Although Joseph Liouville's primary contribution to mathematics was the first proof of the existence of transcendental numbers (real numbers that are not roots of polynomials with integer coefficients), he had a wide range of mathematical interests. Liouville's publishing and teaching activities were vital to French mathematics during the 19th century. He made critical contributions to number theory, differential geometry, celestial mechanics, and rational mechanics. An enthusiastic lecturer, Liouville held numerous teaching positions, usually two or more at a time. Simultaneously, he was a prolific author, publishing 400 pieces in his lifetime, including over 200 on number theory alone.

Liouville was born in St. Omer, Pas-de-Calais, France, on March 24, 1809. He was the second son of an army captain, Claude-Joseph Liouville, and his wife, Thérèse (nee Balland). Liouville received his early education in Commery and Toul, before being accepted at the l'École Polytechnique. He began studying...