This conjecture seems to be confirmed in the introduction of the first volume of the chronicles of Gallus Anonymus concerning the Pomeranians: Although often the leaders of the forces defeated by the Polish duke sought salvation in baptism, as soon as they regained their strength, they repudiated the Christian faith and started the war against Christians anew.

This problem seems to have lain dormant for a time, until J. H. C. Whitehead revived interest in the conjecture, when in the 1930s he first claimed a proof, and then retracted it.

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

It seems almost certain that economic factors alone would have caused considerable emigration from Ireland even without mass starvation, therefore it is a matter of conjecture as to what the population of Ireland would be today had there not been a famine in the 19th century.

However, these exceptions are often unstable solutions and / or do not lead to conserved quantum numbers so that " The ' spirit ' of the no-hair conjecture, however, seems to be maintained ".

The fact that heavy bodies have always a tendency to fall to the earth, no matter at what height they are placed above the Earth's surface, seems to have led Newton to conjecture that it was possible that the same tendency to fall to the earth was the cause by which the moon was retained in its orbit round the earth.

The earliest published statement of the conjecture seems to be in.

Although von Neumann's name is popularly attached to the conjecture, its first written appearance seems to be due to Mahlon Day in 1957.

While a proof of Schanuel's conjecture with number theoretic tools seems a long way off, connections with model theory have prompted a surge of research on the conjecture.

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

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.

Testing other values shows that no particle with enough angular momentum to violate the censorship conjecture would be able to enter the black hole, because they have too much angular momentum to fall in.

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.

If the four-color conjecture were false, there would be at least one map with the smallest possible number of regions that requires five colors.

The answer to this question turned out to be negative: in 1952, Gleason, Montgomery and Zippin showed that if G is a topological manifold with continuous group operations, then there exists exactly one analytic structure on G which turns it into a Lie group ( see also Hilbert – Smith conjecture ).

" And while the conjecture may one day be solved, the argument applies to similar unsolved problems ; to Brouwer, the law of the excluded middle was tantamount to assuming that every mathematical problem has a solution.

Many questions around prime numbers remain open, such as Goldbach's conjecture, which asserts that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, which says that there are infinitely many pairs of primes whose difference is 2.

The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere.

An exposition of attempts to prove this conjecture can be found in the non-technical book Poincaré's Prize by George Szpiro.

Historically, while the conjecture in dimension three seemed plausible, the generalized conjecture was thought to be false.

This so-called smooth Poincaré conjecture, in dimension four, remains open and is thought to be very difficult.

Mark Srednicki has argued that the fundamental postulate can be derived assuming only that Berry's conjecture ( named after Michael Berry ) applies to the system in question.

Berry's conjecture has also been shown to be equivalent to an information theoretic principle of least bias.

In this case A is called the hypothesis of the theorem ( note that " hypothesis " here is something very different from a conjecture ) and B the conclusion ( A and B can also be denoted the antecedent and consequent ).

For example, the Mertens conjecture is a statement about natural numbers that is now known to be false, but no explicit counterexample ( i. e., a natural number n for which the Mertens function M ( n ) equals or exceeds the square root of n ) is known: all numbers less than 10 < sup > 14 </ sup > have the Mertens property, and the smallest number which does not have this property is only known to be less than the exponential of 1. 59 × 10 < sup > 40 </ sup >, which is approximately 10 to the power 4. 3 × 10 < sup > 39 </ sup >.

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 ).

To be considered a conjecture, a statement must usually be proposed publicly, at which point the name of the proponent may be attached to the conjecture, as with Goldbach's conjecture.

He may have been married, a conjecture supported by his writings.

This conjecture is also supported by other letters Galois later wrote to his friends the night before he died.

Current wisdom has it that the massive coronal main sequence stars are late-A or early F stars, a conjecture that is supported both by observation and by theory.

" which argued that the " Bible, alongside our senses, supported the idea that the earth was flat and immovable and this essential truth should not be set aside for a system based solely on human conjecture ".

Regarding his abrupt disappearance, one conjecture is that his master was unhappy with his retainer's association with the demimonde of the kabuki theatre, instead of the more refined Noh theatre which the master supported.

Modern costumers conjecture that it probably consisted of one or more large hoops with horizontal stiffeners which radiated from around the waist in order to produce a flat platter-like shape when supported underneath by the " bumroll " or " French Farthingale " described above.

This conjecture is supported by the presence of Datuidoc's Stone in the north aisle ( originally in the porch ), dating from around AD 550-600.

Precisely how the awning was supported is a matter of 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.

* Crank conjecture, a term coined by Freeman Dyson to explain congruence patterns in integer partitions

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

At the moment, it is not known how the material is produced or if it remains stable without applied pressure, however, there is conjecture that it is possible to produce a new stable state of matter by compressing ultracold deuterium in a Rydberg state.

The most celebrated single question in the field, the conjecture known as Fermat's Last Theorem, was solved by Andrew Wiles but using tools from algebraic geometry developed during the last century rather than within number theory where the conjecture was originally formulated.

Woudhuizen revived a conjecture to the effect that the Tyrsenians came from Anatolia, including Lydia, whence they were driven by the Cimmerians in the early Iron Age, 750 – 675 BC, leaving some colonists on Lemnos.

Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem which was proposed by Leonhard Euler in 1769.

The conjecture was disproven by L. J. Lander and T. R. Parkin in 1966 when they found the following counterexample for k

Another early published reference by in turn credits the conjecture to De Morgan.

This formula, the Heawood conjecture, was conjectured by P. J.

Beyond the Bible, considerable conjecture has been put forward over the centuries in the form of Christian and Rabbinic tradition, but such accounts are dismissed by modern scholars as speculative and apocryphal.

This conjecture, however, is discredited by the Oxford English Dictionary.

But Steinschneider will not admit the possibility of this conjecture, while Renan scarcely strengthens it by regarding " Andreas " as a possible northern corruption of " En Duran ," which, he says, may have been the Provençal surname of Anatoli, since Anatoli, in reality, was but the name of his great-grandfather.

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

A conjecture developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke in 2001, called " mysterious duality ", concerns a set of mathematical similarities between objects and laws describing M-theory on k-dimensional tori ( i. e. type II superstring theory on T < sup > k − 1 </ sup > for k > 0 ) on one side, and geometry of del Pezzo surfaces ( for example, the cubic surfaces ) on the other side.

He was awarded the Bôcher Memorial Prize in mathematical analysis in 1964 for his paper " On a conjecture by Littlewood and idempotent measures ", and lends his name to the Cohen-Hewitt factorization theorem.

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv.

In 1961 Stephen Smale shocked mathematicians by proving the Generalized Poincaré conjecture for dimensions greater than four and extended his techniques to prove the fundamental h-cobordism theorem.

In these papers he sketched a proof of the Poincaré conjecture and a more general conjecture, Thurston's geometrization conjecture, completing the Ricci flow program outlined earlier by Richard Hamilton.