Four Lectures on Mathematics, Delivered at Columbia University in 1911

These four lectures, delivered at Columbia University in 1911 by Jacques Hadamard, capture mathematics at a moment of transformation. Hadamard, already renowned for his work in complex analysis and number theory, guides his audience through the frontier questions of early twentieth-century mathematics: the nature of infinite series, the boundaries of rational thought, and the geometric structures that would later underpin relativity. The lectures possess a rare quality: they do not merely present results but reveal the living, breathing process of mathematical discovery, complete with its uncertainties and its leaps of faith. For anyone curious about how modern mathematics actually gets made, rather than merely presented in polished textbooks, this volume offers an invaluable time capsule. The book remains essential reading for mathematicians, historians of science, and anyone who wants to understand the intellectual atmosphere from which twentieth-century mathematics emerged.