Editing Joseph-Louis Lagrange (section)

==Scientific contribution==
Lagrange was one of the creators of the [[calculus of variations]], deriving the [[Euler–Lagrange equation]]s for extrema of [[Functional (mathematics)|functionals]]. He extended the method to include possible constraints, arriving at the method of [[Lagrange multipliers]]. Lagrange invented the method of solving [[differential equation]]s known as [[method of variation of parameters|variation of parameters]], applied [[differential calculus]] to the [[probability theory|theory of probabilities]] and worked on solutions for [[algebraic equations]]. He proved that [[Lagrange's four-square theorem|every natural number is a sum of four squares]]. His treatise ''Theorie des fonctions analytiques'' laid some of the foundations of [[group theory]], anticipating [[Évariste Galois|Galois]]. In [[calculus]], Lagrange developed a novel approach to [[Lagrange interpolation|interpolation]] and [[Taylor's theorem]]. He studied the [[three-body problem]] for the Earth, Sun and Moon (1764) and the movement of Jupiter's satellites (1766), and in 1772 found the special-case solutions to this problem that yield what are now known as [[Lagrangian point]]s. Lagrange is best known for transforming [[Newtonian mechanics]] into a branch of analysis, [[Lagrangian mechanics]]. He presented the mechanical "principles" as simple results of the variational calculus.