Elza Furtado Gomide

Quick Info

20 August 1925
São Paulo, Brazil
26 October 2013
São Paulo, Brazil

Elza Furtado Gomide was the second Brazilian woman to be awarded a doctorate in mathematics. She served for many years as Head of Mathematics at the Institute of Mathematics and Statistics in the University of São Paulo. She was influential in promoting a debate on the role of the university in the training of qualified professionals.


Elza Furtado Gomide was the daughter of Cândido Gonçalves Gomide (1880-1955) and Sofia Furtado (1885-1955) who were cousins. Elza had a older sister, Clotilde Isabel Furtado Gomide (1922-1999). Cândido Gomide had studied engineering in France and then became a mathematics teacher in São Paulo. He was professor of Arithmetic and Algebra at the São Paulo State Gymnasium between 1921 and 1951. Elza said in the interview [14]:-
He hated engineering. At that time, he studied engineering because there was no mathematics course. But he also had a family issue. In my grandfather's mind, he had an uncle called Cândido, who was an engineer. Since my father was Cândido and he should have been an engineer too.
Elza's paternal grandfather, who was a judge at the São Paulo Court of Justice, had gone with all seven of his children to Switzerland but he died there and her grandmother returned to Brazil in 1918. Following the death of Elza's maternal grandfather, Godofredo Josee Furtado, who had been a mathematics teacher at the Escola Normal in São Paulo, Sofia had been taken by her mother, Maria Isabel Gomide, to France and then to Switzerland to study the piano. She became a pianist and a piano teacher.

Both Elza's parents had therefore spent years in French speaking countries and this strongly influenced her upbringing [11]:-
... as a child, the family influence was much more French than anything else, so everyone spoke French.
Elza was educated at home until she was eleven years of age. She said in the interview [12]:-
... at that time the pressure from the Catholic Church was very strong, and my parents feared that in primary school I would be discriminated against for not having the current religion.
At home, her mother taught her Portuguese, French, and a little German and history, while her father taught her mathematics, physics and chemistry. Her father had a large number of books in Portuguese, French and English, so, having plenty of freedom to read, she spent hours and hours exploring her home library. She also learnt to play the piano [12]:-
We had two wonderful ones! One, which was my mother's, was an upright Steinway, magnificent! And another, which had been an aunt's, my mother's sister, was an old quarter grand Erard. They were two wonderful pianos. The Erard stayed, but I learned to play the other. My mother taught me and my sister. They were remarkable: the two pianos ... and the books!
The family lived in a house on Rua Augusta, on the corner of Rua Antônio de Queirós. In fact Elza was born in that house. The Pinheiros river runs through São Paulo and, from age five to twelve, Elza would swim in the river every day and she became a champion swimmer.

In 1937 Gomide entered the São Paulo State Gymnasium which was the only state gymnasium at the time, located on Rua do Carmo. At this school she was taught mathematics by her father whom she considered one of the best teachers at the school. In [12] she spoke about having her father as a mathematics teacher at school:-
He was much stricter with me than with anyone else. But he was an excellent teacher; he was a famous teacher. He was stimulating and very demanding: he gave much more content than usual. I studied the theory of limits with him in my fifth year of high school, which was later taught in my freshman year of college. He gave my class lessons on limits, derivatives and was very keen on proofs, geometry ... And he understood it! He had studied in Europe, he knew more than most.
The other teacher who impressed her was Febor Gigovatti who taught biology. He later became professor at the Faculty of Medicine. Gomide graduated from the school in 1941 and applied to enter the University of São Paulo. This University had been founded in 1934 as a combination of the newly founded Faculdade de Filosofia, Ciências e Letras (FFCL) and Polytechnic School of Engineering. In order to study Medicine, Engineering or Law, it was necessary for students to have two further years training before entering the courses but for the FFCL this was not necessary and Gomide could begin studying there in 1942.

Mathematics was the subject that Gomide had enjoyed most at Gymnasium and, with the excellent teaching of her father, she had taken that subject to a greater depth than any other. She decided, however, to enter the FFCL to study for a physics degree [18]:-
Elza became interested in Physics, influenced by the success and popularity of that science ...
Let us note at this point that several biographies of Gomide (for example [5] and [18]) claim that the increased interest in physics in Brazil which led to her choosing that subject was due to the Brazilian César Lattes's part in the discovery of the π meson. This cannot be correct since Lattes's work on the π meson took place in 1947.

Gomide soon realised that mathematics was the subject for her and not physics. She did, however, continue to study for her physics degree while taking courses in mathematics and graduated in 1944 with a physics degree. By this time she had reached the third year of the mathematics courses and her abilities were such that she was invited by the Professor of Mathematics, Omar Catunda, to be his assistant. Gomide was awarded a bachelor's degree in mathematics in 1945. We should now give some details about the Mathematics Department of the University of São Paulo.

The University of São Paulo was founded in 1934 and 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 Omar Catunda was appointed as Fantappiè's assistant and they 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. 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. 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. Catunda was appointed, on an interim basis, as professor responsible for the chair of Mathematical and Higher Analysis, replacing Fantappiè. This was the Mathematics department in which Gomide studied but there were changes from 1945 when she became Catunda's assistant. 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. One of the students taking this course was Carlos Benjamin de Lyra, who was an undergraduate between 1946 and 1950.

Gomide undertook research for her doctorate, the topic being suggested by André Weil who left São Paulo in 1947. After that she was advised by Jean Delsarte who spent four summer months as Professor at the University of São Paulo in each of the years 1948, 1949, 1950, 1951. Although much advice came from André Weil and especially Jean Delsarte, it was in fact Omar Catunda who was officially Gomide's research advisor. Speaking of her advisors, Gomide said in the interview [13]:-
I was lucky enough to be guided by a Bourbaki, Jean Delsarte. Delsarte was a lesser-known Bourbaki, but of those who were here he was - perhaps - the one who was most concerned with the transmission of knowledge. Something that Weil, for example, was less good at. If we took advantage of his science that was very well, but if we didn't, so much the worse; it wasn't his concern ...
Her 24-page thesis Sobre o teorema de Artin-Weil was typed with all mathematical symbols, Greek letters, etc. written in by hand. Even the title and her name on the cover are handwritten. She defended her thesis on 27 November 1950 before the examining committee which had Omar Catunda as chair and also included Fernando Fuquim de Almeida (1913-1981), Edison Farah (1915-2006), Benedito Castrucci (1909-1995) and Joao Augusto Breves Filho. The thesis begins with a statement of the Artin-Weil Conjecture which, she writes, came about as the result of studying manifolds over finite fields. She then writes:-
This conjecture has been demonstrated for curves and for other varieties of a particular type. (A Weil, 'Les Courbes Algébriques et les variétés qui s'en déduisent' , and 'Numbers of Solutions of Equations in Finite Fields'). This work contains research on this conjecture.
When Gomide was awarded a doctorate in 1950 she became the first woman to be awarded a doctorate by the University of São Paulo and only the second woman to be awarded a doctorate by a Brazilian university; the first being Marília Chaves Peixoto in 1948 who married the mathematician Maurício Matos Peixoto. Gomide's thesis was published in the Boletim da Sociedade de Matemática de São Paulo.

After the award of her doctorate, Gomide went to Paris to undertake postdoctoral work. Speaking of her time in France, Gomide said in the interview [12]:-
They don't have entrance exams there. Passing the baccalaureate, one enters the university. The university's mathematics course does not train its future teachers. Almost no mathematician has taken the university course. Next to the university, they have the elite institutions, which are the 'grande écoles'. These have a very tough entrance examination, which actually starts from high school. Those who are very good, already start in special classes and end up being able to go to the École National de Administration, from where presidents, ministers, etc. come out; to the École Polytechnique, which produced the top people before they started to be produced by the École Normale Supérieur, which trains researchers in mathematics and physics. I believe the French university system cannot be copied; for it is a very peculiar model.
She spoke about the beginnings of her teaching career in [12]:-
It didn't take long for me to start teaching a class. It so happens that Catunda went to the United States for an internship and during his absence Lyra and I took theoretical classes. That was maybe in the early 50's [Note by EFR: actually it was 1946-47]. I mean that after four or five years I already took classes, and since then I've continued ... I think it was there, when he went to the United States, that I started to take theoretical classes. That was the common relationship. At first the assistant did exercises and studied; and gradually, over time, they would take over the classes as well. ... I started teaching calculus exercises - Catunda gave the theoretical part, and I taught the exercises as his assistant. Sometimes I attended his class; he would then prepare the exercises I was going to do. I think it was four exercise classes a week. There were a lot of classes, four theoretical and four exercises... something like that.
Even while she was Catunda's assistant, Gomide felt that she wanted to change the way that teaching was being done. Fantappiè had set up a syllabus which began with the construction of the real numbers and Catunda had carried on using Fantappiè's syllabus. When Gomide started to study mathematics this was how the lessons were structured. She explained (see [15]):-
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.
She persuaded Catunda to change the approach [15]:-
The Mathematical Analysis course should be given after the Differential and Integral Calculus course; first give a course in Calculus without criticism and then do Analysis, which is actually the justification, the critique of Calculus, with all the theorems, the construction of real numbers, etc. After all, how could students directly understand the criticism of something they didn't even know yet? ... I insisted with Catunda that it was better to start with Calculus than with Analysis and he agreed. He was very liberal; very few full professors gave their assistants the freedom he afforded us.
Her career in the Institute of Mathematics and Statistics in the University of São Paulo is described in [7]:-
Her room at the Institute of Mathematics and Statistics at the University of São Paulo was always open, whether she was inside or not. When the place was empty, colleagues simply went in to borrow a book or read the newspapers. Whoever found her there took the opportunity to talk or ask for some of her wise advice. For professors at the Institute of Mathematics and Statistics, that unlocked door symbolised their open and creative thinking. From her election to head of the Mathematics Department in 1968, during the military regime, she began to act more in matters related to teaching. She had begun to take an interest in the question when she realised that modern mathematics, in her own words, "was doing a lot of damage." She became very involved when the Ministry of Education decided to impose the Licentiate in Science, which she thought would be extremely harmful, especially to Mathematics. This involvement, added to the problems caused by the political situation, with threats from the military regime on the one hand and the pressure of student ferment on the other, made her no longer available for research activities. According to her, at the time it was already very difficult to "keep your nose above water". The separation of the Bachelor and Licentiate courses in Mathematics was finally effected in the late 1960s.
As head of mathematics at the University of São Paulo, Gomide worked so hard that it affected her social life. She said (see [16]):-
... this is not just any job, we start at nine in the morning and finish at five in the afternoon. Either you are engaged, absorbed in work, or you are not. If you are, it sometimes damages other relationships, and that's the kind of accusation you get. I think everyone who is in this life has that experience. Those who asked me were more distant relatives and friends who wanted to meet me and I didn't have time. ... I realised that it was difficult to maintain certain relationships and at the same time work as I wanted. This is difficult.
Gomide gave up research when she became head of mathematics but she did other work such as making translations. For example, she translated Carl Boyer's book A History of Mathematics into Portuguese and it was published in 1974. In an interview in the year 2000 she explained how her ideas on teaching had changed [12]:-
I now have other ideas about the best way to go about things. I was part of a tradition - which I thought was very good - of the Analysis of the Italian school. Now I like to think more about applications, about history. ... Not that I think it's essential to tell a story, it's not that much that is required. It's nice for us to tell a little about the history of the subject, but now that I know a little more about the history of mathematics, it serves as an instrument for reflection. You can see what is the best way to open up the subject to students by thinking about the way things developed. So today I would follow other paths, but I don't think the other ways were wrong.
Gomide's influence on Brazilian mathematics was substantial. She was a founding member of the São Paulo Mathematical Society, of the Brazilian Mathematical Society and of the Brazilian Centre for Physics Research. She supervised many master's and doctoral theses and always enthusiastically devoted herself to teaching activities, which she considered her most important role. She became very involved when the Ministry of Education decided to impose the Licentiate in Science, which she thought would be extremely harmful, especially to mathematics. She participated in the Forum of Licentiates, organised by the University of São Paulo in 1990. She presented a proposal for a curriculum structure for the Licentiate in Mathematics course which, after being approved by the Forum, was implemented in 1994.

Gomide worked at the University of São Paulo from 1945 until her mandatory retirement in 1995. Even after her retirement, she continued to contribute to the University of São Paulo, participating in thesis boards and teaching, as long as her health allowed her to do so. She died aged 88.

References (show)

  1. U D'Ambrosio, Reminiscências do meu tempo de estudante na Maria Antônia, in Maria Cecília Loschiavo dos Santos (ed.), Maria Antônia: uma rua na contramão (Nobel, São Paulo, 1988), 53-65.
  2. A R Calabria and M F Cavalari, Primeiro Colóquio Brasileiro de Matemática: Umabreve Apresentaçãoda Participaçao Feminina, Hipátia, Campos do Jordao (SP) 1 (1) (2016), 30-45.
  3. M F Cavalari, Elza Furtado Gomide: pioneira em pesquisa e docência em Matemática na USP Campus São Paulo, in Encontro Mineiro de Educação Matemática 5 (Editora da Universidade Federal de Lavras, Lavras, MG, 2009).
  4. Elza Furtado Gomide (1925-): Matemática, CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico.
  5. Elza Furtado Gomide, CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico.
  6. Elza Furtado Gomide, Mulheres Matemática Universidade Federal do Rio Grande do Sul (2013).
  7. Elza Furtado Gomide (1925-2013), Mulheres Matemática 6 (20 July 2020), 2/8.
  8. E F Gomide, Preface, Resenhas do Instituto de Matemática e Estatística da Universidade de São Paulo 2 (4) (1996), 352.
  9. E F Gomide, C S Hönig, U D'Ambrosio, L C Dias and A P Azevedo, Depoimentos - Mesa redonda: O Primeiro Colóquio Brasileiro de Matemática -1957, Revista Brasileira de História da Matemática 8 (15) (2008), 75-86.
  10. C S Hönig and E F Gomide, As ciências matemáticas, in S Motoyama and M D Ferri (eds.), História das ciências no Brasil 1 (EDUSP/EPU, São Paulo, 1979), 36-60.
  11. Interview of Elza Furtado Gomide by Arnaldo Aragão Santos and Andréa Paula dos Santos (São Paulo, 15 March 2010).
  12. Interview of Elza Furtado Gomide by Carlos Roberto Vianna, in Carlos Roberto Vianna, Vidas e circunstâncias na educação matemática, Doctoral Thesis (University of São Paulo, 2000).
  13. Interview of Elza Furtado Gomide by Ubiratan D'Ambrosio, in Sergio Nobre (ed.), Anais do 2o Encontro Luso-Brasileiro de História da Matemática e Seminário Nacional de História da Matemática. Sessão Especial: Memórias Vivas (Águas de São Pedro-SP, 1997), 95-106.
  14. Interview of Elza Furtado Gomide by Tana Giannasi Alvarez, in Tana Giannasi Alvarez, A Matemática da Reforma Francisco Campos em ação no cotidiano escolar, Master's Dissertation (Pontifical Catholic University of São Paulo, 2004).
  15. G Loureiro de Lima and B Antonio da Silva, A implantaçao da disciplina inicial de Cálculo Diferencial e Integral no curso de Matemática da USP e o papel da professora Elza Furtado Gomide, Revista de Produçao Discenta em Educação Matemática 1 (1) (2012), 64-80.
  16. A A Santos, Elza Furtado Gomide ea participaçao feminina no desenvolvimento da matemática brasileira no século XX, Dissertaçao de Mestrado (Pontifícia Universidade Católica de São Paulo, Mestrado em História da Ciência, 2010).
  17. R van Putten de Vasconceios, Genealogia E História Da Família Gomide (Clube de Autores, 2019).
  18. R van Putten de Vasconceios, Elza Furtado Gomide biografia, Genealogia E História Da Família Gomide (Clube de Autores, 2019), 271-273.
  19. C R Vianna, Vidas e circunstâncias na educação matemática, Doctoral Thesis (University of São Paulo, 2000).

Additional Resources (show)

Other pages about Elza Furtado Gomide:

  1. Brazil Mathematical Colloquium 1957: photograph

Other websites about Elza Furtado Gomide:

  1. MathSciNet Author profile
  2. zbMATH entry

Honours (show)

Honours awarded to Elza Furtado Gomide

  1. Speaker at the Brazilian Mathematics Colloquium 1959

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