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.

Of this school, which had Joseph Louis Lagrange for its professor of mathematics, there is an amusing account in the life of Gilbert Elliot who met Mirabeau there.

* Lagrange multiplier, a scalar variable used in mathematics to solve an optimisation problem for a given constraint.

In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760.

His teachers recognized his talents in mathematics, but by 15 years of age he had already learned all the material taught at the school, and he began to study differential calculus from the works of Euler and Lagrange.

* Series reversion, in mathematics

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.

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.

There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory ; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.

In one system which is usual in physics ( r, θ, φ ) gives the radial distance, polar angle, and azimuthal angle, whereas in another system used in many mathematics books ( r, θ, φ ) gives the radial distance, azimuthal angle, and polar angle.

Internationally, the university is known for research relating to the genome of the Populus tree ( Life sciences ), contributions to the Gleason problem and function spaces on fractals ( mathematics ) and its school of industrial design which gives degree programs in English open to students from all of the world.

* What gives mathematics its hold on experience?

The applied tools of the mathematics disciplines of Celestial mechanics or its subfield Orbital mechanics ( both predict orbital paths and positions ) about a center of gravity are used to generate an ephemeris ( plural: ephemerides ; from the Greek word ephemeros = daily ) which is a table of values that gives the positions of astronomical objects in the sky at a given time or times, or a formula to calculate such given the proper time offset from the epoch.

* What gives mathematics its hold on experience?

* Multiplicative inverse, in mathematics, the number 1 / x, which multiplied by x gives the product 1, also known as a reciprocal

It gives no indication on which axiomatic system should be prefered as a foundation of mathematics.

Brouwer gives brief synopsis of his belief that the law of excluded middle cannot be " applied without reservation even in the mathematics of infinite systems " and gives two examples of failures to illustrate his assertion.

In combinatorial mathematics, Hall's marriage theorem, or simply Hall's Theorem, gives a necessary and sufficient condition for being able to select a distinct element from each of a collection of finite sets.

Some logicians, while accepting that classical mathematics is correct, still believe that the constructive approach gives a better insight into the true meaning of theorems, in much this way.

In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green, and is the two-dimensional special case of the more general Stokes ' theorem.

In mathematics, a function is well-defined if it gives the same result when the form ( the way in which it is presented ) but not the value of an input is changed.

In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain.

Meanwhile, a mathematics teacher named Elizabeth Whittaker, who was also present at the party, gives Hercule Poirot an important piece of evidence when she reveals that while the party-goers were playing Snapdragon, Elizabeth went out to hall and saw Rowena Drake coming out of the lavatory on the first floor landing.

On the other hand Brouwer gives strong counterexamples, based on properties that hold only in his constructive mathematics.

In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators.

In the mathematical fields of topology and K-theory, the Serre – Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: " projective modules over commutative rings are like vector bundles on compact spaces ".

Most importantly, through its Charitable Trust, it gives help and support to those who are less fortunate, with an emphasis on making a difference in improving education, particularly in the area of mathematics.

In mathematics, Eisenstein < nowiki >' s </ nowiki > criterion gives an easily checked sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers — that is, for it to be unfactorable into the product of lower-degree polynomials with rational coefficients.

In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic.

* Euler gives up his post as director of mathematics at the Prussian Academy of Sciences and returns to Saint Petersburg.