* In mathematics, the modularity theorem ( formerly the Taniyama – Shimura conjecture ) establishes a connection between elliptic curves and modular forms.

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.

Following Desargues ' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was called the " Mystic Hexagram ", Essai pour les coniques (" Essay on Conics ") and sent it — his first serious work of mathematics — to Père Mersenne in Paris ; it is known still today as Pascal's theorem.

In mathematics terminology, the vector space of bras is the dual space to the vector space of kets, and corresponding bras and kets are related by the Riesz representation theorem.

In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem.

In mathematics, a Gödel code was the basis for the proof of Gödel's incompleteness theorem.

* Crystallographic restriction theorem, in mathematics

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below.

The classification theorem has applications in many branches of mathematics, as questions about the structure of finite groups ( and their action on other mathematical objects ) can sometimes be reduced to questions about finite simple groups.

Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development.

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 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.

Gödel's incompleteness theorem, another celebrated result, shows that there are inherent limitations in what can be achieved with formal proofs in mathematics.

The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics.

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.

In mathematics, the Hahn – Banach theorem is a central tool in functional analysis.

Of course, our understanding of what the theorem really means gains in profundity as the mathematics around the theorem grows.

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.

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms.

On the other hand, a deep theorem may be simply stated, but its proof may involve surprising and subtle connections between disparate areas of mathematics.

Some, on the other hand, may be called " deep ": their proofs may be long and difficult, involve areas of mathematics superficially distinct from the statement of the theorem itself, or show surprising connections between disparate areas of mathematics.

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.

Rose – Hulman Institute of Technology ( abbreviated RHIT ), formerly Rose Polytechnic Institute, is a small private college specializing in teaching engineering, mathematics and science.

The American Invitational Mathematics Examination ( AIME ) is a 15-question 3-hour test given since 1983 to those who rank in the top 5 % ( or score at least 100 ) on the AMC 12 high school mathematics contest ( formerly known as the AHSME ), and starting in 2010, those who rank in the top 2. 5 % ( or score at least 120 ) on the AMC 10.

In mathematics, Rodrigues's formula ( formerly called the Ivory – Jacobi formula ) is a formula for Legendre polynomials independently introduced by, and.

Annenberg Hall, formerly Memorial Hall, houses the English, mathematics, and foreign language departments.

His father, Billy Tao () is a pediatrician, and his mother is a physics and mathematics graduate from the University of Hong Kong, formerly a secondary school teacher of mathematics in Hong Kong.

The mathematics faculty is staffed mainly by teachers formerly from other independent schools or junior colleges in Singapore.

The MƒA Fellowship in New York City ( formerly known as the Newton Fellowship Program ) is a five year program for mathematically sophisticated, recent college graduates and mid-career professionals who are interested in using their talents to make a difference in the lives of young people by teaching secondary school mathematics in New York City public schools.

The MƒA Master Teacher Program ( formerly known as the Newton Master Teacher Program ) is a four year program designed to retain exceptional public secondary school mathematics teachers currently teaching in New York City.

The most general setting in which these words have meaning is an abstract branch of mathematics called category theory.

In mathematics, a binary operation on a set is a calculation involving two elements of the set ( called operands ) and producing another element of the set ( more formally, an operation whose arity is two ).

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.

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

Certain categories called topoi ( singular topos ) can even serve as an alternative to axiomatic set theory as a foundation of mathematics.

In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments ( or an n-tuple of arguments ) in such a way that it can be called as a chain of functions each with a single argument ( partial application ).

Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform ( called classical control theory ).

This program is still recognizable in the most popular philosophy of mathematics, where it is usually called formalism.

Instructors in primary and secondary institutions are often called teachers, and they direct the education of students and might draw on many subjects like reading, writing, mathematics, science and history.

Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The latter sort of properties are called invariant ( mathematics ) | invariant s and studying them is the essence of geometry.

Then he moved to the Humboldt University of Berlin ( then called the Friedrich William University ) in 1878 where he continued his study of mathematics under Leopold Kronecker and the renowned Karl Weierstrass.

The reason why we do not deal with sensible objects in mathematics is because of another faculty of understanding called " categorial abstraction.

In mathematics and abstract algebra, a group is the algebraic structure, where is a non-empty set and denotes a binary operation called the group operation.

The physicist Richard Feynman called Euler's formula " our jewel " and " one of the most remarkable, almost astounding, formulas in all of mathematics.

In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.

A number representation ( called a numeral system in mathematics ) specifies some way of storing a number that may be encoded as a string of digits.

This period has been called the Golden Age of India and was marked by extensive achievements in science, technology, engineering, art, dialectic, literature, logic, mathematics, astronomy, religion, and philosophy that crystallized the elements of what is generally known as Hindu culture.

In mathematics, the harmonic mean ( sometimes called the subcontrary mean ) is one of several kinds of average.

In mathematics, an inner product space is a vector space with an additional structure called an inner product.

In mathematics, an identity function, also called identity map or identity transformation, is a function that always returns the same value that was used as its argument.

In mathematics, the inverse limit ( also called the projective limit ) is a construction which allows one to " glue together " several related objects, the precise manner of the gluing process being specified by morphisms between the objects.

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.