Goldbach's conjecture (11698 bytes)
1: In mathematics, '''Goldbach's conjecture''' is one of the oldest [[unsolved problems in ma...
16: ...onhard Euler]] in which he proposed the following conjecture:
18: ... problem, answered with a stronger version of the conjecture:
20: ...nsolved ever since, although the weak form of the conjecture is much closer to resolution than the strong one.
24: The majority of mathematicians believe the conjecture (in both the weak and strong forms) to be true, a...

Goldbach's weak conjecture (3069 bytes)
1: ... conjecture''', also known as the '''odd Goldbach conjecture''' or the '''3-primes problem''', states that:
8: ...rimes, if proven, would establish Goldbach's weak conjecture. (Since if every even number >4 is the sum of two...
10: ...be the sum of three odd primes, the weak Goldbach conjecture is effectively proved! However, the exponent stil...
12: ...ized Riemann hypothesis]] implies Goldbach's weak conjecture. This result combines a general statement valid f...
17: [[es:Conjetura débil de Goldbach]]

Christian Goldbach (883 bytes)
1: ...[[Leonhard Euler]], and [[Nicholas I Bernoulli]]. Goldbach went to work at the newly opened [[St Petersburg ...
3: ...al field. He is remembered today for [[Goldbach's conjecture]].
5: [[Category:1690 births|Goldbach, Christian]]
6: [[Category:1764 deaths|Goldbach, Christian]]
7: [[Category:Mathematicians|Goldbach, Christian]]

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.

Scholz conjecture (1031 bytes)
1: [[Category:Conjectures]]
3: ...''' or the '''Brauer-Scholz conjecture''') is a [[conjecture]] from [[1937]] stating that

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]].'...

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...

Gradient conjecture (804 bytes)
3: The '''gradient conjecture''', due to [[René Thom]], was proved in 2000 by K...

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)

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...

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...

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--...

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

Jacobian conjecture (2220 bytes)
1: In [[mathematics]], the '''Jacobian conjecture''' is a celebrated problem on [[polynomial]]s in ...
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]]

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

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]].

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...

Poincaré conjecture (7277 bytes)
1: ...n [[mathematics]], the Poincaré conjecture is a [[conjecture]] about the characterisation of the [[three-dimen...
3: The Poincaré conjecture is one of the seven [[Millennium Prize Problems]]...
12: ... conjecture'''. Here is the standard form of the conjecture, which is equivalent to the above:
20: ...il [[J. H. C. Whitehead]] revived interest in the conjecture, when in the 1930s he first claimed a proof, and ...
22: ...[low-dimensional topology]]. Work on the Poincaré conjecture has resulted in many interesting mathematical con...

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 Erd&#337;s]] 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...

Geometrization conjecture (4198 bytes)
1: ...an geometry]] [[Category:3-manifolds]] [[Category:Conjectures]]
2: ...]]. Here are some essential concepts used in the conjecture:
9: Here is a formulation of Thurston's conjecture:
27: ...ation about Seifert manifolds, we can restate the conjecture more tersely as:
34: ...o Thurston in 1982 partially for his proof of the conjecture for [[Haken manifold]]s.

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