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Jacob Palis Júnior

Jacob Palis Júnior: Healthy uncertainty

A researcher into dynamic systems and president of the Brazilian Academy of Sciences, the mathematician talks about the maturity of Brazilian research

Léo RamosThe Brazilian community of mathematics researchers is internationally renowned thanks to a name that synthesizes this competency: 69-year old Jacob Palis Júnior. Born in the city of Uberaba, State of Minas Gerais, this son of a Lebanese retailer and a Syrian housewife was one of the leading motivators, in the 1970’s, of the revival of the Pure and Applied Mathematics Institute/Impa, which multiplied the training of high-level mathematicians in the country and gained a strong reputation as a cellar of cutting-edge research in this field of knowledge.

Palis has a degree in engineering, after having gone to engineering school from 1958 to 1962, influenced by his engineer brother. Shortly after graduation, he felt a need to pursue mathematics, his passion ever since his childhood. “In my mind, I would have gone back to engineering, with a much stronger knowledge basis. This never happened”, he recalls. After an internship at Impa under mathematicians Maurício Peixoto and Elon Lima, he decided to pursue a doctorate degree in the United States. To this end, he sent a letter to Stephen Smale, asking Smale to be his advisor. Smale was a leading researcher of dynamic systems, a field of mathematics first pursued by the great French mathematician, Henri Poincaré, at the end of the 19th century. The field of dynamic systems is the study of the trajectories of differential equations in the long term to model phenomena that evolve in time, such as the climate, chemical reactions and planetary systems, among many others. Palis was promptly accepted and a few years later he realized how correct his choice had been. In 1966, Smale was granted the Fields Medal, the most outstanding award in the field of mathematics, considered the Nobel Prize of this science. Palis got his doctorate degree from the University of California in Berkeley in 1967. Soon thereafter, he and his advisor conducted a research project, the results of which led them to formulate a major conjecture in the modern theory of dynamic systems, relating two concepts – namely, the concept of hyperbole and the concept of stability. The proof of the conjecture would be concluded 20 years later by Ricardo Mañé, one of Palis’ doctorate students.

Although he had several invitations to remain in the United States, Palis wanted to come back to Brazil because he foresaw the possibility of contributing to the multiplication of the competent yet restricted community of Brazilian researchers in the field of mathematics. At Impa, he and his colleagues Peixoto, Lima and Manfredo do Carmo, among others, implemented a regular doctorate program, which is nowadays considered a reference of excellence. In the 1970s, Palis dedicated himself to the study of bifurcations (the change of dynamic structures in systems that depend on parameters) and then to the study of the theory of chaotic systems, systems where a certain degree of uncertainty exists: they are sensitive to the initial conditions and it is much more difficult to make predictions. His work and that of several other mathematicians led him to formulate a global conjecture of the dynamic systems, according to which most of the systems’ long-term behavior is governed by a finite number of attractors that constitute the “final destination” of the trajectories.

Palis has written over 80 scientific papers and has been advisor to 41 doctorate theses. He has been awarded a number of national and international prizes and is a member of 12 academies of science, among which are the United States National Academy of Science, the Brazilian Academy of Science, the French Academy of Science and the Russian Academy of Science. Palis was also appointed as a member of France’s Legion of Honor. He was director of Impa from 1993 to 2003. In the last few years, he has dedicated himself to the promotion of scientific and technological activities. He was the president of the International Mathematical Union from 1999 to 2002. In 2006, he was elected president of the Third World Academy of Sciences/TWAS, which is based in Trieste, Italy. Palis travels to Trieste three to four times a year for short stays. Since mid 2007, he has also presided over the Brazilian Academy of Science/ABC in Rio de Janeiro. “The fact that I am the president of the ABC helps my work at the TWAS and vice-versa”, he says. Married – he and his companion Suely Lima will be officially married on July 4th – he has three children and one grandson. Palis gave the following interview to Pesquisa FAPESP:

You left your hometown of Uberaba, in Minas Gerais, to study engineering in Rio de Janeiro. Then you decided to specialize in mathematics. How did this happen? 
I have always been interested in mathematics. I am the youngest child in a family of eight children. My father came from Lebanon and my mother came from the North of Syria. My father owned a big general store in Uberaba. But he never allowed any of his children – five boys and three girls – to help in the store. He wanted all of us to go to the university. It was an obsession. When I was four years old, my parents enrolled me in a small school near my house. I would walk to school and back home by myself. When I went to the public elementary school, I already knew how to add, subtract, multiply and I knew elements of math. The interesting thing is that nowadays it has been confirmed that children have the neurological profile to learn mathematics and languages already at the age of 2. My interest in mathematics goes back to those times.

So your father’s desire was fulfilled.
It was entirely fulfilled. My father paid for our schooling until the very end. One of my brothers studied engineering and he was the one who influenced me the most. I went to Rio de Janeiro at the age of 16, also to go to engineering school, because from my point of view at that time, that’s where the best math classes were held. I finished high school, with special emphasis on math and the sciences in the last two years, which was one of two alternatives in secondary education to enter college. I had a lot of encouragement and a great place to live, because my engineer brother lived in a very comfortable apartment that faced the Sugar Loaf. These were very important years for me, so much so that at the end of my freshman year in high school I took a college entrance exam to enter the University of Brazil (currently named Federal University of Rio de Janeiro/UFRJ) and got the highest grade. But I was not allowed to enroll because I was younger than the required age. The second time I took the college entrance exam I also got the highest grade, and this time I was allowed to enroll. I went to the engineering school but I really liked math and physics and I would ask many questions during class.

Did this cause you any problems?
The answers did not always allay my anxieties. I was called in twice by the dean because of complaints from my professors. One of the professors taught classes on engines; after six such classes, I told him: “Professor, you could have summarized all of this in a single class.” The professor told me to go to the blackboard and I was actually able to provide a good summary during that class period. The professor went to complain to the dean, Rufino Pizarro. He complained that I was being ironical, which was true to some extent. The dean called me in and said, “I have to reprimand you”. When I left his office, he said, “Never change”. The episode repeated itself and another professor went to complain to the dean, who again encouraged me to keep on asking questions.

So how did you get interested in mathematics?
I met math professors at the engineering school – they were engineers who had chosen a professional career linked to mathematics. Maurício Paixoto – who also influenced me later on – was one of these professors. There were relatively few top-level mathematicians in Brazil at that time and a high percentage had studied engineering. This was a common situation in those times – people would enroll in engineering school and midway they would discover physics, math, chemistry… I started attending a math seminar and towards the end of my engineering course I started going to the Impa and, less frequently, to the Brazilian center of Physics Research, the CBPF. My intention was to finish engineering school, go on to study math and physics and then go back to engineering with a much stronger basic academic experience. This “comeback” never happened. I concluded the course and was awarded a prize as the university’s top student at that time. At that moment, I decided that I wanted to go abroad for my doctorate degree. Another aspect of my personality is that I sometimes don’t really know what I’m talking about, but I know which direction I want to follow. I had no idea at that time what studying for a doctorate degree abroad entailed. There were very few examples of this kind at that time.

LÉO RAMOSWhy did you choose the United States?
I asked Elon Lima, one of the great mathematicians I knew, who had been the best in Brazil in recent years. Lima gave me a name: Stephen Smale. I wrote Smale a letter. At that time, Smale was at New York’s Columbia University. I was quite surprised when he promptly accepted becoming my advisor.

What did your family think?
My family was a bit apprehensive, “You’re going to study more? Haven’t you studied enough?” I had to convince them. The interesting thing is that I enrolled in December 1963 to start school the following September in the United States. But in June, Stephen Smale decided to accept an invitation from Berkeley, in California, and left Columbia University. He told me he was going to Berkeley and I wrote back saying that enrollment had already ended some time ago. He replied that he would negotiate with Berkeley to accept my enrollment. And that’s how the story goes. Before this, in March 1964, the Brazilian military had taken over the government and the CNPq [Conselho Nacional de Desenvolvimento Científico e Tecnológico, National Council of Scientific and Technological Development, ] practically stopped taking any action for a few months. The CNPq was the only organization I knew of that granted scholarships for studies abroad. At this point, there was no way I could ask my father for financial help – he had already “supported” me until the end of my university course. So then I heard about a scholarship called Fulbright, granted by the Instituto Brasil-Estados Unidos, a bi-national organization. I applied for the test and, much to my surprise, the Fulbright committee quickly agreed to grant me a scholarship. But the committee told me, “We are going to decide what your profile is and where the best place is for you”. I disagreed. “I will only accept the grant if you let me go to Columbia”. I applied and was accepted. I ended up going to Berkeley on an American scholarship.

How did you adapt?
My advisor welcomed me at first – but not much more than this, and rightly so. He was coordinating a seminar which comprised reports on new research studies related to dynamic systems. I decided to attend this seminar after the end of my first semester at Berkeley. I concluded my doctorate studies in September 1967. I stayed one more year in the United States: I went to the East Coast to visit Brown University, MIT [Massachusetts Institute of Technology] and I visited Harvard. I went back to Berkeley in February – the university had offered me a post as assistant professor. I stayed until August because I wanted to participate in a huge congress in July on global analysis, and then I came back to Brazil. It probably would have been easy for me to remain in the United States, but I really wanted to contribute to my country’s scientific endeavors.

So why did you decide to come back?
At that time, Elon Lima, who had been a professor in Brasilia and then had come back to Impa, was at Berkeley as a visiting professor. Manfredo do Carmo, another colleague and mathematician, was there as well, studying for his post-doctorate degree. I used to talk to them a lot and we had the impression that Brazil had very few mathematicians – but those few were topnotch, especially Leopoldo Nachbin and Maurício Peixoto. These two professors spent long period abroad for scientific and other reasons. Elon, Manfredo and I had the feeling that it would be important to have a permanent scientific environment, where research studies would be conducted systematically and new researchers would also be systematically trained. Going back in time, during my first year at Berkeley I read a short book written by James Watson, a Nobel Prize recipient, describing the discovery of the structure of the DNA. The name of the book is The double helix and it really impressed me. The description of the scientific environment where everything had happened, at the Cavendish Laboratory in Cambridge, England, attracted my attention the most. I think it is important to contribute to the creation of a scientific environment where students and researchers feel motivated. So then I was offered a post at the UFRJ and at the Impa. But in 1970, one year after I had come back to Brazil, I realized that it was impossible to divide my work between the university and the institute.

The Impa had better conditions. At that point, the BNDES [Banco Nacional de Desenvolvimento Econômico e Social, the federal government’s bank for economic and social development] had created the Funtec [Fundo Tecnológico] fund, which significantly increased the budget allocated for basic science and technology. This was coupled with the Sucupira project, prepared by professor Newton Sucupira, of the Federal Council of Education. The project organized the post-graduate system in the country on very advanced bases. These two facts made me feel very enthusiastic. The Impa, thanks to the support from the BNDES, became much stronger, with the potential to hire new researchers, promote that idea of a scientific environment and launch a regular post-graduate program. The Impa already had a doctorate program in conjunction with the UFRJ. For comparative purposes, eight or nine students had received their doctorate degrees from Impa in the 1960s; this number jumped to 30 in the 1970s. Still in 1970, I met José Pelúcio Ferreira, who had become famous for being instrumental in convincing the BNDES to fund scientific endeavors.

Did you ever meet minister João Paulo dos Reis Veloso?
Yes and Reis Veloso was also instrumental in the creation of the Finep [Financiadora de Estudos e Projetos] funding agency. By the way, an unforgettable event happened to me in 1970. I was coming back home on a Saturday afternoon, carrying lots of books. At that time, I was living in the neighborhood of Laranjeiras, close to the Fluminense soccer club. I would usually jump off the bus in front of the Instituto de Cegos, Institute for the Blind, and would walk in a straight line towards my house. But on that day I jumped off at another bus stop – don’t ask me why – and took the longer way home. I walked down a quiet little street and ran into José Pelúcio. He was walking with his two small children and saw that I was carrying lots of books. He asked, “On a Saturday afternoon?” I answered that I was coaching some students and beginning a new doctorate program. He let me go on talking and I went on enthusiastically talking about my field and that of another colleague. I said it would be very good to organize an international conference in 1971 for our students so that they could learn about different views of mathematics and of mathematicians as well, to become better known internationally. Then he asked me, “How much would this conference cost?” Timidly, I calculated a budget in my mind, gave him the numbers and he said, “Is that all?” At the end of the conversation he concluded, “Let’s draw up the first agreement and we’ll give you US$ 150 thousand.”

That was a huge amount of money for those times.
Yes. I had never imagined such a huge amount. But in two to three weeks, we from Impa were at a meeting with minister Veloso and Pelúcio signing the project’s memorandum of understanding.

So if you had jumped off the bus at the right bus stop…
I learned that uncertainty is something very good. Of course everything turned out all right, we organized a great symposium in July 1971 and I was already the advisor of one doctorate student. We  began in late 1969, early 1970 and I had expected good results in regard to doctorate students successfully concluding their programs in no less than four, five years. And these students concluded their doctorate studies much earlier. Welington de Melo was my first doctorate student who concluded the program. He is still at Impa, is a great mathematician, and is from my home state. At that time, the student of a Uruguayan colleague had written a letter saying that he had demonstrated several theorems, solving difficult conjectures in my field. I really liked that letter so I convinced the other members of the organizing committee – namely, Elon and Maurício – that we had to invite this student to our symposium. But how to do this, if he had not even graduated from college yet? I insisted, because what he had written in the letter made a lot of sense. He came to the symposium, talked to me and asked me if I would accept him as my student. I answered, “From the contents of your letter, the answer is yes.” He wrote me again one month later and I accepted to be his advisor during his doctorate studies.

You are referring to Ricardo Mañé, the deceased Uruguayan-born mathematician…
Exactly. Like Welington, he concluded his doctorate studies in record time; he wrote an excellent doctorate thesis. The fact is that in early 1973 I had already been advisor to three doctorate theses. Soon thereafter, I went to the United States on a Guggenheim grant and stayed there for one year. It is important to mention that the doctorate theses of these first three students were published in top scientific journals. I was very excited, because the results materialized earlier than we had expected. The same situation happened in the field of geometry, with Manfredo do Carmo.

LÉO RAMOSA site that maps the genealogy of the mathematicians informs that you advised 41 doctorate students and 128 descendants, who are the students of your former students. I would like you to talk about this relationship between advisers and their mathematics students. 
I’m very proud of my former students, who are now my colleagues, and their descendants. I have no conflicts with them because I think it’s important to acknowledge their own merits and not just the fact that they were my students. Ricardo Mañé, for example, was a brilliant mathematician who could have been awarded the Fields Medal. This award is granted to mathematicians under the age of 40. No Field Medal has ever been granted to a mathematician who developed a professional career in a developing country. Of course the international mathematical environment nowadays has much greater respect for the Brazilian mathematical community than in those times – in the mid 1980’s – even though we already enjoyed a good reputation back then. But the fact is that when you achieve a spectacular result at Princeton or in Paris, the whole world hears about it. Away from the leading centers, the impact of a major achievement tends to be more restricted. Ricardo was a mathematician who certainly could have been awarded the Fields Medal. Marcelo Viana, who came later, is another example. We have a very strong candidate at the moment.

Who is it?
His name is Artur Ávila. He came to Impa at a very young age. He came straight from the Colégio Santo Agostinho school. He studied under Welington de Melo, and got his doctorate degree at the age of 20. He is brilliant. He is 30 years old now. He spends half a year in Paris and, at this young age, is already a research director, linked to the Centre National de la Recherche Scientifique, the CNRS. This is an exceptional feat. Three years ago, he came to Brazil for an extended period of time and Impa wisely invited him to stay here six months a year, with a salary and in a very important position. This kind of arrangement is possible, because Impa is a social organization with a more flexible structure. He is paid a salary for the six months that he stays at Impa; this salary is suspended when he goes to Paris. There’s no doubt that he’s a leader here and there.

How has research in the field of mathematics evolved in the last few years?
It is particularly strong at the moment. In 1974 and in 1978, two Brazilian mathematicians gave lectures at the International Congress of Mathematicians – something unheard-of at that time. The same thing happened in the 1990s. An invitation to be a speaker at a congress of this kind confers enormous prestige. The congress is held every four years and approximately 180 mathematicians (men and women) are invited to participate. The number of Brazilian mathematicians at this congress has been growing and this is one of the signs of our powerful presence in the international scenario. It’s not the only sign, but it is a good indicator.

And more recently?
Two speakers will be at the congress in 2010 – both of them are from Impa: Artur Ávila and Fernando Codá. Artur will speak at a plenary session. As he is very young, this fact is pointing at the Fields Medal. But this is not certain. Marcelo Viana had already spoken at a plenary session in 1998 and was not awarded the Fields in 2002 – in my opinion, this was a mistake, but who am I to say anything. The growing importance of Brazilian scientific research is something recent – Brazilian science as a whole is still very young. In fact, it began to gain strength when the University of São Paulo was established in 1934. Of course we had Carlos Chagas, a renowned scientist, but there were not many like him. Our scientific community began to gain strength in the 1940s and especially in the 1950s. It’s all very new.

How mature is the Brazilian scientific community?
Brazilian scientific production has grown tremendously and this was not mere chance. Thanks to regular investments, which have grown over the last few years, the scientific environments have increasingly become stronger. There is a great concentration in São Paulo, which is followed by Rio. And it’s good that these centers are strong. But it is important to have strong centers in other states as well. One cannot confuse this status with failure to enhance the best teams, the best centers. That’s not the idea. Decentralization is very important and this is why the ABC recently created regional offices headed by vice-presidents. We also created the Affiliated Members category, comprised of scientists under the age of 37. Every year, the Sitting Members from a given region choose the most talented young scientists from that particular region. These Affiliated Members remain as such for a five-year, non-renewable term. This has reverberated very positively, thanks to the enthusiasm of these young members.

The ABC appoints groups of scientists who are in charge of producing documents on major issues. What has been the result of this experience? 
The study groups are another important front of activities. We’re going to have Presidential and state elections next year and the guidelines in this respect are that the study groups in progress conclude their mission, if possible, in a proactive manner in order to offer conclusive documents to the candidates running for office, especially those running for the Presidential office, and to the candidates running for state office whenever it is appropriate to do so. The basis is always scientific. It is very important for the documents to be pro-positive. In this sense, thanks to the ABC study group on bio-fuels, we had excellent exposure at the so-called G8 + 5 meeting of the scientific academies. We have the G8 + 5, which is the group of the seven wealthiest nations, plus Russia, and the five emerging countries (South Africa, Brazil, China, India and Mexico). As the heads of these countries meet once a year, the respective scientific academies are summoned to present proposals on two scientific-technological issues that are crucial for society. This year, the topics were Renewable Energies and Migration. Bio-fuels were not an issue under the first category because of the food safety issue. At this point, I would like to stress that Brazilian scientists defend Brazilian ethanol on purely scientific grounds.

So how was the ABC’s presentation?
I talked about the Brazilian ethanol, in line with the group discussions conducted by the ABC’s Biofuel study group; the text, however, had essentially been written by Carlos Henrique de Brito Cruz, the scientific director of FAPESP, with the help of João Jornada, a very competent professional – he is the president of Inmetro. At one point, I realized that the text was putting us in a defensive position, because it was worded as follows, “We can produce approximately 10% of the global gasoline consumption by using a small percentage of the arable land in Brazil and South America”. The ‘small percentage’ had been calculated by prominent scientists in the field of food safety as being the acceptable limit for the planting of sugar cane. Nonetheless, according to my accounts, the result corresponded to more than 100%. I called Brito from Rome and told him that much more ethanol was being produced than was stated in the document. He replied that he had suggested that figure, taking into consideration an exaggerated risk coefficient. I answered that we should express a more accurate figure, taking into consideration a more believable risk coefficient. He agreed. The conclusion is as follows: by using estimates produced by respectable scientists who criticize biofuels in favor of food safety, we can produce sugar cane ethanol that will cover the entire global consumption of gasoline until 2050 if we merely resort to the arable land that in Brazil and South America is left over from their calculations. This is spectacular. Moreover, ethanol is less polluting and does not fight for space with the arable land necessary for food safety. I believe that this was the best presentation of the meeting. And the final document enhanced our delegation’s position in regard to biofuels.

When you visited FAPESP in April, you listened to an explanation given by the three coordinators of three programs run by the Foundation: the Biota, bioenergy and climate changes. What is your opinion of these reports?
I was greatly impressed by the details of the studies, the enthusiasm of the groups and their productivity. These are dense projects. I understood that the project on climate changes had these characteristics, but the project is still in the developmental stages. Activities have been more intense in the other two projects.

During the presentation, you gave suggestions on training programs for new researchers in fields that still need to be more extensively explored in our country… 
Of course surveys have to be conducted to consolidate my opinion, but I can state right away that oceanography is a field that deserves a special program to train researchers. This effort has already been made, but it has to be renewed. We have an extensive coastline, a very unique environment that is undergoing all sorts of impacts, including climate changes. Engineering is another field – this field suffered greatly in the 1980’s. Engineering is a vital field for the development of any nation. Mathematics is another example: the mathematical community is highly qualified according to various indicators, but it is too small in relation to the demand. To exemplify: the national average in terms of references in comparison to the global average is – 11%. That is, we are close to the world average, which is concentrated in the developed countries. This is an excellent index. But the field of mathematics has not attracted enough talented professionals. I mentioned oceanography and engineering, because I feel that these two fields have the same problem. This is the challenge for us: we must foster motivation so that a higher number of great talents migrate to these fields. As for mathematics in particular, it is an important field because it involves many other fields of knowledge. The situation nowadays is that approximately 120 PhDs graduate every year from institutions that are highly ranked by the Capes agency. This number is not enough to meet the demand coming from universities. Very often the mathematics teaching positions are taken up by theoretical physicists – and they are warmly welcomed, but these professionals are not always interested in these posts.

When you were instated as president of the Third World Academy of Sciences/TWAS two years ago, you mentioned two main challenges, namely, to increase the participation of women and the brain drain issue. Is TWAS coping with these challenges?
Yes, but the challenges up front are huge. This task is not something that will be concluded in a short period of time. To exemplify, I will mention a fact related to our ABC: this year, six women scientists were elected as sitting members. This is an unheard-of number, which corresponds to one-third of the total number of elected sitting members. The percentage of female sitting members has now gone up to 11.5%. But we have to achieve 50% in a natural way, without forcing the issue and always respecting meritocracy! The percentage at TWAS is much lower, but the TWAS runs special doctorate and post-doctorate programs for women from developing countries. We also run programs that are mostly funded by Brazil, China, India and Mexico; these programs offer doctorate grants, sandwich grants and post-doctorate grants to qualified candidates from the countries referred to above. Women are increasingly aware of their skills and are participating more in these kinds of programs. But we have to maintain this strong encouragement for the presence of women in the scientific environment.

What about the brain drain?
Unlike Brazil, the brain drain is dramatic in the African countries, with the possible exception of South Africa. In general, institutions in most African countries are not that stable. It is crucial to make research environments more stable. These countries lack adequate research centers that would retain the local talents and let them conduct their activities without having to worry about their survival. In relation to the program that I mentioned – doctorate, sandwich doctorate and post-doctorate programs for qualified students from developing countries – the TWAS finances the air tickets. The scholarships are the lowest expenses, but they are symbolically important. I also think it is important to create ties that allow students who come from a relatively less developed country to go back to their native country with the assurance that their relationship with scientists from Brazil, China, India and Mexico will continue in the future. This is why it is so important to have a post-doctorate program as part of the entire program. Another major challenge is to convince the governments of these less developed countries to participate in the process.

Why does Brazil have such dramatic difficulty in improving the performance of math students? We have state-of-the-art research, but we are still backwards in terms of basic education.
This is an apparent paradox. State-of-the-art research is conducted by a much smaller community than the community that is involved in elementary and secondary education. The teaching of math, which is conducted in several stages, involves entirely different numbers and millions of children and adolescents. Thus, the dimensions related to research and the teaching of mathematics as a whole are entirely different. There are two issues to be addressed: the main issue is the training of good teachers. But it is not enough to have competent teachers earning reasonable salaries. It is also necessary to have appreciation from society. This appreciation has worsened dramatically in Brazil because in the past we did not have post-graduate programs and high school teachers teaching at the top schools were prominent members of society. This is no longer true. The prestige in this respect migrated to the universities and then to the post-graduate and research programs. This situation has to be improved, as it will influence the entire chain. It is easy to design and difficult to implement. We are beginning to deal with this problem vigorously. We have competitions to motivate students, but we still come up against a lack of skill in those who do the teaching. Teachers often are willing to do a good job but they are unable to teach what they don’t know.