HWB: |
|
How do you perceive the position of mathematics, both as an
independent discipline and as an intermediary between other
sciences?
|
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.
|
HWB: |
|
This "entire thing", do you mean by this the sum of pure and
applied mathematics?
|
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.
|
HWB: |
|
Could you explain this further?
|
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.
|
HWB: |
|
Do you think of modelling here?
|
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.
|
HWB: |
|
This sounds like part of your vision on the future.
|
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.
|
HWB: |
|
From this perspective, what do you think of the development
of the area Dynamical Systems?
|
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.
|
HWB: |
|
Is this what you mean by integration?
|
JP:
|
|
Integration, indeed, both within mathematics and with other
areas.
|
HWB: |
|
A related subject concerns young people's interests in
mathematics. As we all know, this interest is different in
the richer and the poorer countries of the world.
|
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.
|
HWB: |
|
This surely sets a nice example. You have mentioned the
words "charming" and "friendly" in the teaching of mathematics. Is
there not the danger that mathematics is made subordinate to its areas
of application?
|
JP:
|
|
Mathematics should not position herself as the servant of
the other sciences, just more friendly, philosophically
more open minded.
|
HWB: |
|
So that is your advice?
|
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.
|
HWB: |
|
What do you think of the flow of PhD students from the poor
to the rich countries?
|
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.
|
HWB: |
|
Is it a coincidence that we are having this conversation
at the ICTP Abdus Salam in Trieste?
|
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!
|
HWB: |
|
Do you have a conclusive message for this interview?
|
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.
|