Joseph Liouville

Joseph Liouville was a French mathematician whose career bridged the 19th-century worlds of pure analysis and celestial mechanics. Born in 1809 in Saint-Omer, he graduated from the École Polytechnique in 1827 and spent most of his working life in Paris, teaching at the Collège de France, the Sorbonne, and the École Polytechnique itself.

He is best known in physics for Liouville's theorem (1838): under Hamiltonian flow, volume in phase space is exactly conserved. The result is the mathematical backbone of statistical mechanics, the classical limit of quantum mechanics, and every modern symplectic integrator. In parallel Liouville did foundational work on transcendental numbers (the first explicit construction of a provably non-algebraic number, 1844), fractional calculus, differential algebra, and what is now called Sturm-Liouville theory of self-adjoint second-order ODEs.

From 1836 he edited the Journal de Mathématiques Pures et Appliquées — still running today as 'Liouville's Journal' — through which he brought Évariste Galois's posthumous papers to the world in 1846, single-handedly rescuing Galois theory from obscurity. He died in Paris in 1882, with more than three hundred published papers across analysis, number theory, and mechanics to his name.