Ich danke Ihnen und dem Kongress-Komitee herzlich für die grosse Ehre, die ich im Namen der Schweizer und im besondern der Zürcher Mathematik annehme.
Je vous remercie ainsi que le Comité du Congrès trés sincérement pour le grand honneur que vous venez de me témoigner. Je voudrais aussi exprimer ma reconnaissance à nos amis de la Suisse Romande pour leur contribution si importante a la vie mathématique.
Vorrei ringraziare cordialmente il Comitato e tutti i presenti per il grande onore reso a me con questa nomine; e saluto in modo particolare i matematici della Svizzera di lingua italiana.
I accept the great honor in the names of Swiss and, in particular, Zurich Mathematics. I have expressed my most sincere thanks in three of our national languages; to my regret I don't speak the fourth, so I have switched to English. Let me add a few words in that language. I have to confess that I did not participate in the tremendous work of preparing this Congress. So, in any case from that viewpoint, I do not deserve being elected Honorary President. I can accept, however, that honor with not too bad a conscience: Indeed I have been very active in the preparation of two earlier Congresses, namely 1958 Edinburgh and 1962 Stockholm, when I was Secretary of the International Mathematical Union. It can be said that this was a very important and interesting period for international collaboration in all aspects of Mathematics. May I recall first of all that just at that time many countries, which did not up until then adhere to the IMU, became members. One can imagine that quite some difficulties of a political, personal and financial nature had to be overcome, but it was a gratifying challenge. For, through the Union, mathematicians became a truly worldwide family. Secondly, a decision was taken which today seems most natural, namely, that the Scientific Program of the International Congress be prepared by the IMU, since that task could not be handled any longer by a single country. Stockholm was the first Congress where the new scheme was adopted, after several - very friendly - discussions. Nowadays, the functioning of the international collaboration in Mathematics can certainly be considered as a model for many other fields.
Something else has, since these times, considerably changed local and global mathematical life. I think, of course, of the computer, as a tool within our science and as a marvellous means of communication. I believe there are very few mathamaticians who have not taken advantage of any derived great benefit from the fabulous possibilities of this tool. But we should not forget taht the most important tool of a mathematician is the fellow mathematician! And that is why we are all here today: to exchange ideas, views, and results, and to listen to each other.
With regard to the computer I have heard over and over again the saying: Whether mathematicians like it or not, the computer is here to stay. I do not agree with that formulation. We like the computer and we use it. But today I find it important to turn that phrase around and say: Whether the computer likes it or not, mathematics are here to stay. This means Mathematics as the art of creating concepts out of the vague intuition and evidence of the real world and of everyday life; and then to put these concepts to work and experiment with them by all available means; to see relations, conjectures and theorems emerge; and to prove the same by the good old traditional proof, which is at the heart of our science. For mathematics is, and remains, an abstract intellectural enterprise, despite the fact that natural sciences and technology, and much more, bear witness to its practical usefulness. Sometimes it is the same person who speculates and conjectures, provides proofs, and makes applications to our real world; but more often this is done by different people and at different times - personal collaboration always remains an essential feature.
Most beautiful evidence of all the above is given by the scientific program of our Congress - and by the impressive work of the laureates of the Fields Medal, which is the most prestigious distinction in Mathematics. It will be my duty and immense pleasure to hand over the medals to the winners. Let me congratulate them in advance. I share their feelings of pride and accomplishment, and I am looking forward to their continued success - hoping that I will be able for some time to understand their work. I also share the feelings of the many who are disappointed because they did not get the medal; there is simply too much excellent work being done!
Mathematical research indeed seems to live in a golden age. As for the mathematical education of coming generations, however, I must say that I see some danger: there are worlwide trends trying to completely replace rigorous reasoning and proving by computer visualisation and experimentation. This is not the place to elaborate on the theme of the central importance of rigorous proof. Instead let me quote Hermann Weyl (who spent a long and very important period of his scientific life in Zürich):
May I just add: To achieve more we dare not hope; to achieve less we mus t not try.