This book is not a history of the mathematics of the twentieth century. Instead it is a history of the international mathematical community of the twentieth century. As the end of the century draws near it is fitting that we take a look back at the development of international cooperation in mathematics over the past decades. Olli Lehto carefully lays out this history with rich detail and abundant references to material contained in the International Mathematical Union (IMU) archives at the University of Helsinki.
It is interesting, though certaintly not surprising, to note the extent to which the history of international cooperation in mathematics in the twentieth century parallels the political history of the same period. The book begins with some prehistory; a description of the dawning of international cooperation in mathematics in the late 1800's. A systematic cataloging on all international mathematical publications developed in Germany and France in the 1870's and 1880's, and the first International Congress of Mathematics (ICM) was held in Zurich in 1897. The book goes on to describe the early years of the IMU as it struggled to take shape in the years from 1920 through 1932. The recently ended war made it politically difficult to bring together mathematicians from all countries, but some organizations, notably the American Mathematical Society fought against the restrictions on participation in the Congresses which were now being organized by the IMU. In 1928, the IMU separated from the Congresses and in the fall of 1932 activities of the IMU were suspended entirely. They were not to resume until 1952.
The period from 1933 through 1939, leading up to World War II, was without and IMU, but some degree of mathamatical cooperation continued. Fields Medals began being awarded in 1936, an ICM was held in Oslo in 1936, and international cooperation in mathematics education grew. World War II interrupted things briefly and the period from 1945 through 1951, just after the war, was a period of preparation for a "New" IMU. An ICM was held at Harvard in 1950, and preparation of statuses for a rebirth of the IMU were being prepared. In 1952, this New IMU was officially born with the First General Assembly in Rome.
I won't spoil things in this review by telling any more of the story. Lehto tells the full story and tells it well. He concludes the book with an appendix containing lists of things like Members of the IMU, General Assemblies of the IMU, Executive Committee information, International Congresses of Mathematics, Fields Medals, and the like. Also, included are a lengthy set of endnotes and a very complex index.
Lehto has met his goal of writing a book which should make the role of the IMU more widely known and understood by mathematicians and other interested parties. He follows a large number of threads through the tapestry of twentieth century mathematics and gives us a tale of mathematical and historical interest. This book would be of interest to people ranging from university students of mathematics or history to established mathematicians who have lived through a larger piece of the century. It would fit nicely in the mathematics collection of any library -- Carl D. Mueller, American Mathematical Monthly
From the Back Cover
The history of international mathematical co-operation over the last hundred years - from the first international congress in 1897 to plans for the World Mathematical Year 2000 - is a surprisingly compelling story. For reflected in the history of the International Mathematical Union (IMU) is all the strife among world powers, as well as aspirations for co-operation among nations in an increasingly interdependent world. As early as the 1920s, the IMU embraced principles of political neutrality, inviting every national mathematical organisation to join, and this principle of non-discrimination, while sometimes sorely tried, has held the IMU in good stead. A number of issues - the Cold War, the conflict between the Peoples Republic of China and Taiwan, a divided Germany, problems in the emerging nations of Africa - at times led to attempts to influence the IMU Executive Committee in its decisions regarding membership, location of international congresses, committee assignments, handling of protests, and awarding the coveted Fields Medals. Yet throughout, the IMU has sponsored international congresses around the world, and Professor Lehtos gripping story is one of individuals, among them many of the great mathematicians of our century, united in the common purpose of advancing their science, told against the backdrop of world events.