11748-5.
• Ji, Lizhen; Poon, Yat-Sun; Yau, Shing-Tung (2013). Open Problems and Surveys of Contemporary Mathematics (volume 6 in the Surveys in Modern Mathematics series) (Surveys of Modern Mathematics). International Press of Boston. ISBN978-1-57146-278-7.
• Waldschmidt, Michel (2004). 'Open Diophantine Problems'(PDF). Moscow Mathematical Journal. 4 (1): 245–305. arXiv:math/0312440. doi:10.17323/1609-4514-2004-4-1-245-305. ISSN1609-3321. Zbl1066.11030.
• Mazurov, V. D.; Khukhro, E. I. (1 Jun 2015). 'Unsolved Problems in Group Theory. The Kourovka Notebook. No. 18 (English version)'. arXiv:1401.0300v6 [math.GR].

External links

• Open Problem Garden The collection of open problems in mathematics build on the principle of user editable ('wiki') site
• Unsolved Problem of the Week Archive. MathPro Press.
• Ball, John M.'Some Open Problems in Elasticity'(PDF).
• Constantin, Peter. 'Some open problems and research directions in the mathematical study of fluid dynamics'(PDF).
• Serre, Denis. 'Five Open Problems in Compressible Mathematical Fluid Dynamics'(PDF).
• The Open Problems Project (TOPP), discrete and computational geometry problems
• Aizenman, Michael. 'Open Problems in Mathematical Physics'.
• Barry Simon's 15 Problems in Mathematical Physics

The World's Greatest Unsolved Crimes is a book written by Roger Boar and Nigel Blundell which was first published in 1984 by Octopus Books Limited as part of their World's Greatest series.^[1] It contains accounts of various unsolved mysteries such as murders, unexplained disappearances and scandals.

• 1List of entries

List of entries[edit]

Part 1: Crimes Without Call[edit]

• Who Was R.M. Qualtrough? - the case of William Herbert Wallace
• Advertisement of Death - the murder of Josephine Backshall
• The Green Bicycle Murder - better known as the Green Bicycle Case
• The Enigma of Nuremberg - the story of Kaspar Hauser
• Sherlock Holmes' Real Case - the trial of Oscar Slater and Arthur Conan Doyle's involvement
• Dead Men Cannot Talk - the sinking of the MS Georges Philippar
• Disappearing Dorothy - the disappearance of Dorothy Forstein
• Mystery at Wolf's Neck - the death of Evelyn Foster
• Spring-Heeled Jack, The Demon of London - the sightings of Spring-heeled Jack
• The World's Last Airship - the Hindenburg disaster

Part 2: Crimes of Our Time[edit]

• The Computer as Crook - the computer fraud of Jerry Schneider
• A Sadistic Revenge - the disappearance of Dora Bloch in Idi Amin's Uganda
• Piracy 20th Century Style - an account of modern-day piracy in the Caribbean
• Double Dealing at the Dogs - a greyhound racing scam at White City, London in 1945
• A Fatal Flight - the disappearance of two SAETAAirliners over the Andes

Part 3: Crimes of Avarice[edit]

• Conviction Without a Corpse - the disappearance of Murial McKay
• Doctor Death - the trial of John Bodkin Adams
• The Nazi's Gold - the widespread theft carried out by the Nazi Party during World War II
• The Unpaid Debt - the murder of Arnold Rothstein
• The Black Widow - the serial murderer, Belle Gunness
• The Wreck of the Chantiloupe - the sinking of the Chantiloupe and the murder of Mrs. James Burke

Part 4: Vanishing Tricks[edit]

• The Disappearing Parachutist - the aircraft hijacking committed by D. B. Cooper
• The Canine Sherlock Holmes - the discovery of the missing FIFA World Cup Trophy by Pickles the dog
• The Missing Murderers - the fate of Nazi war criminals who fled after World War II
• France's Uncrowned King - Louis XVII of France and the many imposters claiming to be him
• The Sinking of the Salem - the staged sinking of the Salemoil tanker for the sake of an insurance fraud
• A Peer's Great Gamble - the famous disappearance of Richard Bingham, 7th Earl of Lucan
• Suspect Deceased - the disappearance of Linda Sturley
• The Disappearance of Goodtime Joe - Joseph Force Crater
• Death at the Opera House - the disappearance of Ambrose Small
• The Impossible is Possible - the murder of Roy Orsini
• A Riddle in Life and a Riddle in Death - the disappearance of Jimmy Hoffa and the surrounding conspiracy theory
• The Mysterious Mummy - an ornamental mummy which was discovered to contain a real corpse during the filming of a Six Million Dollar Man episode
• The Prairie's Murder Inn - the Bloody Benders, a family of serial killers
• Who Did She Bury? - the disappearance of Nels Stenstrom and the strange funeral ceremony conducted in his absence
• Acrobats of Death - the murder of Ugo Pavesi by a man described by witnesses as a giant
• The Oldest Kidnap Victim? - The discovery of Homo erectus pekinensis and the complete disappearance of the fossils in transit

Part 5: Murder Most Foul[edit]

• House of Horror - the murder by Timothy Evans of his infant daughter
• Poetry, Passion and Prison - the Pimlico Mystery
• The Vicar and the Choirmistress - the murder of Eleanor Mills along with her vicar lover and the severing of their vocal folds
• Death in Happy Valley - the murder of Josslyn Hay, 22nd Earl of Erroll
• Lizzie and the Axe - the trial of Lizzie Borden
• The Harry Oakes Affair - the murder of Harry Oakes
• Killings in the Congo - the murder of Patrice Lumumba and the death of Dag Hammarskjöld
• Streets of Fear - serial killer, Jack the Ripper
• Jack the Stripper - serial killer, Jack the Stripper
• Death in the Churchyard - the murder of Olive Bennett
• The Arm in the Shark Case - the discovery of a severed human arm in the body of a tiger shark and subsequent murder investigation
• The Motorway Monster - the murder of Barbara Mayo, a hitchhiker
• Death of the Black Dahlia - the murder of Elizabeth Short
• The Torso in the Trunk - a gruesome discovery in a trunk at Brighton railway station
• Katyn - 1940 - the unattributed Katyn massacre

References[edit]

1. ^'The World's Greatest Unsolved Crimes' by Roger Boar and Nigel Blundell, Octopus Books Ltd. 1984

External links[edit]

Famous Unsolved Deaths