Whether or not Danchin is correct in suggesting that Thompson's resumption of the opium habit also dates from this period is, of course, a matter of conjecture.

Whether it could be as disastrous for American labor as, say, Jimmy Hoffa of the Teamsters, is a matter of conjecture.

Our conjecture is, then, that regardless of the manner in which school lessons are taught, the compulsive child accentuates those elements of each lesson that aid him in systematizing his work.

Because all clades are represented in the southern hemisphere but many not in the northern hemisphere, it is natural to conjecture that there is a common southern origin to them.

In some applications it is useful to be able to compute the Bernoulli numbers B < sub > 0 </ sub > through B < sub > p − 3 </ sub > modulo p, where p is a prime ; for example to test whether Vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime.

A conjecture is a proposition that is unproven.

In mathematics, a conjecture is an unproven proposition that appears correct.

In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample would immediately bring down the conjecture.

Sometimes a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results.

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

Because many outstanding problems in number theory, such as Goldbach's conjecture are equivalent to solving the halting problem for special programs ( which would basically search for counter-examples and halt if one is found ), knowing enough bits of Chaitin's constant would also imply knowing the answer to these problems.

He is remembered today for Goldbach's conjecture.

Goldbach is most noted for his correspondence with Leibniz, Euler, and Bernoulli, especially in his 1742 letter to Euler stating his Goldbach's conjecture.

In computability theory, the Church – Turing thesis ( also known as the Turing-Church thesis, the Church – Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis ) is a combined hypothesis (" thesis ") about the nature of functions whose values are effectively calculable ; or, in more modern terms, functions whose values are algorithmically computable.

Little is known of his life before he became a bishop ; the assignment of his birth to the year 315 rests on conjecture.

Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular Lorentzian manifold.

Whether this formula produces an infinite quantity of Carmichael numbers is an open question ( though it is implied by Dickson's conjecture ).

While Heydrich believed they had successfully deluded Stalin into executing or dismissing some 35, 000 of his officer corps, the importance of Heydrich's part is a matter of speculation and conjecture.

( The second ~ is not part of the conjecture and is proved by integration by parts.

Pursuing this type of analysis more carefully, Hardy and Littlewood in 1923 conjectured ( as part of their famous Hardy – Littlewood prime tuple conjecture ) that for any fixed c ≥ 2, the number of representations of a large integer n as the sum

* Goldbach's conjecture, part of Chris Caldwell's Prime Pages.

The transcontinental wish seems to have been only naive conjecture on the part of those outside the project.

The surprising part of the conjecture was the extension to factors of Jacobians of modular curves of genus > 1.

Amongst his most original contributions were: his " Conjecture II " ( still open ) on Galois cohomology ; his use of group actions on Trees ( with H. Bass ); the Borel-Serre compactification ; results on the number of points of curves over finite fields ; Galois representations in ℓ-adic cohomology and the proof that these representations have often a " large " image ; the concept of p-adic modular form ; and the Serre conjecture ( now a theorem ) on mod-p representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.

The conjecture was featured by the Australian Mathematical Society Gazette as part of the Millennium Problems series.

In the final part of the paper, Austin further extends the discussion to relations, presenting a series of arguments to reject the idea that there is some thing that is a relation. His argument likely follows from the conjecture of his colleague, S. V. Tezlaf, who questioned what makes " this " " that ".

One of the influential examples, both for the history of the more general L-functions and as a still-open research problem, is the conjecture developed by Bryan Birch and Peter Swinnerton-Dyer in the early part of the 1960s.

( Dwork had already managed to prove the rationality part of the conjectures in 1960 using p-adic methods ), and the remaining conjecture, the analogue of the Riemann hypothesis was proved by Pierre Deligne ( 1974 ) using ℓ-adic cohomology.

The conjecture that ringforts can be seen to have evolved from and be part of an Iron Age tradition has been expanded by Darren Limbert.

Quillen was awarded the Fields Medal in 1978 in part for his proof of the Serre conjecture.

Jean-Louis Matharan, for his part, considers that " any overall figure of detained suspects remain in the state is pure conjecture ," especially since, from August 1792 to Thermidor Year II, " the release of jailed suspects was uninterrupted ," although there were likely fewer arrests, and that there have been claims about the rapid release of those arrested and shorter terms of imprisonment.

It is known that he took an active part in the planning phase of the conspiracy to assassinate Paul I, but his role in the actual killing remains a matter of conjecture.

It only becomes apparent at the end of this section that this conjecture is part of a fiction composed by Zuckerman.

His citations are often contradictory and thought to be based in part on his own conjecture.

In 1934, the Whitehead link was used as part of his construction of the now-named Whitehead manifold, which refuted his previous purported proof of the conjecture.

Schanuel's conjecture is part of this axiomatisation, and so the natural conjecture that the unique model of cardinality continuum is actually isomorphic to the complex exponential field implies Schanuel's conjecture.

As a mathematician he is best known for his part in the Birch and Swinnerton-Dyer conjecture relating algebraic properties of elliptic curves to special values of L-functions, which was developed with Bryan Birch during the first half of the 1960s with the help of machine computation, and for his work on the Titan operating system.

As a proof that Otto had the full confidence and support of the King of England, we find that the moment he obtained his liberty, he wrote to communicate the same to Henry III, who was his cousin, and as Henry's answer dated 6 March 1229 has fortunately been preserved by Thomas Rymer, it becomes a valuable part of these annals, as it puts our conjecture beyond a doubt.

In an episode of Mr. Young, Derby ( Gig Morton ) " solves " the conjecture while experiencing induced sleep deprivation during an sleepover at Finnegan High as part of Young's class project.

If the conjecture were true, it would be a generalization of Fermat's last theorem, which could be seen as the special case n = 2: if, then.

In 1943, Hugo Hadwiger formulated the Hadwiger conjecture, a far-reaching generalization of the four-color problem that still remains unsolved.

the Heawood conjecture, a generalization of the four color theorem, which would require seven.

The Hardy – Littlewood conjecture ( after G. H. Hardy and John Littlewood ) is a generalization of the twin prime conjecture.

Another higher-dimensional generalization of Faltings ' theorem is the Bombieri – Lang conjecture that if X is a pseudo-canonical variety ( i. e., variety of general type ) over a number field k, then X ( k ) is not Zariski dense in X.

A natural generalization of the Hodge conjecture would ask:

pointed out that a generalization of Rankin's result for higher even values of k would imply the Ramanujan conjecture, and Deligne realized that in the case of zeta functions of varieties, Grothendieck's theory of zeta functions of sheaves provided an analogue of this generalization.

showed that b < sub > k </ sub > ≤ 14 for all k. They conjectured that 14 can be replaced by 1 as a natural generalization of the Bieberbach conjecture.

A generalization of the Kakeya conjecture is to consider sets that contain, instead of segments of lines in every direction, but, say, portions of k-dimensional subspaces.

It is also a generalization of the longstanding Dinitz conjecture, which was eventually solved by Galvin in 1994 using list edge-coloring.

The generalized Ramanujan conjecture or Ramanujan – Petersson conjecture, introduced by, is a generalization to other modular forms or automorphic forms.

reformulated the Ramanujan – Petersson conjecture in terms of automorphic representations for GL < sub > 2 </ sub > as saying that the local components of automorphic representations lie in the principal series, and suggested this condition as a generalization of the Ramanujan – Petersson conjecture to automorphic forms on other groups.

It provides a vast generalization of such conjectures as the Hardy and Littlewood conjecture on the density of twin primes or their conjecture on primes of the form n < sup > 2 </ sup > + 1 ; it is also a strengthening of Schinzel's hypothesis H.

* The Shimura-Taniyama-Weil conjecture, a generalization of Fermat's last theorem.

This conjecture, a far-reaching generalization of the four-color problem, was made by Hugo Hadwiger in 1943 and is still unsolved.

He proved that a lattice pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane ( a generalization of Thue's theorem, a 2-dimensional analog of the Kepler conjecture ).