This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1932, reflected above all the trauma of WW I. Since 1950 the current IMU has played an increasing role in defining mathematical excellence, as is shown both in the historical narrative and by analyzing data about the International Congresses of Mathematicians. For each of the three periods discussed, interactions are explored between world politics, the advancement of scientific infrastructures, and the inner evolution of mathematics. Readers will thus take a new look at the place of mathematics in world culture, and how international organizations can make a difference. Aimed at mathematicians, historians of science, scientists, and the scientifically inclined general public, the book will be valuable to anyone interested in the history of science on an international level.

Norbert Schappacher is professor emeritus of mathematics at the University of Strasbourg, France. After decades of research in Arithmetic Algebraic Geometry he turned to the history of science, esp. 19^th and 20^th century. He is particularly interested in interactions between science and politics; several of his papers deal with mathematics in Germany under the Nazis. From 2008 to 2016 he was the managing editor of Revue d'histoire des mathématiques, Paris.

The long 19th century which made the International Mathematical Union, IMU, possible: 1800-1918.- IMU, the first attempt: 1919-1949.- Seventy Years of Globalizations: 1950-2020.