Ladies and Gentlemen,

A hundred years ago, in 1897, the first International Congress of Mathematicians was held in Zurich. In 1932, the Congress met in Switzerland for the second time. On that occasion, the Fields Medal was introduced as your Nobel Prize equivalent. Today, our country hosts your Congress for the third time. No other country has been honoured in such a way by your scientific community and I am sure, that the "genius loci"will show his gratitude for your fidelity and ensure the success of your work.

I feel personally very honoured to open your Congress. It is a rare opportunity to host the world's leading masters of this art and to come into contact with their scientific debate.

If the subject of your congress was cancer research or modern history, for a lay person it would be simpler to understand what the discussion is about. In contrast, mathematics at first sight, seems to be an abstract tool for its own purpose or an exclusive art.

Two years ago, in Rio de Janeiro, under the sponsorship of the UNESCO, the "World Mathematical Year 2000"was launched. On this occasion, the International Mathematical Union defined a vision for mathematics which stresses the relationship between science and society. The DECLARATION OF RIO DE JANEIRO states that "Pure and Applied Mathematics are one of the main keys to understanding the world and its development". I am sure, that society needs these keys.

But since I am not a mathematcian myself, I wonder what doors they open, and what society will find behind them. Therefore like to learn from you how mathematicians view their role in society.

With the relationship between science and society in mind, I sent three questions to over a dozen of world's most eminent mathematicians and I am very grateful for all the answers I received. For the first two questions, I refered to the distinction between pure and applied mathematics cited in the Declaration of Rio.

The first questions concerns *Pure mathematics*. Pure
mathematics seems to function within a realm of complete independence.
Its results have their purpose not in their usefulness to society, but
in their Truth. The clarity of this truthfinds a beauty which elevates
pure mathematics to an art form. But, in contrast to a harpist who
delights others by her music, I fear that the pure mathematician cannot
make his art accessible to a wider public. My questions then was: How
can pure mathemtics justify its art to the State who finances it?

For Breno Eckmann, Mathematics "sets the standard for every objective thought"and according to Friedrich Hirzebruch, "Without mathematics there would be no structure logical thinking".

For Raoul Bott "the treasure (the mathematician) hunts is at the very core of all ... precise inquire into the world. As such (his) search must be a central concern of any enlightened state".

I agree that I am convinced of the need of mathematical thinking as a fundamental component of the modern World. Historically mathematics has been a key to open the doors to Englightment. Today, pure mathematics can still be considered as the guardian of the grail of logical thinking.

But as Roland Bulirsch puts it, "Mathematics is invisible culture". Further Jürgen Moser says that "mathematics may not be accessible for the enjoyment of a broad audience". If this culture of pure mathematicss is invisible and inaccesible how then can one show its practical use and demonstrate its tangible results?

Armand Borel explains that "mathematics resembles an iceberg: beneath the surface is the realm of pure mathematics, hiden from the public view.... Above the water is the tip, the visible part which we call applied mathematics".

According to Phillip Griffiths, one of the deep mysteries of life is the way in which the best pure mathematics, pursued for its own sake, inexplicably and unpredictably turns out to be useful".

Jürgen Moser adds "The difficulty in getting this message across, lies in the longer time span needed to recognize the significance of mathematical discoveries.... sometimes twenty or more years have to elapse... Politicians unformtunately often think in much shorter terms". This is certainly true not only for politicians but for society as a whole. In modern times we insist on increasing shorter timespans for everything in our life. We ask for immediate return on investment. We want real time information. The life span of technologies are getting shorter and shorter: Cost efficiency and speed have become the basic criteria to judge any human activity. This is dangerous because it is shortsighted.

In such an environment it is very important to continue to recognize that knowledge is a value of itself. Mathematics or Philosohpy or any basic research developments only thanks to the principle which is an important part of our civilization. If we start to forget it, we jeopardize the roots of our progress.

The future is unpredictable. We cannot judge knowledge on the basis of its immediate usefulness. As an example, the work of Vaughan Jones, who connected three dimensional knot theory with functional analysis, was awarded the Fields Medal at your last congress in Kyoto on the basis of its intrinsic merit. Later, his theory was utilized by physicists in statistical mechanics and by biologists to explain the structure of DNA. It is only through the recognition and support of basic research that society can ensure the continued and full development of scientific progress.

Let us turn to applied mathematics. Today, *applied
mathematics* has become a basis for all other siciences and has a
tremendous impact on life in modern societies. Applied mathematics is
hereby both hightly relevant and useful to society but it has lost its
innocence. However, in contrast to the debate on the responsability of
nuclear physics and genetechnology, it seems to me that there has been
little ethical discussion on the role of mathemtics in society. Thus
here was my second question: *Has mathematics avoided such
discussions?*

There are mathematicians who claim moral neutrality for their science. René Thom for example writes me that "Mathematics by itself is ethically neutral".

But Sir Michael Attiah reminded me in his answer, that the "atomic bomb was only built after extensive mathematical calculations" and Jürgen Moser adds that "the renown mathematicians von Neumann and Ulam played an important role" in this project.

Armand Boreal asks "should one see the fact that mathematics is at the base of artillery or guided bombs as an ethical problem?" Yes, I think one should.

It is true that "most mathematicians are away from the decisions of the application" of their work, as Friedrich Hirzebruch puts it. Breno Eckmann goes even further, when he days: "For mathematics itself this (ethical and political) discussion is not relevant... As a purely intellectual activity, it could not be influenced by such a discussion, Of course, those who apply mathematics have to face (this) discussion".

However, I do not think that making a distinction between abstract theory and practical application can altogether eliminate the ethical problem. We owe much of our progress in society to mathematicians and we have to recognize their merits while at the same time they have to assume their responsibilities.

Raoul Bott has expressed his argument against ethical neutrality, writing to me "That the age of innocence has come to an end for us all".

I am convinced this is true not only for science, but for most human activities. Today, thanks to science, our socity has developed a tremendous power to control nature. This power enables us to take our destiny in our hands. But this power forces us to assume the responsabilityites bound to it. If the age of innocence has come to an end, we have to recgnize that it is the age of responsability that has replaced it.

Let's turn now to my last question: If, as Minister of Science, I had
the possibility to create 10 new professorhsips in Swiss Universitites,
*how many of them should I give to mathematics and why?*

Phillip Griffiths is generous with his science and answers: "They should all go to mathematical scientists".

So is Gerd Faltings: nine chairs for mathematics, but - as he likes music - he leaves the tenth chair to the harpists.

Sir Michael Attyiah, Friedrich Hirzebruch and Jürgen Moser request four or five chairs for mathematics. That is about the average of all the answers. In fact, in. Switzerland today only one chair out of twenty is held by mathematics.

Some replies focus exclusively on the needs of natural sciences. This is surprinsing. When one considers the complexities of the problems that face society, I am convinced that their solution will require a support and dedi cated effort of the social sciences and humanities in close collaborations with natural sciences.

In view of the growing importance of science I understand why scientist ask for more means, why they want more professorships than they have. Scientists are increasingly expected to find solutions to all of all problems. It is more than legitimate that you ask for the necessary means from society.

Science and research are crucial today. You don't have to convince me of this as minister of science, but together we have to convince the public and the Parlament. We have to convince the taxpayer. This is a difficult task when public budgets are running huge deficits.

One problem is that the growing impact of science in society is not felt when we drive a car or use a phone. Most people are not aware of the scientists whose work is behind everything in our everyday life. Ask for instance any Swiss "Whose portrait is on the ten francs note?" They won't be able to tell you. They have never notice that it is Leonhard Euler. Probably they don't even know who Euler is.

It is the task of the scientific community to tell the public why science matters. It is your task - and it is mine.

I wish all the best for your Congress - Thank you.