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.

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 ).

An unproven proposition that is believed to be true is known as a conjecture.

Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others.

As an unproven conjecture that eluded brilliant mathematicians ' attempts to either prove it or disprove it for generations, his statement became famous as Fermat's Last Theorem.

An unproven statement that is believed to be true is called a conjecture ( or sometimes a hypothesis, but with a different meaning from the one discussed above ).

The conjecture has been shown to hold up through 4 × 10 < sup > 18 </ sup > and is generally assumed to be true, but remains unproven despite considerable effort.

These are unproven ; in 1967, Hooley published a conditional proof for the second conjecture, assuming certain cases of the Generalized Riemann hypothesis.

* Legendre's conjecture and Andrica's conjecture, much weaker but still unproven upper bounds on prime gaps

In graph theory, the unproven Erdős – Gyárfás conjecture, made in 1995 by the prolific mathematician Paul Erdős and his collaborator András Gyárfás, states that any graph with minimum degree 3 contains a simple cycle whose length is a power of two.

The cycle double cover conjecture is the unproven assertion that every bridgeless graph has a cycle double cover.

The Hadwiger conjecture has been proven only for k ≤ 6, but remains unproven in the general case.

As of 2007, this conjecture remained unproven despite having attracted a large amount of research.

* Hadwiger's conjecture, still unproven, relates the size of the largest clique minor in a graph to its chromatic number.

* The Erdős – Faber – Lovász conjecture is another unproven statement relating graph coloring to cliques.

In number theory, the Bateman – Horn conjecture is an unproven statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A. Horn, who proposed it in 1962.

Naik has said that the theory of evolution is " only a hypothesis, and an unproven conjecture at best ".

The Gelfond – Schneider theorem follows from this strengthened version of Baker's theorem, as does the currently unproven four exponentials conjecture.

In fact, Zilber shows that this conjecture holds iff both Schanuel's conjecture and another unproven condition on the complex exponentiation field, which Zilber calls exponential-algebraic closedness, hold.

Tunnell's theorem provides an easily testable criterion for determining whether a number is congruent ; but his result relies on the Birch and Swinnerton-Dyer conjecture, which is still unproven.

In additive number theory, the Pollock octahedral numbers conjecture is an unproven conjecture that every positive integer is the sum of at most seven octahedral numbers.

Baum-Connes conjecture.

" Alternate History " looks at " what if " scenarios from some of history's most pivotal turning points and presents a completely different version, sometimes based on science and fact, but often based on conjecture.

One of the more dramatic successes of his theory was his prediction of the existence of secondary and tertiary alcohols, a conjecture that was soon confirmed by the synthesis of these substances.

The Weil conjecture on Tamagawa numbers proved resistant for many years.

He picked up another credited Weil conjecture, around 1967, which later under pressure from Serge Lang ( resp.

of Serre ) became known as the Taniyama – Shimura conjecture ( resp.

Taniyama – Weil conjecture ) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference.

His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.

' I cannot find, or at this moment learn, beyond vague conjecture where the French Fleet are gone to.

Tertullian named him as the author of the Epistle to the Hebrews, but this and other attributions are conjecture.

For example: the similarity of southern continent geological formations had led Roberto Mantovani to conjecture in 1889 and 1909 that all the continents had once been joined into a supercontinent ( now known as Pangaea ); Wegener noted the similarity of Mantovani's and his own maps of the former positions of the southern continents.

Karl Popper pioneered the use of the term " conjecture " in scientific philosophy.

For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1. 2 × 10 < sup > 12 </ sup > ( over a trillion ).

In anticipation of its eventual proof, some have proceeded to develop further proofs which are contingent on the truth of this conjecture.