The International Mathematical Union (IMU) is often seen as a monolithic entity that mysteriously makes the International Congress of Mathematicians (ICM) happen every four years. The prevalent image of the IMU is that of a group of mathematical high rollers presiding over the most coveted prizes and speaking invitations in the mathematical world; often overlooked is the Union's important work in supporting research mathematics in developing nations. David Mumford of Harvard University, who will become president of the IMU in January 1995, points out that the purpose of the IMU is to facilitate international connections among mathematicians. "For that reason,'' he says, "the IMU having more direct broad input from the rank and file of the mathematical community makes sense.'' Increasing understanding about how the Union works is the first step toward demystifying the IMU and insuring that it is responsive to the needs of the mathematical community.
The membership of the IMU consists of nearly sixty nations, each of which has a corresponding National Committee that serves as a liaison between the mathematicians of that country and the IMU. There are five categories of membership, each presupposing a certain level of mathematical activity and each with its own level of dues. (The member nations in each category are listed at the end of this article.) Dues account for the greatest share of the IMU's' budget, which was about $200,000 in 1993.
To join the IMU, a nation must submit an application describing the level of mathematics research activity in the country, which must meet a certain standard. A country applies through what is called its "adhering organization'', usually either its national academy of sciences or its mathematical society. The IMU General Assembly, which consists of delegations from each member country, meets every four years just prior to the ICM. At its meeting, the General Assembly discusses and votes on various policy matters concerning the IMU; each delegation has a certain number of votes (from one to five) according to its category of membership. There are international unions like the IMU in all other scientific fields, and these unions are in turn members of ICSU, the International Council of Scientific Unions, a Paris-based umbrella organization.
As an example of the kind of issue the General Assembly considers, at its meeting before ICM-90 in Kyoto, the General Assembly passed a resolution about increasing the number of women speakers at the ICM. The resolution appears to have had some effect: at ICM-94 in Zurich, there were two women plenary speakers, as many as at all previous Congresses combined, and ten invited women speakers in all. Sometimes controversy erupts at the General Assembly. At the meeting in Lucerne before ICM-94, a resolution about increasing the number of speakers who are women or members of ethnic minorities was put forth by the American delegation. One female delegate from Eastern Europe said the resolution was insulting to women, who should be able to compete for speaking invitations without special privileges. Another delegate from an African nation wondered about what the term "ethnic minorities" meant in countries like his, where there are dozens of such groups. In the end, the General Assembly decided not to consider the resolution.
The General Assembly is mainly a policy-making body; the IMU is really run by its Executive Committee, which is elected by the General Assembly. Members of the Executive Committee serve for four years, long enough to organize the ICM, and are elected from a slate of candidates proposed by the sitting Executive Committee and the IMU member nations. The Executive Committee oversees all of the operations that go into organizing the ICM. The first step is the selection of a site. After evaluating proposals for sites for the Congress, the Executive Committee presents its recommendation to the IMU General Assembly, which votes on the choice. For ICM-98, proposals from Berlin and Jerusalem, as well as a late proposal from Beijing, were received. The Executive Committee chose Berlin, and the General Assembly approved the choice.
The next step is the appointment of the ICM Program Committee. At its yearly meeting next May, the IMU Executive Committee will appoint the Program Committee for ICM-98. In the past, the names of the Program Committee members were kept secret until after the Congress was over. However, in a small but significant step toward making the organization of the ICM less secretive, the General Assembly voted at its Lucerne meeting to make public the name of the Program Committee chair upon appointment.
The Program Committee meets twice; its first meeting in preparation for ICM-98 will take place in the fall of 1995. At that meeting, the Committee will appoint the chairs and about half the members of the panels that will select speakers for the forty-five-minute parallel sessions. Then these panel appointees, in consultation with the Program Committee, choose the remaining panel members. There are nineteen panels, one for each mathematical section (logic, algebra, number theory, geometry, topology, etc.). The Program Committee decides on the total number of lectures and then assigns to each panel a number of lecturer slots to fill.
One oft-heard complaint about the ICM panels is that the names of the panelists are never revealed, even after the ICM is over. Opinions differ on whether this confidentiality is necessary. Some say the stakes are so high that the panels would come under too much pressure if their names were known, so confidentiality is necessary to insure that the panels are free to choose speakers based purely on mathematical merit; in this regard, the panels are similar to journal referees. Others disagree, noting that because the panel members must consult with experts outside the panel, the names of the panelists cannot be kept entirely secret, making the pressures greater than if the whole process had been open from the beginning. A long discussion of this issue at this year's General Assembly led to the resolution to make the name of the Program Committee chair public at the time of appointment.
The panels develop a list of recommended speakers and alternates and also make recommendations for plenary speakers. All of the lists are submitted to the Program Committee. The alternates are important because sometimes more than one panel chooses the same speaker, or a speaker declines. In addition, the Program Committee must also ensure that the whole program is balanced, representing all major areas of new activity. The Program Committee at its second meeting then makes the final selection. In addition, the Program Committee has the responsibility for choosing plenary speakers.
Traditionally, all of the planning for the mathematical program for the ICM has been carried out by groups under the IMU; advice has not been sought from any other mathematical organizations. However, ICM-98 will be an exception in this regard. The IMU General Assembly has sanctioned collaborations between the IMU and other mathematics organizations in developing the applied areas of the program for ICM-98. This includes applied mathematics in the traditional sense, computer science, mathematical physics, etc.
While organizing the ICM every four years consumes most of the IMU's attention, the Union does have a number of commissions that initiate various international activities. The IMU Commission on Development and Exchange (CDE) provides partial support for mathematical activities in developing nations. Its program of travel grants allows mathematicians to visit mathematical centers which can provide local expenses for the visitor. In 1993 the CDE supported visits by nine mathematicians from China, India, the Ivory Coast, Tunisia, and other countries; over the last four years, thirty-eight such visits have been supported. In addition, the CDE helps support conferences in developing countries. It provided partial funding for seventeen conferences in the last four years, on topics ranging from arithmetic geometry to numerical analysis and in countries ranging from Egypt to China.
In addition to the CDE, the IMU Executive Committee oversees another program to enrich mathematical life in developing countries. The IMU Special Development Fund provides support for young research mathematicians to attend the ICM. For the ICM-94, eighty such mathematicians were supported, approximately double the number the Fund was able to support at the previous Congress. The IMU pays the airfare, and the country hosting the Congress pays the local expenses. Monies for the Special Development Fund are contributed by member nations of the IMU. The U.S. has been the largest contributor; this contribution is coordinated by the AMS, which pools individual donations by means of a check-off box on dues notices. Other major contributors are Brazil, Britain, Germany, Holland, Japan, and France. In some cases, the contribution comes from individual mathematicians, while in others it comes from a national or governmental organization.
The International Commission on Mathematical Instruction (ICMI) has its own quadrennial international congress, ICME (International Congress on Mathematical Education). The next ICME will be held in 1996 in Sevilla, Spain. Out of ICME-92 in Quebec City came the ICMI Solidarity Fund to assist in the improvement of mathematics education in developing countries. In 1993 this fund allowed two mathematics education specialists to present two-week courses in Nicaragua. In addition, ICMI conducts studies on crucial themes and issues in mathematics education. The next ICMI study will focus on the teaching of geometry; the study conference will be held in Sicily in 1995.
The International Commission on the History of Mathematics (ICHM) is a joint commission of the IMU and IUHPS, the International Union for the History and Philosophy of Science. ICHM does not hold its own congress, but it organizes sessions on the history of mathematics for the International Congress of History of Science and for the ICM. Every four years, the ICHM presents the Kenneth O. May Prize for outstanding contributions to the history of mathematics. The Commission also maintains a directory and database of mathematical historians and a photo archive of prominent mathematicians.
As ICM-98 draws near, the IMU will be designing another major event, World Mathematical Year 2000 (WMY2000). The IMU, with the sponsorship of UNESCO and national science organizations in various countries, is organizing a worldwide celebration of mathematics in the year 2000. The celebration is set around three aims. The first is to outline the research challenges for the twenty-first century in the tradition of David Hilbert, who, in a talk at the ICM in Paris in 1900, presented his list of the outstanding mathematical problems of the day. The IMU appointed in 1991 a ``Turn of the Century'' Committee which made preliminary recommendations for such activities to the 1994 General Assembly.
The second aim of WMY2000 is to bring most UNESCO member countries up to a level of mathematical development that permits admission to the IMU. This aim recognizes the importance of mathematics in the economic and scientific development of nations. Improving education, training, and access to scientific information are important means to achieving this goal. The CDE and ICMI will have special responsibilities in this area.
Improving the image of mathematics is the third aim of WMY2000. Mathematics pervades the technological advances of the information age, but often its contributions are invisible. WMY2000 will organize activities to help increase public awareness of the importance of mathematics. One suggestion put forth is to organize a set of world-girdling mathematical meetings-some on history, some on education, some on development issues-which are linked by satellite with common plenary sessions.
UNESCO already collaborates with the IMU in activities of the CDE and ICMI. This collaboration consists mainly of joint publications (such as a selected mathematical bibliography for third-world countries and a directory of mathematicians from developing countries), support for visiting professors and researchers, and support for mathematicians from developing countries to attend international mathematical events. To assist in meeting the aims of WMY2000, UNESCO is stepping up its collaborations with IMU during 1994--1995. UNESCO also plans to establish regional mathematical information and documentation centers in the third world.
The IMU is involved with many other smaller projects and activities to further international mathematical cooperation. It sponsors each year roughly half a dozen international meetings, making financial contributions especially to meetings in the developing countries. It also sponsors a program of occasional IMU Lectures, in which distinguished mathematicians present a series of four or five lectures. Any mathematical center may apply and propose an individual for a series of IMU Lectures. Finally, the IMU, with the assistance of the AMS, publishes once every four years in time for each International Congress, the World Directory of Mathematicians, which strives to list all active research mathematicians in the world.
The IMU has a wide array of responsibilities, from presenting the frontiers of mathematical research at the ICM to helping to improve mathematics education in developing countries. These responsibilities reflect the importance of mathematics as an intellectual, educational, and economic resource for all nations. As World Mathematical Year 2000 draws near, the IMU is looking toward the international mathematical community to join in the celebration and to help in strengthening all aspects of the field the world over.