JP:

This subject has held my interest at an increasing level. I see mathematics as a central discipline with many branches, where fundamental mathematics plays a key role that is essential for a broad development of the entire thing.

JP:

I consider "pure" and "applied" a bad subdivision, remembering the words of Louis Pasteur, who stated that applied sciences do not exist but applications of science do! However, there are many developments, where the key role of fundamental mathematics is denied and where people erroneously yield to the fallacies of the day.

JP:

More and more I am convinced that mathematicians should be more open minded to integration with other sciences. Here, I do not only think of physics and chemistry, but also of biology, meteorology, economy and many other disciplines; or even less discipline-like areas such as "oil & water" or "stockmarket & finance". Much of recent mathematics has been developed from, for example, biological and meteorological applications.

JP:

I like to think in broader terms and try to avoid the word "model". I rather think of mathematical descriptions and explanations. In this respect I am a follower of Henri Poincaré, who saw the total development as more organic. We should integrate better with the areas of application.

I like to add that in my opinion we are now at a historical landmark. From the outside there is huge demand for mathematics at the moment. The mathematical community will have to respond adequately to this. Fortunately many of us are of the same opinion, but in the large still a change of attitude is necessary. That this change is already in progress has a lot to do with the rise of the computer in all sciences.

JP:

In my view, mathematics is a complicated body --- like a lobster. The central part of it is occupied by fundamental mathematics. Both the development of the centre and the sensitivity for questions from the outside should lead us. Only to stay inside the centre would be a serious mistake!

However, until the 1960s this inward orientation was common among mathematicians. At that time people like René Thom and Christopher Zeeman were among the prophets of a more open-minded attitude.

I like to remark that the extremities of the lobster, apart from the applications, also contain things such as the understanding of mathematics and mathematical education. Also these aspects deserve more attention from mathematicians. In the spreading of mathematical ideas, however, we all have to become more charming. Here, among other things, we have to erase the wide-spread misunderstanding that all mathematics already was known to the old Greeks.

For a long time Hardy's A Mathematician's Apology has been the Bible for pure mathematicians including myself. Its philosophy roughly implies, at least to me, that social relevance are utterly unimportant for the development of mathematics. Of course, this is nowadays widely experienced as being wrong and obsolete.

JP:

At the time I was very shocked by the fact that all of us had overlooked the epoch-making paper "Deterministic nonperiodic flow" by Edward Lorenz. Indeed, this 1963 paper was published in the Journal of Atmospheric Science and it only reached the Dynamical Systems community about ten years later. In this paper the celebrated Lorenz (butterfly) attractor was introduced.

Edward Lorenz, an applied mathematician who turned to weather forecasts, the biologist Robert May and the astronomer Michel Hénon --- all three were in some aspects far ahead of us in the late sixties and especially in the early seventies of the last century. The physicist David Ruelle, together with Thom and Zeeman, already mentioned before, were among the first to acknowledge the interest of their work for the area of Dynamical Systems.

JP:

Integration, indeed, both within mathematics and with other areas.

JP:

In the 1930s and 1940s Brazil largely was lagging behind in many branches of science. Many young people came from the engineering sciences or economy to mathematics. It was important that mathematics was taught in a friendly way and directed to people who were not primarily interested in fundamental mathematics. I myself also came from engineering into mathematics; the reason was my curiosity in more fundamental matters. A number of people followed a similar path.

JP:

Mathematics should not position herself as the servant of the other sciences, just more friendly, philosophically more open minded.

JP:

That's true. My advice is that the university curriculum should be opened up, of course always keeping a good equilibrium. For freshmen students intelligence and motivation must be more important than their precise mathematical background and knowledge. Graduates should have qualifications that, on the one hand, could put them on the stockmarket and, on the other hand, turn them into physicists, biologists or chemists: we should offer this kind of flexibility.

We should shake off the image of pedantism of having better brains, but instead should position the discipline of mathematics more visibly. Then, as a direct consequence, many talented students will come to us immediately.

JP:

This is a complicated but very important matter in which things should change at short notice. Evidently, it is in nobody's interest if all scientists would reside in the richest country of the world. Therefore, in principle the talented young people should return to their homeland after their PhD. This return should be stimulated by grants and fellowships, helping the young people to establish themselves as scientists in their country. Indeed, this would be a meaningful use of fundings for underdeveloped countries. Moreover, the richer countries should maintain more joint research projects with the returned PhDs. Here, they would have to compete with the way in which the richer countries treat their own talented young PhDs.

To change the world map of science, countries like Brazil, India, China, South America and Mexico, among others, should play a better and more stimulating role in this, sharing the responsibility of strengthening Science and Technology in other developing countries.

JP:

Not at all, the ICTP stimulates the interaction between the richer and developing countries at a scientific level. For 30 years many scientists from our area of Dynamical Systems now come together and a lot of stimulating cooperation has evolved from this. This interaction and integration should go on!

JP:

I would like to stress that we mathematicians should not miss the opportunity now offered to us. There is a large and urgent demand for mathematics from the outside. If we respond adequately to this, we can achieve more than one goal at the same time: indeed, at the same time we would increase our visibility for the talented young people and help the development of national competence in all countries of the world.