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 ).

* The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, and proved by Melfi in 1996: every even number is a sum of two practical numbers.

* In the cartoon The Adventures of Jimmy Neutron: Boy Genius ( 2003 ), Jimmy stated that he was in the middle of proving Goldbach's prime number conjecture.

stated a preliminary ( slightly incorrect ) version of the conjecture at the 1955 international symposium on algebraic number theory in Tokyo and Nikko.

proved | a < sub > 2 </ sub >| ≤ 2, and stated the conjecture that | a < sub > n </ sub >| ≤ n. and independently proved the conjecture for starlike functions.

With these definitions, the conjecture can be stated as:

The conjecture was first stated by in his paper ' On the six-cornered snowflake '.

In some ways it is the most accessible discipline in pure mathematics for the general public: for instance the Goldbach conjecture is easily stated ( but is yet to be proved or disproved ).

This flat cover conjecture was explicitly first stated in.

Kummer referred to his own partial proof of Fermat's Last Theorem for regular primes as " a curiosity of number theory rather than a major item " and to the higher reciprocity law ( which he stated as a conjecture ) as " the principal subject and the pinnacle of contemporary number theory.

Since Frasier mentioned in an episode of Cheers that he was Episcopalian, it is assumed that Martin and Niles are Episcopalian as well ; however continuity issues within Cheers throw this conjecture into jeopardy, as Frasier also mentions in a Cheers episode that he had no formal religious upbringing ( in one episode, he stated that his father was a scientist who died before Frasier became a psychiatrist ).

There is now another conjecture, expected to hold for n ≥ 3: it is stated in terms of G

Before that, he had stated the famous Catalan's conjecture, which was published in 1844 and was eventually proved in 2002, by the Romanian mathematician Preda Mihăilescu.

In mathematics, the von Neumann conjecture stated that a group G is non-amenable if and only if G contains a subgroup that is a free group on two generators.

The Dinitz conjecture is closely related to graph theory, in which it can be succinctly stated as for natural.

Unaware of Melchior's proof, again stated the conjecture, which was proved first by Tibor Gallai, and soon afterwards by other authors.

The conjecture as stated is due to Takashi Agoh ( 1990 ); an equivalent formulation is due to Giuseppe Giuga, from 1950, to the effect that p is prime iff

As stated above, the conjecture is not true: the single polynomial ƒ < sub > 1 </ sub >( x ) = − x produces only negative numbers when given a positive argument, so the fraction of prime numbers among its values is always zero.

He also formulated the Shafarevich conjecture which stated the finiteness of the set of Abelian varieties over a number field having fixed dimension and prescribed set of primes of bad reduction.

His Theorem I, on the Goldbach conjecture, was stated above.

An equivalent form of the Hadwiger conjecture ( the contrapositive of the form stated above ) is that, if there is no sequence of edge contractions ( each merging the two endpoints of some edge into a single supervertex ) that brings graph G to the complete graph K < sub > k </ sub >, then G must have a vertex coloring with k − 1 colors.

It is also known as the contraction clique number of G. The Hadwiger conjecture can be stated in the simple algebraic form χ ( G ) ≤ h ( G ) where χ ( G ) denotes the chromatic number of G. A related concept, the achromatic number of G, is the size of the largest clique that can be formed by contracting a family of independent sets in G ).

" In 2011, together with Manuel Kauers and Christoph Koutschan, Zeilberger proved the q-TSPP conjecture, which was independently stated in 1983 by George Andrews and David P. Robbins.

Substantial progress has been made on two-dimensional percolation through the conjecture of Oded Schramm that the scaling limit of a large cluster may be described in terms of a Schramm – Loewner evolution.

The generalisation of the Law of Mass Action, in terms of affinity, to equilibria of arbitrary stoichiometry was a bold and correct conjecture.

It is in terms of this L-function that the conjecture of Birch and Swinnerton-Dyer is posed.

It also makes them harder to deal with in terms of the conjectural algebraic geometry ( Hodge conjecture and Tate conjecture ).

( What it is not, is a Galois group ; however in terms of the Tate conjecture and Galois representations on étale cohomology, it predicts the image of the Galois group, or, more accurately, its Lie algebra.

The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in On Interpretation is by using a linking verb e. g. P is S. However, in the Prior Analytics Aristotle rejects the usual form in favor of three of his inventions: 1 ) P belongs to S, 2 ) P is predicated of S and 3 ) P is said of S. Aristotle does not explain why he introduces these innovative expressions but scholars conjecture that the reason may have been that it facilitates the use of letters instead of terms avoiding the ambiguity that results in Greek when letters are used with the linking verb.

In less grandiloquent terms, Charles Lamb, writing about the Tale of Paraguay to Southey in 1825, says, " How she Dobrizhoffered it all out, puzzles my slender Latinity to conjecture.

In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic function to map the open unit disc injectively into the complex plane in terms of the function's Taylor series.

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.

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.

Gilbreath's conjecture is a hypothesis, or a conjecture, in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth.

The Erdős – Straus conjecture states that, in this case, as in the case for the numerator 3, the maximum number of terms in an expansion is three.