Appendix 2:

    Turn of the Century Committee

    Report to the IMU General Assembly 1994

    In 1990, at the previous IMU General Assembly in Kobe, Japan, the American National Committee proposed the creation of the Turn of the Century Committee to provide suggestions for IMU to mark the turn of the century in a manner appropriate to the standard set by David Hilbert in 1900, so that the present Assembly can decide how to proceed.

    Subsequently, such a committeee was set up by the IMU Executive Committee having as members Professors V. Arnold, F. Hirzebruch, L. Lovász, B. Mazur, S. Mizohata, W. Thurston, J. Tits, S. Varadhan and J. Palis.

    Meanwhile, in May of 1992, Professor J.L. Lions, in the name of the Union, declared 2,000 as a World Mathematical Year (WMY 2,000) having as first aim the IMU activities to envision what the great challenges of the next century would be. In his own words, the Turn of the Century Committee suggestions to this General Assembly could be a starting point to organize such efforts. The second aim of the Declaration is Mathematics, keys for development and the third is The image of mathematics.

    Members of the Committee had different views on how to proceed, but one common idea is to have articles/monographs/uniform series of addresses at various Symposia written by main mathematicians with a broad perspective and comprehensive views of mathematics, achievements of the present century and open problems. Unity of mathematics was much stressed. Another very relevant point raised was the connections between mathematics and other sciences. The importance of communication with the general public has also been mentioned. On the other hand, on the issue of how to proceed to obtain these "articles of the turn of the century", the disparity of views was quite clear: several symposia, or one main congress with a format somewhat different from the usual ICMs or perhaps no congress at all but having leading mathematicians to write, individually, a collection of problems (Fields medalists and a few others would be invited to do so).

    From all these discussions and many comments by the members of the present EC, specially Prof. J.L. Lions, and several other colleagues, one possible set of suggestions is the following:

    • to invite a number of Fields medalists/N evalinna prize winners and a few other outstanding mathematicians to write their views (past, present) on topics they consider to be important and corresponding open problems; the invitations should be issued by a small Editorial Board to be designated by the next EC by May, 1995;

    • to organize a small number of symposia in different regions of the world, to be selected by the next IMU Executive Committee, one of the objectives being again the production of a few outstanding surveys/sets of open problems;

    • of particular importance is to organize some symposia on the applications of mathematics to other sciences and their impact on society. To that end, cooperation with other scientific unions and societies should be pursued.

    A detailed set of procedures could be prepared by May, 1995 and be known to all Adhering Organizations/ National Committees immediately after that. Suggestions concerning the set of activities above will be welcome.

    In addition to the consultations done in the framework of the Turn of the Century Committee, I want to mention the other aims of WMY 2000 concerning education and development aspects and to emphasize the work being carried out in this respect by ICMI, CDE and ICHM. For instance, ICMI is experimenting at ICME 96 the use of worldwide communication techniques, to be much pursued at ICME 2000, if successful. I also want to mention the publication of the newsletter WMY 2000, organized through Institut H. Poincaré with the support of the École Polytechnique in Paris.

    In any case, no matter what course we take, it is a formidable task for the international mathematical community. On that, I would very much like to agree with a committee member when he says: "if we choose absolutely any of the suggestions of the committee members and if we follow it diligently, we will come up with something of substantial value for the mathematical community".

    Jacob Palis