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.

This conjecture seems to be supported by Nozick's reputed support for " voluntary slavery ".

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.

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.

In 1897, J. J. Thomson confirmed Stoney's conjecture by discovering the first subatomic particle, the electron ( now denoted e < sup >−</ sup >).

Despite the discovery and exploration of the Solar System and centuries of conjecture, it remained this way until the first confirmed detection of extrasolar planets during the 1990s.

This conjecture was confirmed when he observed his skin to be hotter, his colour to be heightened, and his pulse quickened, whenever Stratonice came near him, while none of these symptoms occurred on any other occasion ; and accordingly he told Seleucus that his son's disease was incurable, for that he was in love, and that it was impossible that his passion could be gratified ; The king wondered what the difficulty could be, and asked who the lady was.

The total energy carried by these tachyons has been calculated in string field theory ; it agrees with the total energy of the D-branes, and all other tests have confirmed Sen's conjecture as well.

The conjecture that there was an amphitheater in the city is confirmed by a passage from the fifteenth-century Vita di Skanderbeg by Marin Barleti: " amphitheatrum mira arte ingenioque constructum ".

The former conjecture became established fanon, and was taken up in the spin-off media and was eventually confirmed by the official BBC website.

Melchior's proof showed that raised the question of whether approaches infinity with n. confirmed this conjecture by proving that.

Searches of this type by Allan Swett confirmed that the conjecture is true for all n up to 10 < sup > 14 </ sup >.

The award cited him " for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds ' Lie algebras, the proof of the Conway-Norton moonshine conjecture and the discovery of a new class of automorphic infinite products.

Mumford's conjecture about the extension to prime characteristic p was proved by W. J., about a decade after the problem had been posed by David Mumford, in the introduction to the first edition of his book Geometric Invariant Theory.

* 1982 Tsit-Yuen Lam for his expository work in his book Algebraic theory of quadratic forms ( 1973 ), and four of his papers: K_0 and K_1-an introduction to algebraic K-theory ( 1975 ), Ten lectures on quadratic forms over fields ( 1977 ), Serre's conjecture ( 1978 ), and The theory of ordered fields ( 1980 ).

In some exceptional cases, the statement of a conjecture, or the introduction of some new method or definition might assume relevance.

The conjecture was first proposed in 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed.

On July 1, 2010, he turned down the prize saying that he believes his contribution in proving the Poincaré conjecture was no greater than that of Hamilton's ( who first suggested using the Ricci flow for the solution ).

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific " Breakthrough of the Year ", the first time this had been bestowed in the area of mathematics.

Hamilton's program for proving the Poincaré conjecture involves first putting a Riemannian metric on the unknown simply connected closed 3-manifold.

In November 2002, Russian mathematician Grigori Perelman posted the first of a series of eprints on arXiv outlining a solution of the Poincaré conjecture.

The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937.

The green bar shows the failure of the Pòlya conjecture ; the blue curve shows the oscillatory contribution of the first Riemann zero.

Alternatively, the first philosopher can modify their claim so that the counterexample no longer applies ; this is analogous to when a mathematician modifies a conjecture because of a counterexample.

Together they devised the first Hardy – Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy – Littlewood conjecture.

Shooter wrote the story in which Ferro Lad died – the first " real " death of a Legionnaire ( although Lightning Lad had been believed dead for a while before ) – and introduced many other enduring concepts, including the Fatal Five, Shadow Lass, the Dark Circle, Mordru, and the " Adult Legion ", a conjecture regarding what the Legionnaires would be like when they grew up.

The first demonstration of this conjecture was published in 2008.

The abc conjecture ( also known as Oesterlé – Masser conjecture ) is a conjecture in number theory, first proposed by and as an integer analogue of the Mason – Stothers theorem for polynomials.

Goro Shimura and Taniyama worked on improving its rigor until 1957. rediscovered the conjecture, and showed that it would follow from the ( conjectured ) functional equations for some twisted L-series of the elliptic curve ; this was the first serious evidence that the conjecture might be true.

The first conjecture ( Agrawal ’ s conjecture ) was the basis for the formulation of the first deterministic prime test algorithm in polynomial time ( AKS algorithm ).