Although generalized to triple integrals by Lagrange in 1773, and used by Legendre, Laplace, Gauss, and first generalized to n variables by Mikhail Ostrogradski in 1836, it resisted a fully rigorous formal proof for a surprisingly long time, and was first satisfactorily resolved 125 years later, by Élie Cartan in a series of papers beginning in the mid-1890s (; ).

Laplace was disgruntled, and at the beginning of 1773, d ' Alembert wrote to Lagrange in Berlin to ask if a position could be found for Laplace there.

Henk and Ziegler attribute this result to Lagrange, in 1773 ( see references, pag.

Pierre Laplace ( in 1773 ) and Joseph Louis Lagrange ( in 1776 ) had already studied the problem, both of them showing that the major axes of the orbits are stable, by using a first degree approximation of the perturbing forces.

With the later development of abstract groups, this result of Lagrange on polynomials was recognized to extend to the general theorem about finite groups which now bears his name.

: EXAMPLE: Hegel here engages in a lengthy survey of the history and development of the Differential and Integral Calculus, citing the works of Cavalieri, Descartes, Fermat, Barrow, Newton, Leibniz, Euler, Lagrange, Landen, and Carnot.

The general theory of Pell's equation, based on continued fractions and algebraic manipulations with numbers of the form was developed by Lagrange in 1766 – 1769.

Lagrange did not prove Lagrange's theorem in its general form.

One may observe that the above computation can be repeated plainly in more general settings than: a generalization of the Lagrange inversion formula is already available working in the-modules, where is a complex exponent.

* Joseph Lagrange ( soldier ) ( 1763 – 1836 ), French infantry general

In Méchanique Analytique ( 1788 ) Lagrange derived the general equations of motion of a mechanical body.

* Lagrange publishes his second paper on the general process for solving an algebraic equation of any degree via Lagrange resolvents ; and proves Wilson's theorem that if n is a prime, then ( n − 1 )!

* Lagrange discusses representations of integers by general algebraic forms ; produces a tract on elimination theory ; publishes his first paper on the general process for solving an algebraic equation of any degree via Lagrange resolvents ; and proves Bachet's theorem that every positive integer is the sum of four squares.

He is most famous as the inventor of tensor calculus, although the advent of tensor calculus in dynamics goes back to Lagrange, who originated the general treatment of a dynamical system, and to Riemann, who was the first to think geometry in an arbitrary number of dimensions.

Mark Oliver Everett is the son of physicist Hugh Everett III, originator of the many-worlds interpretation of quantum theory and of the use of Lagrange multipliers for general engineering optimizations.

Count Joseph Lagrange ( 10 January 1763 – 16 January 1836 ) was a French soldier who rose through the ranks and gained promotion to the rank of general officer during the French Revolutionary Wars, subsequently pursuing a successful career during the Napoleonic Wars and winning promotion to the top military rank of General of Division.

Lagrange, tackling the general three-body problem, considered the behaviour of the distances between the bodies, without finding a general solution.

Lagrange gave a proof in 1770 based on his general theory of integral quadratic forms.

At 15, he was reading the original papers of Joseph Louis Lagrange, such as the landmark Réflexions sur la résolution algébrique des équations which likely motivated his later work on equation theory, and Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired, and his teachers accused him of affecting ambition and originality in a negative way.

In classical field theory, one writes down a Lagrangian density,, involving a field, φ ( x, t ), and possibly its first derivatives (∂ φ /∂ t and ∇ φ ), and then applies a field-theoretic form of the Euler – Lagrange equation.

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.

Supporting this theory, extrasolar planets have been discovered in Lagrange points of each other, and are expected to collide, after co-orbiting for millions of years.

A further step was the 1770 paper Réflexions sur la résolution algébrique des équations by the French-Italian mathematician Joseph Louis Lagrange, in his method of Lagrange resolvents, where he analyzed Cardano and Ferrarri's solution of cubics and quartics by considering them in terms of permutations of the roots, which yielded an auxiliary polynomial of lower degree, providing a unified understanding of the solutions and laying the groundwork for group theory and Galois theory.

Around 1770, Joseph Louis Lagrange began the groundwork that unified the many different tricks that had been used up to that point to solve equations, relating them to the theory of groups of permutations, in the form of Lagrange resolvents.

This innovative work by Lagrange was a precursor to Galois theory, and its failure to develop solutions for equations of fifth and higher degrees hinted that such solutions might be impossible, but it did not provide conclusive proof.

In optimal control theory, the Lagrange multipliers are interpreted as costate variables, and Lagrange multipliers are reformulated as the minimization of the Hamiltonian, in Pontryagin's minimum principle.

Lagrange contributed extensively to the theory, and Legendre ( 1786 ) laid down a method, not entirely satisfactory, for the discrimination of maxima and minima.

The ITN is based around a series of orbital paths predicted by chaos theory and the restricted three-body problem leading to and from the unstable orbits around the Lagrange points – points in space where the gravity between various bodies balances with the centrifugal force of an object there.

Ruffini developed Joseph Louis Lagrange's work on permutation theory, following 29 years after Lagrange ’ s " Réflexions sur la théorie algébrique des equations " ( 1770 – 1771 ) which was largely ignored until Ruffini who established strong connections between permutations and the solvability of algebraic equations.

In this book Gauss brings together results in number theory obtained by mathematicians such as Fermat, Euler, Lagrange and Legendre and adds important new results of his own.

Jayadeva ( जयद े व ) was a ninth-century Indian mathematician, who further developed the cyclic method ( chakravala method ) that was called by Hermann Hankel " the finest thing achieved in the theory of numbers before Lagrange ( 18th century )".

These points remain fixed relative to the Earth and the Moon in theory, although orbital perturbations render only two of the five Lagrange postulated practically stable.

Fermat, Euler, Lagrange, Legendre, and other number theorists of the 17th and 18th centuries proved some theorems and made some conjectures about quadratic residues, but the first systematic treatment is § IV of Gauss's Disquisitiones Arithmeticae ( 1801 ).

Applying the Lagrange interpolation formula to do quadratic interpolation on the inverse of f yields

Lagrange gave a proof in 1775 that was based on his study of quadratic forms.

The discriminant of the quadratic form is defined to be ( this is the definition due to Gauss ; Lagrange did not require the term to have even coefficient, and defined the discriminant as ).

Lagrange proved that all forms of discriminant − 1 and are equivalent ( a form satisfying this conditions is said to be reduced ).

He had read extensively in Leibniz, Joseph Louis Lagrange, Thomas Simpson, and Lacroix and was seriously disappointed in the mathematical instruction available at Cambridge.

French Dominicans founded and administer the École Biblique et Archéologique française de Jérusalem founded in 1890 by Père Marie-Joseph Lagrange O. P.

They associated with their work the chemist Louis-Bernard Guyton de Morveau, the mathematician and astronomer Joseph-Louis Lagrange, the astronomer Joseph Jérôme Lefrançois de Lalande, the mathematician Gaspard Monge, the astronomer and naval geographer Alexandre Guy Pingré, and the poet, actor and playwright Fabre d ' Églantine, who invented the names of the months, with the help of André Thouin, gardener at the Jardin des Plantes of the Muséum National d ' Histoire Naturelle in Paris.

In the distant future, Mankind has colonized space ( with clusters of space colonies at each of the five Earth-Moon Lagrange points ), and, down on the Earth, the nations have united as the United Earth Sphere Alliance.

Paths have been calculated which link the Lagrange points of the various planets into the so-called Interplanetary Transport Network.

* 1736 – Joseph-Louis Lagrange, Italian-born mathematician ( d. 1813 )

* Lambda denotes a Lagrange multiplier in multi-dimensional calculus.

The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them.

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhata, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.

Lagrange proved that for any natural number n that is not a perfect square there are x and y > 0 that satisfy Pell's equation.

This algebra is quotiented over by the ideal generated by the Euler – Lagrange equations.

Despite initial opposition from her parents and difficulties presented by a sexist society, she gained education from books in her father's library and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss.

" Germain obtained the lecture notes and began sending her work to Joseph Louis Lagrange, a faculty member.

" When Lagrange saw the intelligence of M. LeBlanc, he requested a meeting, and thus Sophie was forced to disclose her true identity.

Fortunately, Lagrange did not mind that Germain was a woman, and he became her mentor.

Germain also proved or nearly proved several results that were attributed to Lagrange or were rediscovered years later.

In 1772, Italian-born mathematician Joseph-Louis Lagrange, in studying the restricted three-body problem, predicted that a small body sharing an orbit with a planet but lying 60 ° ahead or behind it will be trapped near these points.

These leading and trailing points are called the and Lagrange points.

However, no asteroids trapped in Lagrange points were observed until more than a century after Lagrange's hypothesis.