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This article lists some '''[[List of unsolved problems|unsolved problems]] in [[mathematics]]'''. See individual articles for details and sources.
 
== Millennium Prize Problems ==
Of the seven [[Millennium Prize Problems]] set by the [[Clay Mathematics Institute]], six have yet to be solved:
* [[P = NP problem|P versus NP]]
* [[Hodge conjecture]]
* [[Riemann hypothesis]]
* [[Yang–Mills existence and mass gap]]
* [[Navier–Stokes existence and smoothness]]
* [[Birch and Swinnerton-Dyer conjecture]].
The seventh problem, the [[Poincaré conjecture]], has been solved. The smooth four-dimensional Poincaré conjecture is still unsolved. That is, can a four-dimensional topological sphere have two or more inequivalent [[smooth structure]]s?
 
==Other still-unsolved problems==
 
===[[Additive number theory]]===
* [[Beal's conjecture]]
* [[Goldbach's conjecture]] (Proof claimed for [[Goldbach's weak conjecture|weak version]] in 2013)
* The values of ''g''(''k'') and ''G''(''k'') in [[Waring's problem]]
* [[Collatz conjecture]] (3''n''&nbsp;+&nbsp;1 conjecture)
* [[Lander, Parkin, and Selfridge conjecture]]
* [[Diophantine quintuple]]s
* [[Gilbreath's conjecture]]
* [[Erdős conjecture on arithmetic progressions]]
* [[Erdős–Turán conjecture on additive bases]]
* [[Pollock octahedral numbers conjecture]]
 
===[[Algebra]]===
* [[Hilbert's sixteenth problem]]
* [[Hadamard conjecture]]
* Existence of [[Euler brick#Perfect cuboid|perfect cuboids]]
 
===[[Algebraic geometry]]===
* [[André–Oort conjecture]]
* [[Bass conjecture]]
* [[Deligne conjecture]]
* [[Fröberg conjecture]]
* [[Fujita conjecture]]
* [[Hartshorne conjectures]]
* [[Jacobian conjecture]]
* [[Nakai conjecture]]
* [[Resolution of singularities|Resolution of singularities in characteristic p]]
* [[Standard conjectures| Standard conjectures on algebraic cycles]]
* [[Section conjecture]]
* [[Virasoro conjecture]]
* [[Witten conjecture]]
*[[Zariski multiplicity conjecture]]
 
===[[Algebraic number theory]]===
* Are there infinitely many [[Class number problem#Real quadratic fields|real quadratic number fields]] with [[unique factorization]]?
* [[Brumer–Stark conjecture]]
* Characterize all algebraic number fields that have some [[Algebraic number field#Bases for number fields|power basis]].
 
===[[Mathematical analysis|Analysis]]===
* The [[Jacobian conjecture]]
* [[Schanuel's conjecture]]
* [[Lehmer's conjecture]]
* [[Pompeiu problem]]
* Are <math>\gamma</math> (the [[Euler–Mascheroni constant]]), [[Pi|{{pi}}]]&nbsp;+&nbsp;''[[e (mathematical constant)|e]]'', {{pi}}&nbsp;&minus;&nbsp;''e'', {{pi}}''e'', {{pi}}/''e'', {{pi}}<sup>''e''</sup>, {{pi}}<sup>[[Square root of 2|&radic;{{overline|2}}]]</sup>, {{pi}}<sup>{{pi}}</sup>, e<sup>{{pi}}<sup>2</sup></sup>, [[Natural logarithm|ln]]&nbsp;{{pi}}, 2<sup>''e''</sup>, ''e''<sup>''e''</sup>, [[Catalan's constant]] or [[Khinchin's constant]] rational, [[Algebraic number|algebraic]] irrational, or [[Transcendental number|transcendental]]? What is the [[irrationality measure]] of each of these numbers?<ref>{{MathWorld|Pi|Pi}}</ref><ref>{{MathWorld|e|e}}</ref><ref>{{MathWorld|KhinchinsConstant|Khinchin's Constant}}</ref><ref>{{MathWorld|IrrationalNumber|Irrational Number}}</ref><ref>{{MathWorld|TranscendentalNumber|Transcendental Number}}</ref><ref>{{MathWorld|IrrationalityMeasure|Irrationality Measure}}</ref><ref>[http://www.math.jussieu.fr/~miw/articles/pdf/AWSLecture5.pdf An introduction to irrationality and transcendence methods]</ref><ref>[http://www.math.ou.edu/~jalbert/courses/openprob2.pdf Some unsolved problems in number theory]</ref>
* The [[Khabibullin’s conjecture on integral inequalities]]
 
===[[Combinatorics]]===
* Number of [[magic square]]s {{OEIS|id=A006052}}
* Finding a formula for the probability that two elements chosen at random generate the [[symmetric group]] <math>S_n</math>
* 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
* The [[Lonely runner conjecture]]: if <math>k+1</math> runners with pairwise distinct speeds run round a track of unit length, will every runner be "lonely" (that is, be at least a distance <math>1/(k+1)</math> from each other runner) 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?
* The [[1/3–2/3 conjecture]]: does every finite [[partially ordered set]] 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?
*[[Conway's thrackle conjecture]]
 
===[[Discrete geometry]]===
* Solving the [[Happy Ending problem]] for arbitrary <math>n</math>
* Finding matching upper and lower bounds for [[K-set (geometry)|K-sets]] and halving lines
* The [[Hadwiger conjecture (combinatorial geometry)|Hadwiger conjecture]] on covering ''n''-dimensional convex bodies with at most 2<sup>''n''</sup> smaller copies
 
===[[Dynamical system]]===
* [[Hillel Furstenberg|Furstenberg]] conjecture – Is every invariant and [[ergodicity|ergodic]] measure for the <math>\times 2,\times 3</math> action on the circle either Lebesgue or atomic?
* [[Grigory Margulis|Margulis]] conjecture — Measure classification for diagonalizable actions in higher-rank groups
 
===[[Graph theory]]===
* [[Barnette's conjecture]] that every cubic bipartite three-connected planar graph has a Hamiltonian cycle
* The [[Erdős–Gyárfás conjecture]] on cycles with power-of-two lengths in cubic graphs (proof claimed - <ref>Heckman and Krakovski, “Erdös-Gyárfás Conjecture for Cubic Planar Graphs.” Elect. J. of Combinatorics 20 (2013), http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i2p7.</ref>)
* The [[Erdős–Hajnal conjecture]] on finding large homogeneous sets in graphs with a forbidden induced subgraph
* The [[Hadwiger conjecture (graph theory)|Hadwiger conjecture]] relating coloring to clique minors
* The [[Erdős–Faber–Lovász conjecture]] on coloring unions of cliques
* The [[total coloring conjecture]]
* The [[list coloring conjecture]]
* The [[Graceful labeling|Ringel–Kotzig conjecture]] on graceful labeling of trees
* The [[Hadwiger–Nelson problem]] on the chromatic number of unit distance graphs
* Deriving a closed-form expression for the [[percolation threshold]] values, especially <math>p_c</math> (square site)
* Tutte's conjectures that every bridgeless graph has a [[nowhere-zero flows|nowhere-zero 5-flow]] and every bridgeless graph without the [[Petersen graph]] as a [[minor (graph theory)|minor]] has a nowhere-zero 4-flow
* The [[Reconstruction conjecture]] and [[New digraph reconstruction conjecture]] concerning whether or not a graph is recognizable by the vertex deleted subgraphs.
* The [[cycle double cover conjecture]] that every bridgeless graph has a family of cycles that includes each edge twice.
* Does a [[Moore graph]] with girth 5 and degree 57 exist?
 
===[[Group theory]]===
* Is every [[finitely presented group|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]] {{nowrap|B(''m'',''n'')}} finite? In particular, is {{nowrap|B(2, 5)}} finite?
* Is every group [[surjunctive group|surjunctive]]?
 
===[[Model theory]]===
* [[Vaught's conjecture]]
* The [[Stable group|Cherlin-Zilber conjecture]]: A simple group whose first-order theory is [[Stable theory|stable]] in <math>\aleph_0</math> is a simple algebraic group over an algebraically closed field.
* The Main Gap conjecture, e.g. for uncountable [[First order theory|first order theories]], for [[Abstract elementary class|AEC]]s, and for <math>\aleph_1</math>-saturated models of a countable theory.<ref>Shelah S, ''Classification Theory'', North-Holland, 1990</ref>
* Determine the structure of Keisler's order<ref>Keisler, HJ, “Ultraproducts which are not saturated.” J. Symb Logic 32 (1967) 23—46.</ref><ref>Malliaris M, Shelah S, "A dividing line in simple unstable theories." http://arxiv.org/abs/1208.2140</ref>
* The stable field conjecture:  every infinite field with a [[Stable theory|stable]] first-order theory is separably closed.
* Is the theory of the field of Laurent series over <math>\mathbb{Z}_p</math> decidable? of the field of polynomials over <math>\mathbb{C}</math>?
* (BMTO) Is the Borel monadic theory of the real order [[Decidability (logic)|decidable]]? (MTWO) Is the monadic theory of well-ordering consistently decidable?<ref>Gurevich, Yuri, "Monadic Second-Order Theories," in J. Barwise, S. Feferman, eds., ''Model-Theoretic Logics'' (New York: Springer-Verlag, 1985), 479-506.</ref>
* The Stable Forking Conjecture for simple theories<ref>Peretz, Assaf, “Geometry of forking in simple theories.” J. Symbolic Logic Volume 71, Issue 1 (2006), 347-359.</ref>
* 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 [[Type (model theory)|types]]. If K has a model of cardinality <math>\aleph_{\omega_1}</math> does it have a model of cardinality continuum?<ref>Shelah S, “Borel sets with large squares.” Fund. Math. 159 (1999) 1—50.  arxiv:9802134</ref>
* Is there a logic satisfying the interpolation theorem which is compact?<ref>Makowsky J, “Compactness, embeddings and definability,” in ''Model-Theoretic Logics'', eds Barwise and Feferman, Springer 1985 pps. 645-715.</ref>
* If the class of atomic models of a complete first order theory is [[Categorical (model theory)|categorical]] in the <math>\aleph_n</math>, is it categorical in every cardinal?<ref>Baldwin, John, ''Categoricity in AECs'', AMS 2009. http://www.math.uic.edu/~jbaldwin/pub/AEClec.pdf</ref><ref>S Shelah, “Introduction to classification theory for abstract elementary classes.” http://front.math.ucdavis.edu/0903.3428</ref>
* Is every infinite, minimal field of characteristic zero algebraically closed? (minimal = no proper elementary substructure)
* Kueker's conjecture<ref>Hrushovski, Ehud, “Kueker's conjecture for stable theories.” Journal of Symbolic Logic Vol. 54, No. 1 (Mar., 1989), pp. 207-220.</ref>
* Does there exist an [[o-minimal]] first order theory with a trans-exponential (rapid growth) function?
* Lachlan's decision problem
* Does a finitely presented homogeneous structure for a finite relational language have finitely many reducts?
* Do the Henson graphs have the finite model property? (e.g. triangle-free graphs)
* 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?<ref>Cherlin G, Shelah S, “Universal graphs with a forbidden subtree.”  J. Comb Thy Ser B, vol 97 pps. 293—333. arxiv:0512218</ref>
* The universality spectrum problem: Is there a first-order theory whose universality spectrum is minimum?<ref>D\v{z}amonja, Mirna, “Club guessing and the universal models.” ''On PCF'', ed. M. Foreman, (Banff, Alberta, 2004).</ref>
 
===[[Number theory| Number theory (general)]]===
* [[abc conjecture|''abc'' conjecture]] (Proof claimed in 2012, currently under review.)
* [[Erdős–Straus conjecture]]
* Do any [[perfect number#Odd perfect numbers|odd perfect numbers]] exist?
* Are there infinitely many [[perfect numbers]]?
* Do [[quasiperfect number]]s exist?
* Do any odd [[weird number]]s exist?
* Do any [[Lychrel number]]s exist?
* Is 10 a [[solitary number]]?
* Do any [[Generalized taxicab number|Taxicab(5, 2, n)]] exist for ''n''>1?
* [[Brocard's problem]]: existence of integers, ''n'',''m'', such that ''n''!+1=''m''<sup>2</sup> other than ''n''=4,5,7
* [http://garden.irmacs.sfu.ca/?q=op/distribution_and_upper_bound_of_mimic_numbers Distribution and upper bound of mimic numbers]
* [[Littlewood conjecture]]
* [[Congruent number problem]] (a corollary to [[Birch and Swinnerton-Dyer conjecture]], per [[Tunnell's theorem]])
* [[Lehmer's totient problem]]: if φ(''n'') divides ''n''&nbsp;−&nbsp;1, must ''n'' be prime?
* Are there infinitely many [[amicable numbers]]?
* Are there any pairs of [[relatively prime]] [[amicable numbers]]?
 
===[[Number theory| Number theory (prime numbers)]]===
* [[Catalan's Mersenne conjecture]]
* [[Twin prime|Twin prime 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?
* Are there infinitely many [[prime quadruplet]]s?
* Are there infinitely many [[Mersenne prime]]s ([[Lenstra–Pomerance–Wagstaff conjecture]]); equivalently, infinitely many even [[perfect number]]s?
* Are there infinitely many [[Sophie Germain prime]]s?
* Are there infinitely many [[regular prime]]s, and if so is their relative density <math>e^{-1/2}</math>?
* Are there infinitely many [[Cullen prime]]s?
* Are there infinitely many [[palindromic prime]]s in base 10?
* Are there infinitely many [[Fibonacci prime]]s?
* Are all [[Mersenne number]]s of prime index [[Square-free integer|square-free]]?
* Are there infinitely many [[Wieferich prime]]s?
* Are there for every a ≥ 2 infinitely many primes p such that a<sup>''p'' &minus; 1</sup> ≡ 1 (mod ''p''<sup>2</sup>)?<ref>{{cite book | last = Ribenboim | first = P. | authorlink = Paulo Ribenboim | title = Die Welt der Primzahlen | publisher = Springer | edition = 2 | year = 2006 | pages = 242–243 | language = German | url = http://books.google.de/books?id=XMyzh-2SClUC&lpg=PR5&dq=die%20welt%20der%20primzahlen&hl=de&pg=PA242#v=snippet&q=die%20folgenden%20probleme%20sind%20ungel%C3%B6st&f=false | doi = 10.1007/978-3-642-18079-8 | isbn = 978-3-642-18078-1}}</ref>
* Can a prime ''p'' satisfy 2<sup>''p'' − 1</sup> ≡ 1 (mod ''p''<sup>2</sup>) and 3<sup>''p'' − 1</sup> ≡ 1 (mod ''p''<sup>2</sup>) simultaneously?<ref>{{Citation | last = Dobson | first = J. B. | title = On Lerch's formula for the Fermat quotient | origyear = 2011 | year = 2012 | month= 06 | page = 15 | arxiv = 1103.3907}}</ref>
* Are there infinitely many [[Wilson prime]]s?
* Are there infinitely many [[Wolstenholme prime]]s?
* Are there any [[Wall–Sun–Sun prime]]s?
* Is every [[Fermat number]] 2<sup>2<sup>''n''</sup></sup>&nbsp;+&nbsp;1 composite for <math>n > 4</math>?
* Are all Fermat numbers [[Square-free integer|square-free]]?
* Is 78,557 the lowest [[Sierpiński number]]?
* Is 509,203 the lowest [[Riesel number]]?
* Fortune's conjecture (that no [[Fortunate number]] is composite)
* [[Polignac's conjecture]]
* [[Landau's problems]]
* Does every prime number appear in the [[Euclid–Mullin sequence]]?
* Does the [[Wolstenholme's theorem#The converse as a conjecture|converse of Wolstenholme's theorem]] hold for all natural numbers?
* [[Elliott–Halberstam conjecture]]
 
===[[Partial differential equations]]===
* Regularity of solutions of [[Vlasov–Maxwell equations]]
* Regularity of solutions of [[Euler equations]]
 
===[[Ramsey theory]]===
* The values of the [[Ramsey's theorem#Ramsey numbers|Ramsey numbers]], particularly <math>R(5, 5)</math>
* The values of the [[Van der Waerden number]]s
 
===[[Set theory]]===
* The problem of finding the ultimate [[core model]], one that contains all [[Large cardinal property|large cardinals]].
* If ℵ<sub>ω</sub> is a strong limit cardinal, then 2<sup>ℵ<sub>ω</sub></sup> < ℵ<sub>ω<sub>1</sub></sub> (see [[Singular cardinals hypothesis]]). The best bound, ℵ<sub>ω<sub>4</sub></sub>,  was obtained by [[saharon Shelah|Shelah]] using his [[PCF theory|pcf theory]].
* [[W. Hugh Woodin|Woodin's]] [[Ω-logic|Ω-hypothesis]].
* Does the [[consistency]] of the existence of a [[strongly compact cardinal]] imply the consistent existence of a [[supercompact cardinal]]?
* ([[W. Hugh Woodin|Woodin]]) Does the [[Continuum hypothesis#The generalized continuum hypothesis|Generalized Continuum Hypothesis]] below a [[strongly compact cardinal]] imply the [[Continuum hypothesis#The generalized continuum hypothesis|Generalized Continuum Hypothesis]]  everywhere?
* Does there exist a [[Jónsson cardinal|Jonsson algebra]] on ℵ<sub>ω</sub>?
* Without assuming the [[axiom of choice]], can a [[Reinhardt cardinal|nontrivial elementary embedding]] ''V''→''V'' exist?
* Is it consistent that <math>{\mathfrak p < \mathfrak t}</math>? (This problem was solved in a 2012 preprint by Malliaris and [[Saharon Shelah|Shelah]],<ref>{{citation|title=Cofinality spectrum theorems in model theory, set theory and general topology|first1=M.|last1=Malliaris|first2=S.|last2=Shelah|author2-link=Saharon Shelah|year=2012|arxiv=1208.5424}}</ref> who showed that <math>{\mathfrak p = \mathfrak t}</math> is a theorem of ZFC.)
* Does the [[Continuum hypothesis#The generalized continuum hypothesis|Generalized Continuum Hypothesis]] entail [[Diamondsuit|<math>{\diamondsuit(E^{\lambda^+}_{cf(\lambda)}})</math>]] for every [[singular cardinal]] <math>\lambda</math>?
 
===Other===
* [[Invariant subspace problem]]
* [[Problems in Latin squares]]
* [[Problems in loop theory and quasigroup theory]]
* [[Dixmier conjecture]]
* [[Baum–Connes conjecture]]
* [[Generalized star height problem]]
* Assorted [[sphere packing]] problems, e.g. the densest irregular hypersphere packings
* [[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.<ref>{{citation
| last = Barros | first = Manuel
| Article Stable URL = http://www.jstor.org/stable/2162098
| journal = American Mathematical Society
| pages = 1503–1509
| title = General Helices and a Theorem of Lancret
| volume = 125
| year = 1997}}.</ref>
* [[Toeplitz' conjecture]] (open since 1911)
 
{{see also|List of conjectures}}
 
== Problems solved recently ==
* [[Mikhail Leonidovich Gromov|Gromov's]] problem on distortion of [[Knot (mathematics)|knots]] ([[John Pardon]], 2011)
* [[Circular law]] ([[Terence Tao]] and [[Van H. Vu]], 2010)
* [[Hirsch conjecture]] ([[Francisco Santos Leal]], 2010<ref>{{cite journal |author= Franciscos Santos|year= 2012 |title= A counterexample to the Hirsch conjecture |journal= Annals of Mathematics|volume=176|issue=1|pages=383–412|publisher=Princeton University and Institute for Advanced Study |doi=10.4007/annals.2012.176.1.7|url= http://annals.math.princeton.edu/2012/176-1/p07}}</ref>)
* [[Serre's modularity conjecture]] ([[Chandrashekhar Khare]] and [[Jean-Pierre Wintenberger]], 2008<ref>{{Citation |last=Khare |first=Chandrashekhar |last2=Wintenberger |first2=Jean-Pierre |year=2009 |title=Serre’s modularity conjecture (I) |journal=Inventiones Mathematicae |volume=178 |issue=3 |pages=485–504 |doi=10.1007/s00222-009-0205-7 }} and {{Citation |last=Khare |first=Chandrashekhar |last2=Wintenberger |first2=Jean-Pierre |year=2009 |title=Serre’s modularity conjecture (II) |journal=Inventiones Mathematicae |volume=178 |issue=3 |pages=505–586 |doi=10.1007/s00222-009-0206-6 }}.</ref>)
* [[Squaring_the_square#Squaring_the_plane|Heterogeneous tiling conjecture (squaring the plane)]] (Frederick V. Henle and James M. Henle, 2007)
* [[Road coloring conjecture]] ([[Avraham Trahtman]], 2007)
* The [[Angel problem]] (Various independent proofs, 2006)
* The [[Langlands–Shelstad fundamental lemma]] ([[Ngô Bảo Châu]] and [[Gérard Laumon]], 2004)
* [[Stanley–Wilf conjecture]] ([[Gábor Tardos]] and [[Adam Marcus (mathematician)|Adam Marcus]], 2004)
* [[Green–Tao theorem]] ([[Ben J. Green]] and [[Terence Tao]], 2004)
* [[Cameron–Erdős conjecture]] ([[Ben J. Green]], 2003, Alexander Sapozhenko, 2003, conjectured by [[Paul Erdős]])<ref>{{citation
| last = Green | first = Ben | author-link = Ben J. Green
| arxiv = math.NT/0304058
| doi = 10.1112/S0024609304003650
| issue = 6
| journal = The Bulletin of the London Mathematical Society
| mr = 2083752
| pages = 769–778
| title = The Cameron–Erdős conjecture
| volume = 36
| year = 2004}}.</ref>
* [[Strong perfect graph conjecture]] ([[Maria Chudnovsky]], [[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul Seymour]] and [[Robin Thomas (mathematician)|Robin Thomas]], 2002)
* [[Poincaré conjecture]] ([[Grigori Perelman]], 2002)
* [[Mihăilescu's theorem|Catalan's conjecture]] ([[Preda Mihăilescu]], 2002)
* [[Kato's conjecture]] (Auscher, Hofmann, Lacey, McIntosh, and Tchamitchian, 2001)
* The [[Langlands correspondence]] for function fields ([[Laurent Lafforgue]], 1999)
* [[Modularity theorem|Taniyama–Shimura conjecture]] (Wiles, Breuil, Conrad, Diamond, and Taylor, 1999)
* [[Kepler conjecture]] ([[Thomas Callister Hales|Thomas Hales]], 1998)
* [[Milnor conjecture]] ([[Vladimir Voevodsky]], 1996)
* [[Fermat's Last Theorem]] ([[Andrew Wiles]] and [[Richard Taylor (mathematician)|Richard Taylor]], 1995)
* [[De Branges' theorem|Bieberbach conjecture]] ([[Louis de Branges de Bourcia|Louis de Branges]], 1985)
* [[Princess and monster game]] ([[Shmuel Gal]], 1979)
* [[Four color theorem]] ([[Kenneth Appel|Appel]] and [[Wolfgang Haken|Haken]], 1977)
 
==See also==
* [[Hilbert's problems]]
* [[Smale's problems]]
* [[List of conjectures#Open_problems|List of conjectures]]
* [[Millennium prize problems]]
* [[List of statements undecidable in ZFC]]
* [[Timeline of mathematics]]
 
==References==
{{Reflist}}
*{{MathWorld |urlname=UnsolvedProblems |title=Unsolved problems}}
* Winkelmann, Jörg, "''[http://www.iecn.u-nancy.fr/~winkelma/mirror/unibas/problem.html  Some Mathematical Problems]''". 9 March 2006.
* {{cite journal | first=Michael | last=Waldschmidt | authorlink=Michel Waldschmidt | title=Open Diophantine Problems |journal=Moscow Mathematical Journal |volume=4 |number=1 |year=2004 |pages=245–305 |url=http://www.math.jussieu.fr/~miw/articles/pdf/odp.pdf | zbl=1066.11030 | issn=1609-3321}}
 
=== Books discussing unsolved problems ===
* {{cite book |author=Fan Chung; Ron Graham |title=Erdos on Graphs: His Legacy of Unsolved Problems |publisher=AK Peters |year=1999 |isbn=1-56881-111-X}}
* {{cite book |author=Hallard T. Croft; Kenneth J. Falconer; Richard K. Guy |title=Unsolved Problems in Geometry |publisher=Springer |year=1994 |isbn=0-387-97506-3}}
* {{cite book |author=Richard K. Guy |title=Unsolved Problems in Number Theory |publisher=Springer |year=2004 |isbn=0-387-20860-7}}
* {{cite book |author=[[Victor Klee]]; [[Stan Wagon]] |title=Old and New Unsolved Problems in Plane Geometry and Number Theory |publisher=The Mathematical Association of America |year=1996 |isbn=0-88385-315-9}}
* {{cite book |author=Marcus Du Sautoy |title=The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics |publisher=Harper Collins|year=2003|isbn=0-06-093558-8}}
* {{cite book |author=John Derbyshire |title=Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics |publisher=Joseph Henry Press|year=2003|isbn=0-309-08549-7}}
* {{cite book |author=Keith Devlin |title=The Millennium Problems – The Seven Greatest Unsolved* Mathematical Puzzles Of Our Time |publisher=Barnes & Noble |year=2006|isbn=0-7607-8659-8{{Please check ISBN|reason=Check digit (8) does not correspond to calculated figure.}}}}
* {{cite book | author=Vincent D. Blondel, Alexandre Megrestski | title=Unsolved problems in mathematical systems and control theory | publisher=Princeton University Press | year=2004 | isbn=0-691-11748-9}}
 
=== Books discussing recently solved problems ===
* {{cite book | author=[[Simon Singh]] | title=[[Fermat's Last Theorem (book)|Fermat's Last Theorem]] | publisher=Fourth Estate | year=2002 | isbn=1-84115-791-0}}
* {{cite book | author=Donal O'Shea | title=The Poincaré Conjecture | publisher=Penguin | year=2007 | isbn=978-1-84614-012-9}}
* {{cite book | author=George G. Szpiro | title=Kepler's Conjecture | publisher=Wiley | year=2003 | isbn=0-471-08601-0}}
* {{cite book | author=Mark Ronan | title=Symmetry and the Monster | publisher=Oxford | year=2006 | isbn=0-19-280722-6}}
 
==External links==
* [http://unsolvedproblems.org/ Unsolved Problems in Number Theory, Logic and Cryptography]
* [http://www.claymath.org/millennium/ Clay Institute Millennium Prize]
* [http://www.openproblems.net/ List of links to unsolved problems in mathematics, prizes and research.]
* [http://garden.irmacs.sfu.ca Open Problem Garden] The collection of open problems in mathematics build on the principle of user editable ("wiki") site
* [http://aimpl.org/ AIM Problem Lists]
* [http://cage.ugent.be/~hvernaev/problems/archive.html Unsolved Problem of the Week Archive]. MathPro Press.
* [http://cs.smith.edu/~orourke/TOPP/ The Open Problems Project (TOPP)], discrete and computational geometry problems
 
{{unsolved problems}}
 
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[[Category:Unsolved problems in mathematics| ]]<!--Keep at start of list (eponymous category) -->
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Latest revision as of 00:03, 10 November 2014

A BMI examination result of 25 to 29.9 means which anyone is obese or overweight. Getting chubby poses numerous wellbeing hazards. A some of the well-being difficulties which are prevalent to obese folks are: Diabetes, Asthma, Heart Complications, Cancer plus Hypertension. Each 1 of these ailments is frequently prevented by shedding off several kilos plus maintaining a healthy body body weight that could be reached by way of correct eating practices and work out. A person's bodyweight will greatly lower by just taking away sweets and fatty foods off their diet regime. Frequent strolling might even help shed those fats.



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