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| | 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.<br><br><br><br>Utilizing a Shape Mass Index chart is a respectable means for you to discover in the event you are at a wholesome weight or not. Because the selection for standard weight is substantial for a specific individual of any peak, adult males and many women whom falsely are convinced that there is a individual "magic number" which they must weigh is reassured by functioning with the BMI. The calculator and chart are additionally uncomplicated to use and are generally available online and inside health plus wellness institutions.<br><br>You will find different prospective problems that you may encounter if you make use of the [http://safedietplans.com/calories-burned-walking calories burned while walking] being an signal of health and health.<br><br>The newly improved formula makes Phen375 effective because it synthesized your hormones to better a bodies ability to assimilate fat cells, additionally stimulates the muscle tissue to aid we create more fat burning muscles rather of losing muscles. That is what makes burning fat or losing fat easily with Phen375.<br><br>Everyone knows the suggesting that obese children become obese adults. In many cases it's true, and among the good presents we can provide your kids is to teach them to eat healthy food plus to be physically active. It can serve them effectively in later life.<br><br>Shun we excessive eating habit. Should you have this habit cut up allowable greens like celery, carrot and capsicum into sticks or chunks plus keep them in the fridge to munch them when we feel hungry.<br><br>A low calorie/low nutrition trend diet might generally contain anywhere from 800 to 1600 calories per day plus may not contain all nutrition you need to stay healthy. Our bodies are extremely adaptable and may adjust for many days, nevertheless it is very not advantageous to continue with this kind of program over 3 days. |
| 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]]
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| * [[Hodge conjecture]]
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| * [[Riemann hypothesis]]
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| * [[Yang–Mills existence and mass gap]]
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| * [[Navier–Stokes existence and smoothness]]
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| * [[Birch and Swinnerton-Dyer conjecture]].
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| 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?
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| | |
| ==Other still-unsolved problems==
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| | |
| ===[[Additive number theory]]===
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| * [[Beal's conjecture]]
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| * [[Goldbach's conjecture]] (Proof claimed for [[Goldbach's weak conjecture|weak version]] in 2013)
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| * The values of ''g''(''k'') and ''G''(''k'') in [[Waring's problem]]
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| * [[Collatz conjecture]] (3''n'' + 1 conjecture)
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| * [[Lander, Parkin, and Selfridge conjecture]]
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| * [[Diophantine quintuple]]s
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| * [[Gilbreath's conjecture]]
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| * [[Erdős conjecture on arithmetic progressions]]
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| * [[Erdős–Turán conjecture on additive bases]]
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| * [[Pollock octahedral numbers conjecture]]
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| | |
| ===[[Algebra]]===
| |
| * [[Hilbert's sixteenth problem]]
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| * [[Hadamard conjecture]]
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| * Existence of [[Euler brick#Perfect cuboid|perfect cuboids]]
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| | |
| ===[[Algebraic geometry]]===
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| * [[André–Oort conjecture]]
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| * [[Bass conjecture]]
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| * [[Deligne conjecture]]
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| * [[Fröberg conjecture]]
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| * [[Fujita conjecture]]
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| * [[Hartshorne conjectures]]
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| * [[Jacobian conjecture]]
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| * [[Nakai conjecture]]
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| * [[Resolution of singularities|Resolution of singularities in characteristic p]]
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| * [[Standard conjectures| Standard conjectures on algebraic cycles]]
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| * [[Section conjecture]]
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| * [[Virasoro conjecture]]
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| * [[Witten conjecture]]
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| *[[Zariski multiplicity conjecture]]
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| | |
| ===[[Algebraic number theory]]===
| |
| * Are there infinitely many [[Class number problem#Real quadratic fields|real quadratic number fields]] with [[unique factorization]]?
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| * [[Brumer–Stark conjecture]]
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| * Characterize all algebraic number fields that have some [[Algebraic number field#Bases for number fields|power basis]].
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| | |
| ===[[Mathematical analysis|Analysis]]===
| |
| * The [[Jacobian conjecture]]
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| * [[Schanuel's conjecture]]
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| * [[Lehmer's conjecture]]
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| * [[Pompeiu problem]]
| |
| * Are <math>\gamma</math> (the [[Euler–Mascheroni constant]]), [[Pi|{{pi}}]] + ''[[e (mathematical constant)|e]]'', {{pi}} − ''e'', {{pi}}''e'', {{pi}}/''e'', {{pi}}<sup>''e''</sup>, {{pi}}<sup>[[Square root of 2|√{{overline|2}}]]</sup>, {{pi}}<sup>{{pi}}</sup>, e<sup>{{pi}}<sup>2</sup></sup>, [[Natural logarithm|ln]] {{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]]
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| | |
| ===[[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]]
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| | |
| ===[[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]]?
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| | |
| ===[[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'' − 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'' − 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> + 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>?
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| | |
| ===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)
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| * [[Princess and monster game]] ([[Shmuel Gal]], 1979)
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| * [[Four color theorem]] ([[Kenneth Appel|Appel]] and [[Wolfgang Haken|Haken]], 1977)
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| ==See also==
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| * [[Hilbert's problems]]
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| * [[Smale's problems]]
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| * [[List of conjectures#Open_problems|List of conjectures]]
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| * [[Millennium prize problems]]
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| * [[List of statements undecidable in ZFC]]
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| * [[Timeline of mathematics]]
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| ==References==
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| {{Reflist}}
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| *{{MathWorld |urlname=UnsolvedProblems |title=Unsolved problems}}
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| * Winkelmann, Jörg, "''[http://www.iecn.u-nancy.fr/~winkelma/mirror/unibas/problem.html Some Mathematical Problems]''". 9 March 2006.
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| * {{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}}
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| === Books discussing unsolved problems ===
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| * {{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}}
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| * {{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}}
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| * {{cite book |author=Richard K. Guy |title=Unsolved Problems in Number Theory |publisher=Springer |year=2004 |isbn=0-387-20860-7}}
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| * {{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}}
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| * {{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}}
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| * {{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}}
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| * {{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.}}}}
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| * {{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}}
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| === Books discussing recently solved problems ===
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| * {{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}}
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| * {{cite book | author=Donal O'Shea | title=The Poincaré Conjecture | publisher=Penguin | year=2007 | isbn=978-1-84614-012-9}}
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| * {{cite book | author=George G. Szpiro | title=Kepler's Conjecture | publisher=Wiley | year=2003 | isbn=0-471-08601-0}}
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| * {{cite book | author=Mark Ronan | title=Symmetry and the Monster | publisher=Oxford | year=2006 | isbn=0-19-280722-6}}
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| ==External links==
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| * [http://unsolvedproblems.org/ Unsolved Problems in Number Theory, Logic and Cryptography]
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| * [http://www.claymath.org/millennium/ Clay Institute Millennium Prize]
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| * [http://www.openproblems.net/ List of links to unsolved problems in mathematics, prizes and research.]
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| * [http://garden.irmacs.sfu.ca Open Problem Garden] The collection of open problems in mathematics build on the principle of user editable ("wiki") site
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| * [http://aimpl.org/ AIM Problem Lists]
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| * [http://cage.ugent.be/~hvernaev/problems/archive.html Unsolved Problem of the Week Archive]. MathPro Press.
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| * [http://cs.smith.edu/~orourke/TOPP/ The Open Problems Project (TOPP)], discrete and computational geometry problems
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| {{unsolved problems}}
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| <!--Categories-->
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| [[Category:Unsolved problems in mathematics| ]]<!--Keep at start of list (eponymous category) -->
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| [[Category:Conjectures| ]]
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| [[Category:Lists of unsolved problems|Mathematics]]
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| [[Category:Mathematics-related lists]]
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