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.

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

In mathematics, the Poincaré conjecture ( ; ) is a theorem about the characterization of the three-dimensional sphere ( 3-sphere ), which is the hypersphere that bounds the unit ball in four-dimensional space.

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.

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

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and in all of mathematics.

As with many famous conjectures in mathematics, there are a number of purported proofs of the Goldbach conjecture, none accepted by the mathematical community.

* The television drama Lewis featured a mathematics professor who had won the Fields medal for his work on Goldbach's conjecture.

In mathematics the modularity theorem ( formerly called the Taniyama – Shimura – Weil conjecture and several related names ) states that elliptic curves over the field of rational numbers are related to modular forms.

In mathematics, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S < sup > 3 </ sup >.

" On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific " Breakthrough of the Year ", the first such recognition in the area of mathematics.

Context is also relevant ; in mathematics, the Pólya conjecture is true for numbers less than 906, 150, 257, but fails for this number.

Assuming something to be true for all numbers when it has been shown for over 906 million cases would not generally be considered hasty, but in mathematics a statement remains a conjecture until it is shown to be universally true.

The Hodge conjecture is a problem in mathematics that remains unsolved.

** Roger Frye used experimental mathematics techniques to find the smallest counterexample to Euler's sum of powers conjecture.

* Goldbach's conjecture, one of the oldest unsolved problems in number theory and in all of mathematics.

In mathematics, the Mertens conjecture is the incorrect statement that the Mertens function M ( n ) is bounded by √ n, which implies the Riemann hypothesis.

In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory.

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 ).

He pursued mathematics as an amateur, his most famous achievement being his confirmation in 1901 of Leonhard Euler's conjecture that no 6 × 6 Graeco-Latin square was possible .< ref >

His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.

In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.

In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.

In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

In mathematics, specifically commutative algebra, Hilbert's basis theorem states that every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated.

Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle which states that for any proposition, either that proposition is true, or its negation is.

The thought experiment illustrates quantum mechanics and the mathematics necessary to describe quantum states.

The thesis states that Turing machines indeed capture the informal notion of effective method in logic and mathematics, and provide a precise definition of an algorithm or ' mechanical procedure '.

The Church – Turing thesis states that this is a law of mathematics — that a universal Turing machine can, in principle, perform any calculation that any other programmable computer can.

Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order ( number of elements ) of every subgroup H of G divides the order of G. The theorem is named after Joseph Lagrange.

In mathematics, the well-ordering theorem states that every set can be well-ordered.

Hilbert's goals of creating a system of mathematics that is both complete and consistent were dealt a fatal blow by the second of Gödel's incompleteness theorems, which states that sufficiently expressive consistent axiom systems can never prove their own consistency.

During the 290s BC, Hellenistic civilization begins its emergence throughout the successor states of the former Argead Macedonian Empire of Alexander the Great resulting in the diffusion of Greek culture throughout the Ancient world and advances in Science, mathematics, philosophy and etc.

In mathematics, the convolution theorem states that under suitable

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side ( and, if the setting is a Euclidean space, then the inequality is strict if the triangle is non-degenerate ).< ref name = Khamsi >

In mathematics, de Moivre's formula ( a. k. a. De Moivre's theorem and De Moivre's identity ), named after Abraham de Moivre, states that for any complex number ( and, in particular, for any real number ) x and integer n it holds that

The Sumerians were incredibly advanced: as well as inventing writing, they also invented early forms of mathematics, early wheeled vehicles, astronomy, astrology and the calendar and they created the first city states / nations such as Uruk, Ur, Lagash, Isin, Umma, Eridu, Nippur and Larsa.

In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact.

In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements for short exact sequence are equivalent.

In mathematics, the parity of an object states whether it is even or odd.

In mathematics, the well-ordering principle states that every non-empty set of positive integers contains a smallest element.

In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space.

In engineering, mathematics and the physical and biological sciences, common terms for the points around which the system gravitates include: attractors, stable states, eigenstates / eigenfunctions, equilibrium points, and setpoints.