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Jacobian conjecture (2220 bytes)
1: In [[mathematics]], the '''Jacobian conjecture''' is a celebrated problem on [[polynomial]]s in ... 7: ...cient]]s in the [[complex number]]s ''C''. The [[Jacobian determinant]] ''J'' of the ''F''<sub>''i''</sub>,... 31: The '''Jacobian conjecture''' is the [[converse]]: it states that 39: ...u/~ttm/jacobian.html Web page of T. T. Moh on the conjecture] 41: ...omials]][[Category:Algebraic geometry]][[Category:Conjectures]] Jacobian (4869 bytes) 1: ...Jacobian matrix''' or its [[determinant]], the '''Jacobian determinant'''. 3: ...ian''' of a [[algebraic curve|curve]] means the [[Jacobian variety]]: a [[group (mathematics)|group structur... 5: ...e mathematician [[Carl Gustav Jacobi]]; the term "Jacobian" may be pronounced as "yah-KO-bee-un". 7: == Jacobian matrix == 8: ...e function near a given point. In this sense, the Jacobian is akin to a derivative of a multivariate functio... Conjecture (4836 bytes) 2: ...[fr:Conjecture]][[zh:猜想]][[Category:Conjectures]] 3: In [[mathematics]], a '''conjecture''' is a mathematical statement which has been pro... 5: ...ns must be extremely careful about their use of a conjecture within logical structures. 9: ==Famous conjectures== 11: ...elf a longstanding open problem, was proven; this conjecture has since been completely proven. Kepler conjecture (8280 bytes) 1: ...mathematics]], the '''Kepler conjecture''' is a [[conjecture]] about [[sphere packing]] in three dimensional [... 3: ...of the correctness of Hales' proof. So the Kepler conjecture is now very close to becoming a [[theorem]]. 12: The Kepler conjecture says that this is the best that can be done - no ... 15: ...s named after [[Johannes Kepler]], who stated the conjecture in [[1661]] in ''Strena sue de nive sexangula''. ... 18: ...olution in [[1831]]. Gauss proved that the Kepler conjecture is true if the spheres have to be arranged in a r... Erdös conjecture (1205 bytes) 1: {{wrongtitle|title=Erdős conjecture}} 3: ...rious collaborators made many famous mathematical conjectures, over a wide field of subjects. 6: ...s-Faber-Lovász conjecture|Erdős-Faber-Lovász conjecture]] 7: * [[Erdös-Graham conjecture|Erdős-Graham conjecture]] 8: * [[Erdös-Gyárfás conjecture|Erdős-Gyárfás conjecture]] (graph theory) Reconstruction conjecture (1629 bytes) 2: [[Category:Conjectures]] 6: ...r graphs with at least three vertices it has been conjectured in 1942 by P. J. Kelly and [[S. M. Ulam]] that i... 8: More formally, the '''reconstruction conjecture''' states: 13: ...beled [[tree (graph theory)|tree]]s. However, the conjecture remains open for arbitrary graphs. Hodge conjecture (3957 bytes) 1: The '''Hodge conjecture''' is a major unsolved problem of [[algebraic geo... 3: == Formulating the conjecture == 11: The summand relevant to the conjecture is the 'central' one, 19: ...the vector space ''H*'' of interest for the Hodge conjecture. It consists of the vectors in ''H(k,k)'' that ar... 27: == What the Hodge conjecture states == Mertens conjecture (1557 bytes) 3: [[Category:Number theory]][[Category:Conjectures]] 9: ...function]], then the '''[[Franz Mertens|Mertens]] conjecture''' is that 15: ...[[1985]], te Riele and Odlyzko proved the Mertens conjecture false. 22: ...') is the [[Riemann zeta function]]. The Mertens conjecture would mean that this integral converges for Re(''... 25: ...hworld.wolfram.com/MertensConjecture.html Mertens conjecture] at MathWorld Artin conjecture (3854 bytes) 1: ...n [[mathematics]], there are two notable '''Artin conjectures''', the legacy of [[Emil Artin]]. 3: ...or space]] of finite dimension. Then the '''Artin conjecture''' states that the Artin L-function 13: ...ons, just as the [[Riemann hypothesis]] family of conjectures is. It is believed that it would follow from str... 15: The second '''Artin conjecture''' relates to the density of the set of primes ''... 21: [[Hooley]] proved that the second conjecture is a consequence of the first (a [[conditional pr... Deligne conjecture (1331 bytes) 1: ...ed by [[Pierre Deligne]]. These are independent [[conjecture]]s in various fields of mathematics. 3: The '''Deligne conjecture in [[deformation theory]]''' is about the [[categ... 5: The '''Deligne conjecture on special values of [[L-function]]s''' is a form... 7: There is a '''Deligne conjecture on 1-motives''' arising in the theory of [[motive... 9: There is a '''Gross-Deligne conjecture''' in the theory of [[complex multiplication]]. Gradient conjecture (804 bytes) 3: The '''gradient conjecture''', due to [[René Thom]], was proved in 2000 by K... New Mersenne conjecture (748 bytes) 1: ...jecture''' (or '''Bateman, Selfridge and Wagstaff conjecture''') is a statement concerning certain [[prime num... 9: ... and Wagstaff, Jr., Samuel S., ''The new Mersenne conjecture'', Amer. Math. Monthly, 96 (1989) 125-128 Mumford conjecture (1213 bytes) 1: In [[mathematics]], the '''Mumford conjecture''' states that for any [[semisimple]] [[algebraic... 5: ... the extension to prime characteristic ''p''. The conjecture was proved in 1975 by W. J. Haboush, about a deca... 9: ''There are other '''Mumford conjectures''', for example on the [[mapping class group]].'... Scholz conjecture (1031 bytes) 1: [[Category:Conjectures]] 3: ...''' or the '''Brauer-Scholz conjecture''') is a [[conjecture]] from [[1937]] stating that Seifert conjecture (2221 bytes) 1: ...istence as a conjecture. He also established the conjecture for perturbations of the [[Hopf fibration]]. 3: The conjecture was disproven in 1974 by [[Paul Schweitzer]], who... 6: ...-smooth counterexample to the Hamiltonian Seifert conjecture in <math>R^4</math>]'', Ann. of Math. (2) 158 (... 7: ...''<math>C^2</math> counterexamples to the Seifert conjecture'', Topology 27 (1988), no. 3, 249--278. 8: ...A volume-preserving counterexample to the Seifert conjecture'', Comment. Math. Helv. 71 (1996), no. 1, 70--... Dinitz conjecture (584 bytes) 1: In [[combinatorics]], the '''Dinitz conjecture''' was a problem on the extension of arrays to ''... 3: ...n ''n''-element set of the symbols. The '''Dinitz conjecture''', now a theorem, is that it is then possible to... Littlewood conjecture (1560 bytes) 1: In [[mathematics]], the '''Littlewood conjecture''' is a open problem ([[as of 2004]]) in [[Diopha... 7: ...ay, in group-theoretic terms. This is now another conjecture, expected to hold for ''n'' ≥ 3: it is stated ... 9: '''''Conjecture''''': for any ''g'' in ''G''/Γ such that ''... 11: This in turn is a special case of a general conjecture of [[Grigory Margulis|Margulis]] on [[Lie group]]... 13: ...s (α,β) violating the statement of the conjecture must be small. Einsiedler, Katok and Lindenstraus... Collatz conjecture (3700 bytes) 1: ...n as the '''3''n'' + 1 conjecture''', the '''Ulam conjecture''' or the '''Hailstone sequence''' or '''Hailston... 13: The sequence of Collatz conjecture can be easily computated by: 35: The Collatz conjecture says that this process ''always'' stops, no matte... 37: ...ul Erdös|Paul Erdős]] said about the Collatz conjecture: "Mathematics is not yet ready for such problems.... 39: ...e heuristic, statistical arguments supporting the conjecture: if one considers only the ''odd'' numbers in the... Linearization conjecture (560 bytes) 1: The linearization conjecture states that a finite group action on the 3-sphere... 3: ...ptization conjecture]] is true, the linearization conjecture would be true. Property P conjecture (907 bytes) 1: ...ery on the knot is non-[[simply-connected]]. The conjecture states that all knots, except the unknot, have Pr... 3: ...rted by [[RH Bing]], who popularized the name and conjecture. 5: ...ht of as a first step to resolving the [[Poincare conjecture]], since the [[Lickorish-Wallace theorem]] says a... 10: [[Category:3-manifolds]][[Category:Conjectures]]
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