Luiz Henrique Jacy Monteiro

Quick Info

6 November 1918
Rio de Janeiro, Brazil
20 May 1975
São Paulo, Brazil

Luiz Henrique Jacy Monteiro was a Brazilian mathematician who played a major role in the development of Brazilian mathematics in the middle of the 20th century. He did much to introduce modern mathematics to Brazilian school teachers as well as to university students.


Luiz Henrique Jacy Monteiro was the son of Ernesto Maia Jacy Monteiro (1888-1971) and Manoelita de Castiho (born 1888). Ernesto and Manoelita were married on 20 November 1909 in Rio de Janeiro. Luiz Henrique had an older brother Roberto Jacy Monteiro (born 1918) and a younger sister Maria da Gloria Jacy Monteiro (born 1923). Ernesto Jacy Monteiro was a mining engineer with a talent for languages which he employed as a translator.

The first difficulty that we have to consider is the date of Luiz Henrique's birth. Most biographies we have consulted give his date of birth as 6 July 1921. On the form he completed when entering the United States in 1947, however, he gives his date of birth as 6 November 1918. Some facts support the 1921 date such as having Osvaldo Sangiorgi (born 1921) as a close childhood friend, and the fact that Jacy Monteiro began his university studies in 1940. To add to the confusion, he gives his age on other travel forms which seem inconsistent with both these possible dates, for example he gave age 27 on 10 September 1947, and age 29 on 14 January 1949. The form approving his Rockefeller Scholarship in 1947, however, gives his age as 29 which is consistent with the 1918 date of birth.

Luiz Henrique spent his first years in Rio de Janeiro where he began his primary education. When he was ten years old the family moved to a big house in Vila Galvão to the north east of the city of São Paulo. There he became friends with Osvaldo Sangiorgi (1921-2017) and the two remained friends for life. Sangiorgi also became a mathematician, teaching and writing textbooks. At Vila Galvão, Sangiorgi and Jacy Monteiro enjoyed bicycle rides and they swam in the Lago dos Patos close to the Jacy Monteiro house. When they wanted to rest, they often listened to music, particularly Bach and Vivaldi.

Jacy Monteiro showed great abilities in mathematics and in languages when at school. He also showed great talent as a chess player and surprised all his friends with his remarkable memory. Not surprisingly, his father wanted him to become an engineer so after an outstanding performance in the maturity examinations, he began studying engineering at the Colégio Universitário da Escola Politécnica of the University of São Paulo in 1940. He quickly found that, although he greatly enjoyed the mathematics courses, he did not enjoy the technical studies required for the engineering course. He took a Mathematical Analysis course at the Escola Politécnica taught by Cândido Lima da Silva Dias. Silva Dias had himself been a student at the Escola Politécnica but, finding mathematics more to his liking than engineering, had continued his studies at the newly founded Faculdade de Filosofia, Ciências e Letras where he became an assistant to Luigi Fantappiè. Silva Dias encouraged Jacy Monteiro to leave the Escola Politécnica and study at the Department of Mathematics in the Faculdade de Filosofia, Ciências e Letras. In 1941 he began his studies there taking courses in Pure Mathematics which were much more to his liking. The classes were small and he graduated in 1943 with four classmates. Let us give some details of the Department of Mathematics.

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. 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. In 1944 Jacy Monteiro was appointed as Cândido Silva Dias's assistant in Higher Geometry. Elza Gomide was appointed as Catunda's assistant in 1945 and, in the same year Oscar Zariski arrived to give courses on "Modern Algebra" and "Introduction to Algebraic Geometry." Jean Dieudonné was appointed professor of mathematics at Sao Paulo for 1946-47.

Zariski lectured in English and Dieudonné lectured in French. Jacy Monteiro's outstanding language skills were put to good use and he was able to attend Zariski's courses and Dieudonné's courses and take notes directly into Portuguese. Elza Gomide wrote (see [17]):-
Zariski's influence on Jacy Monteiro was enormous, he wrote the class notes and published them in the form of a handout. The impulse received by the algebraist was decisive for his research and was also extended when Zariski took him to Harvard to continue developing the research started in Brazil. I think Zariski was a very effective teacher.
As an example, let us note that Zariski's course Introduction to the Theory of Ideals was translated into Portuguese by Jacy Monteiro and published as [18]. It begins:-
Algebraic Geometry had great development in the Italian school; the works of Segre, Bertini and especially those of Castelnuovo, Enriques and Severi gave a classic aspect to this branch of Mathematics. These masters developed Algebraic Geometry from the point of view of geometric intuition. It should be noted that the Algebraic Geometry developed by the Italian school had a major defect: lack of rigour. For this reason - due to the lack of rigorous methods - the Italian school declined and Algebraic Geometry was isolated from Modern Mathematics. In the last 15 years, works have appeared in which new methods and concepts have been developed for the study of Algebraic Geometry. The first works are due to van der Waerden, O Zariski, Weyl, Chevalley, etc. We have a resurgence of Algebraic Geometry from which we are going to point out two fundamental consequences: 1st the use of algebraic methods guarantees us perfect definitions and the absolute rigour of the demonstrations; 2nd the use of these methods, leads us to a great generality of study, because the theorems of Algebraic Geometry, which will be demonstrated by algebraic means, are valid not only in the field of complex numbers, but also in abstract fields.
The São Paulo Mathematical Society was founded in 1945 with Omar Catunda as its first president. Jacy Monteiro served as General Secretary during 1945-48. After 1948 he became Director of Publications of the Society. In this role he was in continual correspondence with mathematicians from several countries, and postcards still exist which were sent to him from countries such as Venezuela, Yugoslavia, Romania and Japan.

Jacy Monteiro produced many booklets and these were sold to the students. Not only did he translate lecture courses by foreign teachers but he also produced Analysis Course handouts since he was teaching that course himself. Omar Catunda wrote to Jacy Monteiro from Miami on 14 September 1946 thanking him for his work and asking about printing costs and money received from selling the booklets. Eventually Catunda worried that he was expecting so much of Jacy Monteiro in producing these booklets that he may not have time to undertake other work. He wrote this in a letter of 15 April 1947 when he also expressed concern about André Weil's departure. Jacy Monteiro was employed as an assistant to Jean Dieudonné in 1947 but later that year he took up the Rockefeller scholarship he had received. He had been awarded this scholarship with Zariski's support.

By the time that Jacy Monteiro's Rockefeller scholarship was approved, on 9 June 1947, he had married Martha Anna Dorothea Wallbaum and they had a child, Luiz Henrique Jacy Monteiro Filho, who was one year old. [We can note here that he later had a second child, a daughter Layse Helena Jacy Monteiro.] The letter approving the award of the scholarship states:-
He will return to Brazil to his full time post as Assistant in the Department of Mathematics in the Faculdade de Filosofia, Ciências e Letras of the University of São Paulo. His sponsors are Dean Andre Dreyfus and Prof Jean A Dieudonné of the Faculdade de Filosofia, Ciências e Letras of the University of São Paulo. Program: Algebraic Geometry with Prof Oscar Zariski, University of Illinois; and/or other authorised centres. A fellowship for Luiz Henrique Jacy Monteiro is hereby approved for a period not to exceed twelve months beginning approximately September 15, 1947, with stipend of $175 per month and provision for necessary fees and travel expenses.
He entered the United States at New York on 11 September 1947 on his way to Harvard University. Details on his record of temporary admission to the USA are: Home Address, Christiane Viana 551, São Paulo; Hair, brown; Eyes, green; Height, 5ft 9 in. We should note that he was not accompanied by his wife and son who both remained in São Paulo. At Harvard, he attended lectures by Oscar Zariski, then he went to the University of Chicago where he attended the Algebraic Functions course taught by Saunders Mac Lane. Jacy Monteiro's paper Derivations of a field (Portuguese), was published in 1947. Jean Dieudonné writes in the review [2]:-
This is mainly an expository article on derivations of a field, most of the results being well-known theorems of A Weil, O Zariski and S Mac Lane. The most original part of the paper concerns the case of separable extensions in the sense of N Bourbaki (extensions "preserving p-independence'', introduced by S Mac Lane); the author proves that they are exactly the extensions in which any derivation of the subfield can be extended; from that criterion he deduces new proofs of results of S Mac Lane on the existence of separating transcendence bases.
He returned to Brazil leaving New York on 14 January 1949 on the ship Uruguay. He took up the position of assistant to Candido Lima da Silva Dias on 2 May 1949. On 21 April 1949 Zariski had written to Harry Milton Miller (1895-1980), the Associate Director of the Rockefeller Foundation reporting on Jacy Monteiro:-
My estimate of Jacy Monteiro takes into account the relatively low level of mathematics in Brazil. I am judging the man against the background of local conditions. While I am not sure that he will do research of more than average in Brazil, he will contribute substantially to the development of Brazilian mathematics. He has a first hand working knowledge of the modern methods in algebra and geometry which nobody else in São Paulo possesses. He is not a genius, of course, but he is intelligent, capable and very industrious, and I fully expect him to play a leading part among the mathematicians of São Paulo. I know of only one young man in Brazil who is more promising that Monteiro, and that is Leopoldo Nachbin.
Zariski's assessment of Jacy Monteiro proved very accurate.

Jacy Monteiro wrote to Harry Milton Miller on 30 December 1949:-
I have your letter of December 9, 1949. We have in the library of the Department of Mathematics all the publications of the Bourbaki Group. I thank you very much for the help you offered us. I shall take in the next year the examinations for getting my doctor's degree: on this occasion I shall present a thesis which I wrote under Zariski's direction. I would like to ask you for some help in getting micro-films which are made by the Mathematical Reviews.
The Rockefeller Foundation approved a grant for providing the micro-films and Jacy Monteiro defended his thesis Sobre as potências simbólicas de um ideal primo de um anel de polinômios on 19 April 1951. The examining board was composed of Cândido Lima da Silva Dias, Omar Catunda, Benedito Castrucci, Afonso Penteado de Toledo Piza and Leopoldo Nachbin. The board was chaired by Cândido Lima da Silva Dias who was Jacy Monteiro's official thesis advisor even though in practice he had been advised by Zariski. He wrote in the thesis:-
I want to express my thanks to Prof O Zariski for suggesting the above problem and for the guidance provided during the preparation of this work.
Jacy Monteiro had taken examinations on the two subsidiary subjects Algebra and Projective Geometry on 12 April and he was awarded the maximum score for both these examinations, and for his defence of his thesis.

In addition to teaching at the University of São Paulo, from 1956 he also taught Modern Algebra at Mackenzie University in São Paulo. This private Protestant University had been founded as the American School in 1870 and later became Mackenzie College before achieving university status in 1952. Jacy Monteiro was also professor of Algebra and Trigonometry at the School for Officers of the Police Force of the State of São Paulo in the district of Sant' Anna, Barro Branco.

Jacy Monteiro attended the first Brazilian Mathematics Colloquium in 1957 at Poços de Caldas, Minas Gerais and delivered one of the courses on Teoria de Galois .
You can see more about the Brazilian Mathematics Colloquiums at THIS LINK and you can see him in the conference photograph at THIS LINK.

He was the organiser of both the Fifth Brazilian Mathematics Colloquium in 1965 and the Sixth Brazilian Mathematics Colloquium in 1967. He gave the Scientific Initiation Course on Teoria de Galois at the Seventh Brazilian Mathematics Colloquium in 1969. These three Colloquia were all held in Poços de Caldas. We can note that the São Paulo Mathematical Society, in which Jacy Monteiro played a highly active role, ceased to exist when it became part of the Brazilian Mathematical Society founded during the Seventh Brazilian Mathematics Colloquium.

He published his lectures on Galois Theory in 1969 and these were reviewed by J S Joel [7]:-
These are notes from a 1968 graduate course. The treatment is close to those in E Artin's classic books. After some preliminaries in Chapter 1, Chapter 2 is devoted to algebraic elements and algebraic extensions, centred around the existence of the splitting field of a non-constant polynomial. Chapter 3 is concerned with geometric constructions, such as the impossibility of solving via straightedge and compass the classical problems of the quadrature of the circle, the duplication of the cube and the trisection of an angle. Chapter 4 is devoted to separable and normal extensions, preparatory to the study of Galois extensions in Chapter 5 (including the fundamental theorem of Galois theory). Chapter 6 contains applications of Galois theory: rational symmetric fractions, simple extensions, roots of unity (including the construction of the regular polygons); finite fields; cyclic extensions, the solution of algebraic equations by radicals.
This book was only one of several by Jacy Monteiro. Others include: Álgebra linear (1960); Álgebra multilinear (1964); Algebra moderna (1964); Tópicos de álgebra (1970); Iniciação às estruturas algébricas (1971); and Elementos de Algebra (1974). These works were part of a long term project by Jacy Monteiro to make Brazilian teachers at all different levels aware of modern mathematical developments. For example, in July 1961 he gave one of three courses put on for secondary school teachers which were delivered in Santos. Later that year, from 1 August to 30 September, the First Improvement Course for Secondary Mathematics Teachers was held at Mackenzie University, in São Paulo. At both of these Jacy Monteiro delivered a course on Modern Algebra. In October 1961, GEEM (Grupo de Estudos do Ensino da Matemática) was created with Osvaldo Sangiorgi as its president. Jacy Monteiro became its director of publications. GEEM put on many series of courses aimed at improving mathematics education in schools, but it also held discussion sessions in which the members of GEEM debated the best ways to teach modern mathematics. As an example, let us note that he gave a Modern Algebra course in February 1965 to around 400 teachers from schools across the whole of Brazil. It was claimed to be the largest gathering of mathematics teachers ever to have taken place in São Paulo up to that time. Jacy Monteiro's 1971 book listed above is published by GEEM and is a printed version of one of the courses he gave.

In [3] Duarte reports on a interview by Ubiratan D'Ambrosio and Alexandre Rodrigues Martins in 1998 in which they discussed a course they had taken from Jacy Monteiro:-
D'Ambrosio: A third year advanced course ... The Higher Geometry course, which was actually a Commutative Algebra course.

Martins: Given by Jacy ...

D'Ambrosio: Given by Jacy, a great teacher.

Martins: Yes, a great teacher, an excellent course. In fact, a course that at that time would have been considered a very good course at any university in the world. ... It was something that scientifically and mathematically was well advanced in relation to what was published in the world.
There is no doubt that Zariski's assessment of Jacy Monteiro at an early stage in his career was very accurate. His research contributions were relatively minor yet his teacher training work and his making available to Brazilian students the works of leading algebraists proved extraordinarily valuable to the building of mathematical education in Brazil.

In 1975, when still in his 50s, Jacy Monteiro underwent a surgical operation. After the operation he suffered a stroke which resulted in his death. His lifelong friend Osvaldo Sangiorgi wrote in [14]:-
Apparently, Jacy Monteiro presented himself as phlegmatic and introverted, characteristics that could be confused with shyness, but, in fact, those who approached him clearly perceived his immense human warmth, the rectitude of his character, tempered by a fine sense of humour, supported by a prodigious memory. He jokingly and extremely easily stored phone numbers and important dates of his friends. I remember a certain occasion, when I didn't remember my first phone number at the house where I lived in Vila Mariana. Five years after moving house, Jacy, provoked by a friendly challenge, instantly reproduced the old telephone number.
Sangiorgi also described Jacy Monteiro as [14]:-
... one of the more active and beloved professors. As a professor of the highest calibre, he honoured student activities, from the seriousness with which he presided over elections, to the enthusiastic participation in chess and table tennis tournaments, sports in which he was a master and almost always came out victorious.

References (show)

  1. M M B de Almeida Ferreira and J C Lando, Um Olhar Sobre a Obra Matemática Criativa: Identificando a Presença de Teorias Modernas, in E B Lima, L P S Gomes, L A A Freire and L M S Farias (eds.), Livros Didáticos e Algumas Histórias: Teorias Modernas da Matemática (EDUFAB, Salvador, 2018), 31-46.
  2. J Dieudonné, Review: Derivations of a field (Portuguese), Mathematical Reviews MR0043775 (13,315a).
  3. A R S Duarte, Matemática e Educação Matemática: a dinâmica de suas relações ao tempo do Movimento da Matemática Moderna no Brasil (Doctoral Thesis, Pontifícia Universidade Católica de São Paulo, 2007).
  4. A R S Duarte, Luiz Henrique Jacy Monteiro e o ensino secundário de matemática, Revista Brasileira de História da Matemática 12 (24) (2012), 55-70.
  5. A R S Duarte, Notas de matemática e física: um elo entre pesquisa e ensino. Revista Diálogo Educacional 5 (16) (2005), 39-54.
  6. A R S Duarte, Cultura Acadêmica e Cultura Escolar: relações entre matemáticos e professores de matemática, Revista Diálogo Educacional 8 (25) (2008), 647-662.
  7. J S Joel, Review: Teoria de Galois, by L H Jacy Monteiro, Mathematical Reviews MR0422192 (54 #10184).
  8. Luiz Henrique Jacy Monteiro, grande matemático, Jornal O Estado de São Paulo (6 June 1975).
  9. F de Oliveira Filho, O School Mathematics Study Group e o Movimento da Matemática Moderna no Brasil (Master's thesis, Universidade Bandeirante de São Paulo, 2009).
  10. P C B Oliveira and J L Ferreira, Iniciação às Estruturas Algébricas: Jacy Monteiro e as Teorias Modernas da Matemática, in E B Lima, L P S Gomes, L A A Freire and L M S Farias (eds.), Livros Didáticos e Algumas Histórias: Teorias Modernas da Matemática (EDUFAB, Salvador, 2018), 61-72.
  11. L M Trivizoli, Intercâmbios acadêmicos matemáticos entre EUA e Brasil: uma globalização do saber (Doctoral thesis, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, 2011).
  12. L M Trivizoli, Sociedade de Matemática de São Paulo: um estudo histórico institucional (Master's thesis, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, 2008).
  13. L M Trivizoli, V de Oliveira Santos and S Nobre, From a Regional Society to a National Society: The foundation of the Brazilian Society of Mathematics, Archives Internationales d'Histoire des Sciences 66 (176), (2016), 7-22.
  14. O Sangiorgi, Prefácio. in Luiz Henrique Jacy Monteiro, Paulo Boulos and Renate Watanabe, Matemática: para cursos de 2º grau 1 (Cia. Editora Nacional, São Paulo, 1975).
  15. O Sangiorgi, Luiz Henrique Jacy Monteiro, O Estado de São Paulo (6 June 1975).
  16. C P da Silva, Início e Consolidação da Pesquisa em Matemática no Brasil (Editora Edgard Blücher Ltda., São Paulo, 2022).
  17. C M S da Silva, Oscar Zariski e os Primórdios da Álgebra no Brasil, Revista Brasileira de História da Matemática (Festschrift Ubiratan D'Ambrosio) (2007), 381-391.
  18. O Zariski, Introdução à teoria dos ideais. Notas de aula redigidas por Luiz Henrique Jacy Monteiro (University of São Paulo, 1945).

Additional Resources (show)

Honours (show)

Honours awarded to Jacy Monteiro

  1. Speaker at the Brazilian Mathematics Colloquium 1957

Cross-references (show)

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