In this program, Professor Marcus du Sautoy addresses mathematical advances of 20th-century Europe and America. Topics include Georg Cantor’s exploration of the concept of infinity; chaos theory, formulated by Henri Poincaré; Kurt Gödel’s incompleteness theorems; the work of André Weil and his colleagues with algebraic geometry; and the influence of Alexander Grothendieck, whose ideas have influenced mathematical thinking about the hidden structures behind all mathematics. The program concludes by considering one of the great as-yet-unsolved problems of mathematics: the Riemann Hypothesis. Original Open University title: To Infinity and Beyond. A part of the series The Story of Math. (58 minutes)