*David Mumford*

As the incoming president of the IMU, one of my goals is to help explain to the whole mathematical community what the IMU is and how you can help make it work. My own first contact with the IMU was when I spoke at the Stockholm Congress in 1962 and received various letters from this mysterious organization, the International Mathematical Union. Over the intervening years, I had contact with it from time to time, and it came to represent a rarified high-level mathematical establishment, located in places like Zurich and Helsinki, from which benign powers kept the Congresses running through the viscissitudes of the cold war and the postwar explosion of mathematical research. One day, C.S. Seshadri, one of the least political beings that I've ever met, called me up on behalf of the Union and said, "Please accept a nomination to the Executive Committee of the IMU." Not having a ready excuse and being cornered by his assurances that the only duties were to meet at a pleasant locale once a year with a friendly group og colleagues, I had to accept. having gotten into it, I have gradually learned a bit about its history and now have my own ideas of waht it is good for and what it is not good for. That is what I want to explain in this short article.

First, some history: The first International Congress was held in 1897, and the International Mathematical Union was formed in 1919 to organize these and other international activities. However, the period between World War I and World War II was full of political infighting and boycotts, and the Union collapsed with the beginning of World War II. In 1950 the Union was reborn at the Cambridge (Massachusetts) Congress with a strong sense that its goal was to avoid politics and to find ways to bring mathematicianss together to talk mathematic regardless of what their governments stood for or did. I have heard that this goal was sorely tested at the height of the cold war, with some very strong personalities seeking to alter the IMU, but, by one means or another, serious mathematical congresses were still pulled off, from Moscow to Berkeley. When I got involved in the Executive Committee, Serre told me what he considered the two secrets of its success. First, no one was ever nominated to the Executive Committee who wanted the job; second, the IMU has no money to speak of.

One of the techniques used to avoid political interference has been precisely the secrecy of its operation-which is now being rethought. The Program Committee of each congress, the many panels to select speakers, the Fields and Nevanlinna Prize Committees have all been confidential. The only publication of the IMU is a leaflet called *Bulletin of the IMU*, which is sent to each "Adhering Organization", usually a National Academy of Science, and "National Committee" and gets filed away there. This issue of secrecy was extensively debated at the last General Assembly (see the article by Allyn Jackson). Curiously, some of the French seem most insistent on the continuing importance of secrecy, although (or perhaps because) the Paris gossip mill is so effective that the Fields Medal winners became known there this spring within a week of the committee's final vote!

My personal belief is that the IMU should move away from its tradition of confidentiality, which is no longer essential. But one must not forget the underlying reason it was introduced: to avoid political interference. If the IMU wants to avoid being interfered with, it must not be tempted to interfere politically either. There are some who believe that high-level organizations like the IMU must, by virtue of their height, have political clout and should try to exercise this clout to improve conditions in various countries: to snub or threaten one or another country, for example. This seems to me to be exactly what destroyed the IMU in the 1920s and 1930s. The goals which are stated in the Statutes of the IMU are only "to promote international cooperation in mathematics".

I would like to discuss another very different challenge to the IMU and to the mathematical community of the world. For most of my career I took for granted the unity of mathematics: that ideas from one field of mathematics routinely had an impact on many other fields and that we listened to talks in all the different fields of mathematics from time to time. When my own interests shifted from algebraic geometry to the mathematics of pattern recognition and artificial intelligence, however, I realized that mathematics was an exception in this regard. In many disciplines, there are few or no meetings in which people in overlapping subfields get a chance to hear the best new ideas from a different subfield and to seek applications of these ideas in their own specialty. There is no analog of the ICM in computer science, for example, or even in physics in recent years. Then I also became aware that in mathematics too, with so many people travelling routinely on Peano curves through the world, specialized international meetings bringing together every key player in some specialty were becoming common. Maybe we too are not listening as often to each other! I think mathematicians should be aware how rare a gift it is that we listen to each other as much as we do, and how easy it is to split into separate subdisciplines with narrower focuses. We all know how easy it is to give overly technical talks, in which all the basic examples an definitions of a small specialty are assumed known to the whole audience.

As president, I would like to facilitate a broader involvement of the whole mathematical community in the next International Congress so that this tradition of listening to and drawing inspiration from our colleagues is not lost. This is another reason for dropping the veil of secrecy: to encourage everyone to suggest to the Program Committee topics and speakers they would like to hear, especially in fields other than their own. Specifically, the General Assembly passed a resolution to make public the name of the chair of the Program Committee so suggestions can be sent directly to a person, not a faceless committee.

The split in cultures between pure and applied mathematics has been especially apparent to me since I changed my own field. (I use the words "applied mathematics" broadly to include not only the applied math of SIAM but computer science, mathematical physics, statistics, and operations research.) While proving theorems drives pure mathematics, inventing and analyzing the right mathematical model is the essence of much applied mathematics. There are many international meetings in applied mathematics, and I would say that the ICM has always been a meeting whose intellectual center was pure mathematics: 60 percent of the talks at Zürich, by my count, were in the core pure mathematics areas. The Zurich Congress was, I believe, very successful in presenting excellent talks both in pure and applied mathematics (thanks to all the committees that organized it and especially to the chairman, Louis Nirenberg). But, without having statistics to back this up, I believe a substantial majority of the attendees were pure mathematicians. It may be possible to use the approximately one-third of the Congress devoted to applied math to create more discussion and interchanges between the pure and applied communities. One move in this direction was the resolution passed at the last General Assembly asking the Program Committee to explore the possibility of introducing sessions cosponsored with other scientific bodies.

Finally, I want to inform everyone that, thanks to the marvels of the "worldwide-web", the IMU has now started a home page in which a great deal of information will be posted. This will be updated and will serve to keep everyone informed of what this now very public union is up to. Connect up by mosaic, for instance, to:

icm98.zib-berlin.de/icm/IMU.html

I welcome reactions to these ideas and comments on these issues from everyone: write to me via

mumford@math.harvard.edu

or, of course, by surface mail to Department of Mathematics, Harvard University, Cambridge, MA 02138.