Joseph-Louis Lagrange

Joseph-Louis Lagrange was an Italian-born mathematician who spent much of his career in Prussia and France and whose 1788 treatise Mecanique Analytique reformulated the whole of classical mechanics using purely algebraic and analytical methods, dispensing almost entirely with geometric diagrams and instead deriving the equations of motion of a physical system from a single scalar quantity, an approach now called Lagrangian mechanics that remains a central formulation used throughout physics and engineering. Lagrange made foundational contributions to the calculus of variations, a branch of mathematics concerned with finding the function that minimizes or maximizes a particular quantity, building substantially on and formalizing earlier work by Leonhard Euler. He also contributed significant results in number theory, including a proof that every natural number can be expressed as the sum of at most four perfect squares, and in the theory of equations, work on the general unsolvability of the quintic by radicals that helped set the stage for Evariste Galois's later breakthrough. Lagrange served on the French commission that helped design the metric system in the 1790s and was a founding member of the Bureau des Longitudes, and Napoleon Bonaparte, who made him a count and senator, is reported to have called him the lofty pyramid of the mathematical sciences.