## Interview with Professor Cândido Lima da Silva Dias (1913-1998)

 The following interview of Cândido Lima da Silva Dias was granted to Vera Rita da Costa, for Science Today. It was published in Science Today in November 1997. The original article, in Portuguese, is available at: http://www.canalciencia.ibict.br/notaveis/livros/candido_lima_da_silva_dias_45.html We give an English version of this interview below:

The 25 January 1934 is a remarkable date in the life of Professor Cândido Lima da Silva Dias. On that day, when he opened the newspaper, he came across the news: the "subsection" of mathematics had just been created. "This is for me!", thought the then Polytechnic student, who was on vacation in the city of Mococa, in the interior of São Paulo. It was there, encouraged to play by his engineer father, that he learned to count with huge numbers before the age of seven, numbers followed by 30 or 40 zeros. So when he joined the school group, the four operations were no secret to him and mathematics became his natural path. He was an assistant of the Italian professor Luigi Fantappié at the University of São Paulo in 1937, and taught there for 54 years until his retirement in 1990, including the period in which he directed the mathematics section of the National Council for Scientific and Technological Development (CNPq), which, he confesses today, is more dedicated to the research which he misses the most. But nostalgia is not a welcome word in the teacher's dictionary: for him, the past is inspirational but should not be deified. And after learning and living with some of the characters that are now part of the history of science, he says: mathematics courses are better and more up-to-date.

 How was your early career in mathematics? Did you have mathematical skills as a child?

Since I was little I played with numbers. My father was an engineer and he enjoyed making me count. He liked, for example, playing with huge numbers, followed by 30 or 40 zeros. I remember a question my father asked when I was only seven or eight years old: "How many cubic centimetres fit in a cubic millimetre?" Because of this fun with him, I had a very early notion of numbers. When I joined the school group, doing mathematics was banal for me.

 Did you excel at school?

I had good grades, but I never got noticed. I was born in Mococa, in the interior of São Paulo, more precisely in the city square at 100 meters from the Barão de Monte Santo School group. Going to school was part of childhood games and my memories of that time are excellent. The school group was very well constituted and organized, with good teachers. Then I came to the capital, to study at the Franco-Brazilian College, which operated in the building which today is the Pinacoteca do Estado. That was in 1924, because the following year the college moved to Vila Mariana. Also from the Franco-Brazilian Lyceum I have great memories: it was very liberal and we had excellent relations with the teachers. Just as there were students who were boarders - I was one of them - there were also teachers who lived in the school. My children always criticized me for not being interested in clubs and I always answered: why do I want a club if I had the best in the world for seven years - the Franco-Brazilian Lyceum in São Paulo?

 Your choice for mathematics was made at a time when this was at least unusual. No university course existed in São Paulo. How do you explain your choice?

The big-number games, made by my father, made mathematics easy for me. Besides, when I came back to Mococa on vacation, my father used to study with me for two hours a day. He was an electrical engineer who graduated from the Polytechnic School of São Paulo in 1905. After graduating, he majored in electrical engineering in Liège, Belgium, and when he returned from there he worked in Mococa. At the height of coffee production, my father became reasonably rich, but he died early, at age 60 in 1939.

I have very good memories of living with him: during the holidays we studied together and progressed to what was to be studied the following year. Even after I entered the Polytechnic School in 1932, I kept the habit of going on holiday in the interior, and it was on one of them, in 1934, that I decided to become a mathematician. I was at an uncle's house when the newspaper arrived. I remember opening it and coming across the news of the creation of the Faculty of Philosophy, Sciences and Letters, with its section of sciences and the subsection of mathematics. I distinctly remember talking to myself: this is for me. It is curious that the creation of the University of São Paulo was a surprise and that I did not have much news about it; it was from the reading of that newspaper that I became interested in the new university. In this news it was already talking about the arrival of foreign teachers to São Paulo.

 When was your first effective contact with the Faculty of Philosophy, Sciences and Letters?

 Did you give up the Polytechnic School or try to take the two courses?

After the examination, I made the decision to do only the mathematics course. Physically that did not mean much, because the Department of Mathematics, or rather, the subsection of mathematics, took place in the building of the Polytechnic School and remained there until 1938.

 From your father's side there was no reaction when you abandoned engineering?

No. I even admired him for not having reacted because the decision was so easy. I think he knew it would happen and he recognized my vocation for mathematics. That was in 1935 and he died four years later.

What did it mean to be a mathematician back then?

Mathematics did not exist as a career: the prospect was to be a teacher. When a person stood out, he could claim a place in his own university. This is what happened to me: when I graduated in 1936, I was immediately invited to become Fantappié's assistant. I was nominated on 10 March 1937. You see, in 1978 I retired from the University of São Paulo and, in 1990, from the Federal University of São Carlos. I was, therefore, a university professor for 54 years!

When I started my career, there was a curious classification in the university: the professors were ranked as professors of first and second categories. In the case of Fantappié, the first category was Omar Catunda and I was the second. I remember receiving a salary from a tale and two hundred reis [the Brazilian currency], which at that time represented a reasonable gain, which allowed me to live well. So much so that by the end of 1937 I was able to get married.

 What were the duties of an assistant at that time?

I had to follow the lessons and give the exercise classes. It was also necessary to accompany the students, giving them assistance and clearing up their difficulties.

 Did you know or follow Fantappié's personal research work?

Even as a student I had contact with the subject in which Fantappié worked. When I took the course, the subject was analytical functional theory, in which he was working at the time. It was a very advanced course and I worked hard on this theory. I remember dealing with the applications of partial differential equations.

 Who were your classmates in the mathematics course?

One of them was Mario Schemberg. Another, Fernando Furquim de Almeida. And, even younger than I, there was Abraham de Morais. All of them migrated from the Polytechnic to Mathematics, even though it was a migration they did not leave the place, because the courses were in the same building. I was a close friend of Furquim, with whom I studied together for the examinations. Schemberg and I also studied together. At that time, we were more systematic and the organization of our day-to-day life was greater because we went to college in the morning and afternoon. Our main job was to follow the courses and do some good examinations.

The 1930s was a time of political and cultural effervescence, especially in São Paulo. Did you have any kind of political participation or acquaintance with the intelligentsia of this time?

I had a little contact in my own college, but that was not an important fact in my life. I was really watching; the student's concern at that time was really to study. I read a lot, but I did not take much of these questions. I think the arrival of the Italian masters - the first was Gleb Wataghin - was important. Wataghin was remarkable; as soon as he arrived, he set up a research and work group on cosmic rays, which was new at the time. His influence on Schemberg and Marcelo Damy de Souza Santos was very great. Paulus Aulus Pompéia was already an engineer, but I think he was interested too.

 Did Wataghin's activities draw attention to the University?

Ah yes. The press itself was interested. In 1936 Giacomo Albanese and Giuseppe Occhialini also arrived in Brazil. Occhialini, who was a physicist, exerted a great influence on Caesar Lattes and remained in Brazil until the beginning of the war.

 What was the relationship between the foreign teachers and the students?

They were very affable. Fantappié, for example, had a good time with the students. Even with regard to the question of language there was no problem: they spoke in Italian, we in Portuguese, and understood each other as if we were speaking the same language. In other areas there were also foreign teachers, usually French. In mathematics and physics, however, the great influence was from the Italians. In Mococa, as in the entire state of São Paulo, the influence of Italian immigration was strong, and this meant that although I had never studied Italian, I understood the language easily. Italian was a familiar sound to me, to the point that I remember an Italian conversation with Fantappié. Since I was in Rome in 1951, I called him and found it reasonable to try to speak Italian, he noticed it and commented, "I did not know you spoke Italian."

Fantappié returned to Italy in November of 1939, to become professor of Higher Mathematics in the Institute that had just been created in Rome. The head was a well-known mathematician, Enrico Fermi. He and Fantappié had been classmates. Fermi was already remarkable. I remember a visit Fermi made to Brazil in 1934 and the two together. That seemed fantastic to me: they were people born in 1901, who were only 33 years old. Very young ... At that time I was 20. This is the memory I have: for me, the beginning of the University of São Paulo and my youth are the same. Fantappié died young, in 1955, only 54 years old.

 Who chose these teachers?

A great figure: Teodoro Ramos. He was a very educated and very involved man. He was also a good mathematician: he had not long ago defended a very good doctoral thesis in Rio. Besides, he was a man of sensibility. He knew how to choose - and in the mathematics and physics sector he could act only with his own judgment - great teachers from outside. In addition, to come, Italian and French teachers must have received a tempting proposal. In France and Italy, Teodoro Ramos found much official support. Also in Germany the reception by the government was great, so much so that German teachers came to the area of chemistry. The creation of University of São Paulo was taken seriously abroad and I believe that in the area of mathematics, too, it has strengthened Teodoro Ramos' personal prestige.

 In what year did you do your first academic work?

My first self-study, after graduating, is from 1941. It was about the analytic functional theory that Fantappié was working on. It was not yet a thesis, but then, in 1942, one of those works became a thesis. By that time Fantappié had already returned to Italy.

 How was the production of a mathematical work at that time? Was it individual or relied on teachers?

In part the research work came from the coexistence with the teachers and the seminars in which we were encouraged to participate. In fact, it was these teachers who introduced into Brazil the system of seminars, in which individual works were exhibited. Thanks to these meetings, I became aware of how far Fantappié had developed functional theory. So it was natural for me to work on that too.

 Did the Italians and the French come to Brazil at the same time?

I think the first to come were the French, but with little time difference. When Fantappié arrived in April, Pierre Deffontaines was already in geography. Then came a remarkable teacher, Pierre Mombeig, who was interested in knowing the interior of Brazil and ended up writing a book about the country. He was very active and stayed here until the 1950s. Claude Lévi-Strauss also came after Fantappié. In fact, this is another story, that of the second wave of foreign teachers during World War II.

Also mathematicians came to Brazil to escape from the war. For example, André Weil, a great mathematician, brother of writer Simone Weil, was invited to the Higher Analysis school. He arrived in 1945 and stayed for almost three years. He never commented on his sister, who had died three years earlier, in 1943, in England. It was only after I was in the United States in the late 1940s that I learned that they were siblings - and very close, as explained in her book, in which André is quoted.

Along with Weil came an American mathematician, but of Italian and Russian origin, Oscar Zariski, a specialist in algebraic geometry. Also shortly after, invited by the Weil, came Jean Dieudonné. It was in these circumstances that what I consider to be one of the most important things for Brazilian mathematics happened: in 1946, here in São Paulo, there were two of the most important members of the Bourbaki group - a true concentration of Bourbaki, right here.

 What is the Bourbaki group?

This is the story of a great success. In 1934 some young French mathematicians (among them Weil, Dieudonné and Jean Delsarte), who wanted to write a treatise reformulating the basic part of mathematics, formed a group with that name. Their motives were mainly pragmatic: they wanted to facilitate the courses they taught. This initial plan was greatly expanded and they eventually reworked the fundamentals of mathematics, including logic. These "new" grounds were published in fascicles. I think the first came out in 1939, just before the war.

Bourbaki was a small group - seven or eight people - but the work was a collective elaboration: one wrote the argument, then all met and discussed the details. Another one elaborated the manuscript and only after much discussion the work was approved unanimously and published. In this sense, it was a truly collective work. Many chapters have been reworked several times before being accepted by the group.

 Why the name Bourbaki?

It was a joke. They all had one thing in common: they were former students of the École Normale, very famous in France. There, on the first day of school, the freshmen were sent to Professor Bourbaki's room. In fact, the class was a con: Bourbaki was a great French general who participated in the war of 1870. The name adopted by the group came from this joke. There was another particularity in the group's constitution: the requirement to be young. When a member reached the age of 50, he was no longer active. He could even hear the arguments, but they did not ask him to collaboration or to vote.

 Does this group still exist?

Ah! yes, it is renewing itself and continues to this day. Weil, born in 1906, remained a Bourbakian until 1956. When he came to Brazil, we learned of his existence. In college, we had access to copies of the group's essays, including some that were not published, and we discussed them. I've kept some of them until today. Therefore, in the 1940s, in São Paulo, we had a relative intimacy with one of the most remarkable groups in world mathematics.

 Did the presence of these members of the Bourbaki group influence Brazilian mathematics?

Faced with the importance of the group to mathematics, I think the impact on us could have been greater. But I think this was limited by the personality of Weil and Dieudonné: they were very busy people with the work of the group and they did not take much interest in other activities. This limited our conviviality with them. But the work of the Bourbaki group has influenced mathematics in various parts of the world. In Brazil this influence was anticipated. I think I was one of the first influenced, because I got on very well with Weil. Today, it's water under the bridge ... even the works of the Bourbaki are already considered outdated.

 Did you know that recently the Bourbaki group was "buried"?

I did not know that, but I think it would be an exaggeration to bury Bourbaki. There is still something published of the group and its influence is still much debated. It's too early for that. My impression of the work is extremely positive.

 How did the return to France of Weil and Dieudonné feel?

Weil left in 1947, but I did not feel "orphaned" because between 1948 and 1949 I also went to the United States. So from a personal point of view, Weil's departure was a little dissipated. As for the Bourbaki group, the contact was not broken either, because between 1949 and 1951 one of its members, Professor Delsarte spent three months a year in Brazil.

 At a conference, you said that Levi-Strauss influenced Weil's coming. What was the relationship like between the two in France and Brazil?

It is true. Weil and his family left France around 1941, shortly after the Germans took Paris and went to the United States. There he was hired as a teacher at a relatively minor university in a Pennsylvania town. At the same time, Lévi-Strauss also left France and came to Brazil. They knew each other from France. In 1944, when Weil was invited to Brazil, he asked Lévi-Strauss for information. I remember Weil talking about him and telling how he influenced his decision. With Dieudonné it was different: he stayed in France during the war and came directly to Brazil in 1946.

 Was there close coexistence between the two here?

I think so. One of the books of Lévi-Strauss, 'Elemental Structures of Kinship', has an appendix on the mathematical part of Levi-Strauss's theory written by Weil. In addition, the two were long-time friends in France and were the same age. I think Weil may have helped Levi-Strauss, but not influenced his thinking.

 How was your experience in the United States?

I went in 1948 and it was my first experience abroad. I've been to Harvard, Chicago and Princeton. They were the top three mathematics centres at that time and being there was very exciting. In Chicago, I met Weil, who had gone there six months earlier. While I was there, Leopoldo Nachbin also arrived. I met him in 1942 - I do not think he even graduated - when a group of students and teachers from Rio came to São Paulo.

 Did you do some work together?

Not proper work. But to elaborate my thesis, we talked a lot. Some proofs are even suggestions from Nachbin. In mathematics it is not common to co-author, although there are works signed by two colleagues. Nachbin and I came very close to each other after the creation of the National Council for Scientific and Technological Development, when in 1951 I became director of the Council's mathematics section.

 Did you participate in the creation of the National Council for Scientific and Technological Development?

No. The National Council for Scientific and Technological Development was created in 1951. In July, Admiral Álvaro Alberto, who was the president of the Council, was in São Paulo and we talked about the Institute of Pure and Applied Mathematics, which would be created as an institute belonging to the National Council for Scientific and Technological Development.

 Why the creation of the Institute of Pure and Applied Mathematics soon after the National Council for Scientific and Technological Development?

I think it shows that mathematics at the time had prestige. The Institute of Pure and Applied Mathematics was the first institute created by the National Council for Scientific and Technological Development. The proposal to create it completely unconnected with the university was a delicate matter: it meant doing outside the university what could be done within it. And there is the Institute of Pure and Applied Mathematics to this day, not connected to the university and producing. Later, the National Council for Scientific and Technological Development created other institutes, such as the Brazilian Centre for Physical Research and the National Institute of Amazon Research (INPA).

The creation of institutes insulated from the university only generated more controversy because it was much discussed. The project of creation of the Institute of Pure and Applied Mathematics was presented in 1951 and took a year to mature. There was no great opposition on the day of the vote. Even in São Paulo the idea was well received; there was a closer relationship between the Institute of Pure and Applied Mathematics and São Paulo, some of the professors hired there worked in São Paulo, such as Alexandre Grothendieck, who was in Brazil between 1953 and 1954.

 Between teaching, administration, and research in mathematics, what activity attracted you most?

The one I exercised most was teaching, but I would say it was due to circumstances. My most nostalgic period is when I was most active in research in the 1950s. I would say it was a shame to be dispersed in other activities. It's a confession I make now, at this point in my life. As of 1951, administrative activities began to absorb much of my time. This dispersion was not my option: at the time of the decision, you believe it will be a passing phase, but it ends up absorbing more than you imagined. I never wanted to leave the university and if I went back, I would not have any other choice. For family reasons, I had to worry about business for a certain time, but I regret that too: it took me a while to dedicate more time to what I liked, to mathematics.

 How do you rate mathematics students today and those of the past?

I talk a lot about this with my fellow teachers and I consider myself optimistic: I do not see much difference. Mathematics courses today are better and updated with the very evolution of mathematics in the last 40 years. Although I am not currently in direct contact with students, what I could feel in the last few courses I gave is that they are no more unprepared than we were. I believe that in the most pessimistic evaluations there is a certain "deification" of the past. We have to abandon this tendency ... It seems to be part of the age, but it is totally silly. We can seek the past, remember, inspire in it, but in a healthier way, in which what is worth is the moment.

JOC/EFR September 2018