Omar Catunda

Quick Info

23 September 1906
Santos, Brazil
12 August 1986
Salvador, Brazil

Omar Catunda was a Brazilian mathematician. He worked hard to improve the level of mathematics education at both school and university level across Brazil.


Omar Catunda was the son of Thomaz Catunda (1865-) and Maria Pagels Lima Verde (1867-1939) from Ceará in the north east of Brazil. Thomaz, who was a medical doctor, married Maria in Fortaleza, Ceará, Brazil on 25 March 1891. Maria had considerable literary skills being particularly fond of classical and romantic French literature. Their first child Wagner Catunda was born on 12 March 1892 and they went on to have thirteen further children, with Omar, the subject of this biography, being the second youngest of his parents' five sons and nine daughters. We note also that Omar's paternal great-grandfather, Joaquim Catunda (1834-1907), had been a professor, historian and Brazilian politician of the First Republic, serving as a senator from 1890 to 1907.

Omar's first school was the Grupo Escolar Cesário Bastos where he described himself as a 'distracted and careless student'. From the age of twelve he studied at the Commercial Liceu in Santos, where he distinguished himself in Portuguese and Mathematics. He attended the last two grades of the José Bonifácio School of Commerce and then, in 1922, went to Rio de Janeiro to prepare to take university entrance examinations. He wanted to be a mathematician but Brazil did not have any specialist mathematics courses at this time so his only option was to take an engineering degree. He studied hard at the Colégio Pedro II then at the Gymnasium in São Paulo. These did not provide the depth that he wished for, so he worked, often for eleven hours a day, undertaking self-study from books. His favourite book was Comberrousse's Geometria Elementar . In 1925 he took the entrance examinations of the Escola Politécnica de São Paulo, and was ranked first.

At the Escola Politécnica, Catunda began with the Preliminary Course where he had lectures on geometry and also studied the differential and integral calculus. He was taught mathematics as part of the engineering course by Theodoro Augusto Ramos (1895-1935). Ramos was keen to improve the teaching of mathematics in Brazil and, finding Catunda enthusiastic for the subject, supported his studies. Catunda received the Cesário Motta Award, a gold medal awarded to the best student in the Preliminary Course. He graduated with an engineering degree in 1930 but never intended to have a career building roads or bridges. Unable to move forward as a mathematician, however, he took a job as an engineer for the City of Santos while looking for a way to become a professional mathematician [35]:-
... after a brief period of work in the City Hall of Santos, Catunda applied for the Chair of Infinitesimal Calculus at the Escola Politécnica in 1933, at the age of 27. On the panel were two of the biggest names in mathematics in Brazil at the time: Teodoro Ramos and Lélio Gama. Both gave first place to Catunda, while the other three members chose the candidate José Octávio Monteiro de Camargo, who won the contest and was responsible for the discipline for many years.
Catunda was fortunate that the University of São Paulo was founded in 1934 as a combination of the newly founded Faculdade de Filosofia, Ciências e Letras and the engineering school, the Escola Politécnica. To make sure that the new university was of a high international standard, professors were brought to São Paulo from France, Italy and Germany. The first mathematics professor that was brought was Luigi Fantappiè who travelled to Brazil from Italy in 1933. Cândido Silva Dias began studying mathematics at the Polytechnic School in 1932 and became one of Fantappiè's first students. In 1934 Catunda was appointed as Fantappiè's assistant for, although he only had an undergraduate engineering degree, Catunda was able to show that he had gained, through self-study, mathematical skills well above the level of the courses he had taken. This appointment meant that Catunda was in a position to marry. He married Eunice do Monte Lima (1915-1990) on 15 September 1934 in Rio de Janeiro. Eunice, born in Rio de Janeiro on 14 March 1915, was a pianist, music educator and composer. You can read about the career of Eunice Catunda (who changed her name to Katunda after her divorce in 1964) in the article [14]. They had a son, Igor Catunda, born in 1937.

Fantappiè and Catunda collaborated on starting up the Mathematics Subsection of the Faculty of Philosophy, Sciences and Letters at the University of São Paulo with Fantappiè as its head. It later became the Institute of Mathematics and Statistics. Catunda began undertaking research for a mathematics doctorate advised by Fantappiè. The Mathematics Department soon gained new members of staff. Giacomo Albanese was sent from Italy to Brazil in 1936 to join the new University of São Paulo Mathematics Department. He was appointed to the chair of Analytical, Projective and Descriptive Geometry. Cândido Silva Dias was appointed as Fantappiè's assistant in 1937 and taught in the Mathematics Department for 54 years retiring in 1990. Catunda's research progressed exceptionally well and Fantappiè supported his application for an Italian grant to support a research visit to Italy in 1938 [43]:-
Fantappiè encouraged his Brazilian students to go to Italy, such as Omar Catunda, who stayed there for four months in the late 1938 with an Italian grant. During his stay, Catunda published in the 'Atti' of the Reale Accademia dei Lincei and gave lectures at the Mathematical Seminary of the University of Rome. In addition, part of the results obtained by Catunda in Italy would be used in his thesis for the public tender in Mathematical Analysis in 1939, after Fantappiè's departure.
Catunda published Un teorema sugl'insiemi che si reconnette alla teoria dei funzionali analitici in the Rendiconti dell'Accademia Nazionale dei Lincei. Fantappiè returned to Italy at the outbreak of World War II in 1939 when he was offered the Chair of Higher Analysis in the University of Rome, a position he held for the rest of his life. On 25 October 1939 Fantappiè commented on Catunda's thesis suggesting that Catunda should be appointed as his successor. He wrote that his thesis [43]:-
... serves as a basis for the studies about Volterra's harmonic functionals, on which Hodge has recently made important researches; it was in fact these investigations by Hodge that caught the attention of His Excellency Prof Severi, in Rome, due to their possible applications to the study of Abelian integrals and algebraic geometry, on which Severi himself is one of the universally known specialists. Severi invited Mr Omar Catunda, who was in Rome at that time, to make an exposition of this theory at the Mathematical Seminar of that University, for an audience composed of the most eminent Italian mathematicians, an exposition that in my opinion should be published in the "Rendiconti" of that Seminary to serve as a guide for the specialists.
Catunda was appointed, on an interim basis, as professor responsible for the chair of Mathematical and Higher Analysis, replacing Fantappiè.

In 1944 Catunda presented the thesis Sobre os fundamentos da teoria dos funcionais analíticos :-
... in a competition for the chair of Mathematical Analysis at the Faculty of Philosophy, Sciences and Letters, University of São Paulo.
This thesis begins:-
The main purpose of this work is the systematic study of the fundamental part of the theory of analytic functionals. This branch of the theory of functionals, inaugurated by Prof Fantappiè, was developed by him with great success, mainly in applications to the theory of matrix and operator functions, to the explicit resolution of certain types of differential equations, to the rigorous foundation of symbolic calculus, etc. All these results are obtained by means of reasoning of great generality and relative simplicity, from concepts that appear naturally in the study of the functionals of analytic functions. In particular, the concept of the indicatrix of a linear functional, as well as Prof Fantappie's fundamental formula, are rich in consequences for these applications.

The greatest difficulties of the theory, however, appear precisely in the foundations, which will not come as a surprise to those who have already become acquainted with the different functional spaces in the real field, which sometimes present quite large complications.
Elza Gomide was a student at the University of São Paulo from 1942 to 1945. She took Catunda's first year analysis course which largely followed the syllabus Fantappiè had set up. It began with the construction of the real numbers and Gomide spoke about the course in an interview (see [23]):-
The course started with the construction of real numbers. This is a beautiful construction, but extremely elaborate. I remember very well that I thought the idea of Dedekind cuts was wonderful, but making the students' first contact with calculus by defining operations and their properties based on the notion of cuts is a tragedy! ... It was over the students' heads. ... The course only began to be of interest when it entered the notions of derivative and integral.
Gomide was appointed as Catunda's assistant in 1945. In that year André Weil was appointed to Fantappiè's chair which Catunda had filled on a temporary basis. Catunda, with a scholarship from the Rockefeller Foundation, spent 1946-47 at Princeton University and Jean Dieudonné was appointed professor of mathematics at São Paulo for 1946-47 but it was Gomide who took over teaching Catunda's Mathematical Analysis course. At Princeton University, Catunda attended courses given by Emil Artin, Harald Cramér, Heinz Hopf, Hermann Weyl and John von Neumann.

Aparecida Rodrigues Silva Duarte writes in [11]:-
In 1947, after finishing his studies at Princeton University, Catunda returned to São Paulo. There, he engaged in the campaign in defence of Brazilian oil, becoming president of the Centro de Estudos e Defesa do Petróleo. He was also a candidate for state deputy, supported by the Communists and the Brazilian Labour Party, but his candidacy was challenged by the electoral justice. Catunda, although a militant, did not join the Brazilian Communist Party. He criticised the Getúlio Vargas government for neglecting the education of most of the Brazilian people, worrying only about the elite. For Catunda, the government had decided to "democratise secondary education, without realising (or pretending not to realise) that there were no people to carry out this democratisation with the necessary seriousness." This would be the reason why students arrived at universities without proper preparation. He also advocated greater investments in higher education, so that they would train qualified professionals to improve and expand secondary education.
Elza Gomide also spoke about Catunda in various interviews [38]:-
According to Professor Elza, Professor Omar Catunda was an extremely important person in her professional career. He didn't talk much about politics, but he was a militant. According to Professor Elza, he would have participated in all the 'oil is ours' campaigns! During class breaks, he would talk, sell raffle tickets, talk about the campaign and the need for Petrobras [a State Brazilian Oil and Gas Company].
Ubiratan D'Ambrosio (1932-2021) was a student who was awarded his doctorate from the University of São Paulo in 1963. He then became a colleague working with Catunda. He said [35]:-
Catunda was an excellent teacher, not because of the quality and clarity of his classes. These were very tiring, in a monotonous tone of voice ... . Catunda was extremely dedicated, attentive and patient, an exemplary teacher. It was very common for him to invite groups of students to spend an afternoon at his house, talking about various cultural subjects, particularly literature ... When, in 1952, a group of students decided to make a magazine, Catunda's support was invaluable. He was one of the great examples that I try to follow.
We have already said a little about the analysis course that Catunda took over from Fantappiè in 1939. Slowly he made changes in the material, making it less abstract. In 1952 a 7-part 'student notes' version of Curso de analise matematica appeared and various versions of this were produced over the following years. In 1962 the book appeared as a 2-volume text. The Preface begins:-
The first chapters of this Mathematical Analysis Course are already well known to students in São Paulo, as they have been published for several years in the form of mimeographic handouts.

The present edition, which we intend to complete, will include all the basic material given in the first three years of the Mathematical Analysis chair at the Faculty of Philosophy, Sciences and Letters of the University of São Paulo. It has been carefully revised and updated, particularly in simplifying the proofs without sacrificing mathematical rigour, and at the same time in maintaining the constant approximation of Analysis with geometric intuition; in this sense, this course has been moving away little by little from the excessively abstract character that Professor Luigi Fantappié gave to his course, when he taught here from 1934 to 1939. However, in its general lines, the course still follows the guidance of that professor. Furthermore, we must also point out the constant consultations that we have made to the classic treatises of Francesco Severi, Édouard Goursat, Jacques Hadamard, Charles de La Vallée Poussin, etc., and more recent ones, such as those of Lucian Godeaux, Georges Valiron, Philipp Franklin, etc.
In January 1963 Catunda left São Paulo and moved to the Federal University of Bahia in Salvador, Brazil. His contacts with the University of Bahia went back to 1955 when he had attended the First National Congress of Mathematics Teaching in Secondary Schools at that university. At this Congress he had met Martha Dantas and Arlete Cerqueira Lima, and worked with both of them over the following years, the first with an interest in teaching mathematics in secondary schools and the second with teaching mathematics in higher education. In about 1961 he was invited by Edgard Santos (1894-1962), the dean at the University of Bahia, to become the Director of the Institute of Mathematics and Physics. At first he declined the offer, saying he was happy at São Paulo. Things changed, however, when he went through a very difficult time as his marriage broke up with divorce in 1962. He decided that his best course of action was to change his environment, so, after checking with Arlete Cerqueira Lima that the offer still stood, he went to Salvador and took over the directorship of the Institute of Mathematics and Physics in September 1963. In 1968 there was university reform in Brazil [24]:-
... in 1968 there was a reform of higher education, modernising a significant part of universities. Lifetime chairs were abolished with the introduction of departmental regime and the academic career was institutionalised, with the admission and teaching progression based on academic titles.
Following this reform, the Institute of Mathematics and Physics of the Federal University of Bahia was split into two separate Institutes, one for mathematics and one for physics. Catunda held the positions of full professor and coordinator of the Master's degree at the Institute of Mathematics at Federal University of Bahia, until his mandatory retirement in 1976. It may be surprising to see that Catunda was not made director of the Institute of Mathematics after the reform. It is clear that this was because of his political views. We mentioned above his political activities such as the "oil is ours" campaign but his views on education were critical of the government [20]:-
On the other hand, he published, mainly in the 1960s and 1970s, articles expressing his opinions on educational problems, involving political and social issues, in a Brazil that lived under the shadow of a military dictatorship. In such articles, he ideologically insisted that the low cultural level of the Brazilian people was due to a precarious educational system, in particular higher education, making it impossible, in turn, to train highly qualified professionals to solve highly relevant problems such as: dependence on foreign techniques and capital, the drought in the northeast and the protection of the physical space of the Amazon.
In 1967 he published an article in which said that examiners faced a dilemma. If they kept standards high, students failed and the government reduces funding for their institutions (see [18]):-
... or they give in, opening the doors for the entry, 'en masse', of students who do not present the minimum conditions for taking advantage of the courses. This solution has been adopted, but the results are disastrous: the presence of a majority of students who are not qualified to attend classes inexorably lowers the level of education, which leads to a general lowering of the technical and professional level of graduates, particularly of those heading to the teaching profession, without having the competence and security necessary to prepare students who will have to face new examining boards. And Brazil has been living in this vicious circle for many, many years, which obviously does not exclude the existence, in our midst, of some exponents of science and technology, whose value is universally recognised.
Catunda did his best to improve the situation. He wrote in the same article (see [18]):-
... the student must have his mentality formed in the daily exercise of logical reasoning, demonstrations of theorems, in the clear and rigorous understanding of the fundamental concepts of continuity, limit, differential, integral, etc., which only a serious teaching of mathematical science can provide. ... The Institute of Mathematics will provide the basic teaching of this science - eventually at various levels of depth - for all students in the areas that need this knowledge. There will be a single library and professors working in the same location will have frequent opportunities to exchange ideas, ask questions, take part in seminars and mutually stimulate their research, taking advantage of the presence of professors with scientific works in progress.
He undertook the writing of secondary school texts with teachers from the Centre for Teaching of Science of Bahia (CECIBA) of the Federal University of Bahia. He is the first named author on four volumes of Matemática moderna and of the four volumes of Ensino atualizado da matemática produced by CECIBA. Marshall Stone was interested in the work Catunda was doing with CECIBA and wrote to him on 11 October 1965 (see [32]):-
Dear Catunda,
As you may already know, I am planning to attend meeting on mathematical education in Campos next January 10-15. I do not know whether this will give me any time to visit Salvador again, but I would like to do so if it can be arranged. If I could be invited for a lecture or two at your Institute, it might be easier for me to find the time ... I believe that January is a very interesting month for those who are attracted the Salvador. For that reason, I would like to find out on what days there may be any special festivals this year in particular on what days during January the celebration of Bonfim takes place.
After retiring in 1976 Catuda remained in Salvador for the final ten years of his life. It is not surprising he chose to continue living in Salvador given what he said a year before he died:-
Before I met her, from childhood to mature age, I already loved Bahia, this legendary city that today is called Salvador.

References (show)

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Written by J J O'Connor and E F Robertson
Last Update November 2022