Harold Hotelling (1895-1973) was a major contributor to twentieth-century American economics. The overall thrust of his research, and his view of the role of mathematics in the discipline, have so far received little attention. Based on an unprecedented examination of his work and professional archives, this article provides a thorough analysis of Hotelling’s background and contribution to economics. A self-taught economist in the 1920s, Hotelling built a research program that, despite apparently being highly technical, was primarily conceived as applied science to solve concrete social and economic issues, from spatial competition to natural resource exhaustion and public utility regulation. Although Hotelling’s research was not exempt from criticism, it remains profoundly inspiring for the twenty-first century, from both a theoretical and epistemological point of view. When we remember that he trained the greatest, from Kenneth J. Arrow to William Vickrey, his career and ideas are all the more worthy of consideration.