Lagrange

Lagrange refers primarily to Joseph-Louis Lagrange, the Italian-born French mathematician and physicist whose work in analysis, mechanics, and astronomy had a lasting impact on science. Born in 1736 in Turin as Giuseppe Luigi Lagrangia, he later settled in France, becoming a leading figure of the Enlightenment in mathematics. He contributed to calculus of variations, number theory, and celestial mechanics, and he died in Paris in 1813.

Many concepts and methods bear his name. In classical mechanics, the Lagrangian framework uses a function L, defined as the difference between kinetic and potential energy, L = T − V, to derive equations of motion via the Lagrange equations. The method of Lagrange multipliers provides a way to find extrema of functions subject to constraints. In algebra and numerical analysis, Lagrange interpolation constructs polynomials that pass through a given set of points, yielding the Lagrange form of the interpolating polynomial. In group theory, Lagrange’s theorem states that the order of any finite subgroup divides the order of the group.

In celestial mechanics, the Lagrange points are five special positions in a two-body system where a small object can maintain a stable or semi-stable orbit relative to the two larger bodies. Lagrange’s work also includes resolvents for solving polynomial equations and foundational results used in the study of dynamical systems.

Together, these contributions have left a lasting legacy across mathematics, physics, and astronomy.