# Monteiro, António A.

# MONTEIRO, ANTóNIO A.

(*b*. Moçâmedes, Angola, 31 May 1907; *d*. Bahía Blanca, Argentina, 29 October 1980),

*mathematics*.

Monteiro conducted his research in mathematics in four countries: Portugal, France, Brazil, and Argentina; his work also had an impact on the perception of modern mathematics in Spain. Monteiro’s main contributions pertain to functional analysis, general topology, algebra and algebraic logic.

**Early Life** . António A. Monteiro was born on 31 May 1907 in Moçâmedes (later Namibe), Angola, then Portuguese West Africa. He was the son of a Portuguese army officer who was stationed there, and who was killed in action in 1915 when his son was only eight years old.

At the age of ten Monteiro entered the Lisbon Military College, graduating in 1925; he then joined the Faculty of Science of the University of Lisbon as a mathematics student. In 1929 he married Lídia Maria de Faria Torres and in the following year graduated as a *Licenciado* in mathematics.

With a scholarship from the Portuguese science research council, the *Instituto para a Alta Cultura*, (IAC) he moved to the Institut Henri Poincaré, where he was a student of Maurice Fréchet. Monteiro received a *Doctorat d’État es-Sciences Mathématiques* from the University of Paris in 1936. He worked on integral equations, a topic in the background of new developments in the theory of linear compact operators in Banach spaces.

His studies in France would later play an important role in the transmission of the French contemporaneous perceptions of mathematics to Portugal and later to Brazil and Argentina. While in France, he also became interested in the research developed in the United States, by Garrett Birkhoff on lattice theory and by Marshall Stone on Boolean algebras and general topology. Later, developments in the United States influenced deeply his views on research and on mathematics education.

**Renovation of Mathematics in Portugal** . Back in Portugal, Monteiro’s research interests moved steadily in the direction of the more abstract areas of functional analysis and topology, some of which had been considered or even introduced by Fréchet. From the late 1930s he exhibited a unique gift for attracting colleagues and graduate students to join him in the areas of research in which he worked. In 1938 the *Academia de Ciências de Lisboa* awarded him the Artur Malheiros Prize for his work on the theory of infinite sets.

From 1938 Monteiro gave a series of mathematical seminars on abstract analysis at the Faculty of Sciences; from 1942, these continued at the *Centro de Estudos Matemáticos de Lisboa*, an institution sponsored by the IAC. Also in 1942, a similar research institute was created in Porto under the direction of his life-long friend Ruy Luís Gomes. The two institutes coordinated their research work and exchanged lecturers and students; this was a novelty in the mathematical Portugal of these years.

Following his return to Lisbon from Paris, in 1936, Monteiro gave careful consideration to the development of the institutional side of his discipline. In 1937 he launched the first exclusively mathematical research journal ever to appear in his country, *Portugaliae Mathematica*. He also recognized the difficulty of raising mathematical standards at the university while the secondary school mathematics education remained at a low level; in 1940 he contributed to the creation of *Gazeta de Matemática*, a journal aimed at raising the level of teachers and students in the final years of Portuguese secondary schools. An outstanding group of young Portuguese mathematicians emerged from Monteiro’s seminars; with their help and enthusiasm he supported the creation of the *Sociedade Portuguesa de Matemática* (SPM), of which he was elected the first secretary in 1940. Since then, the SPM has become a focal point for mathematicians and mathematics teachers in his country.

**Move to Argentina** . A highly principled man with deep democratic convictions, Monteiro soon found himself in opposition to the oppressive regime of António de Oliveira Salazar, who ruled Portugal for more than thirty-five years, from 1932 to 1968. As a result of his independent attitude, his situation became untenable and he was finally forced to emigrate. In 1945 he moved to the University of Brazil, in Rio de Janeiro; there he continued with his own research work and the training of research students. One of them, Leopoldo Nachbin, became a leading mathematician, later a professor at the University of Rochester. The journal Monteiro founded in Rio de Janeiro in 1948, *Notas de Matemática*, was published in the early twenty-first century by an international publishing house.

In 1949, through the invitation of Julio Rey Pastor, Monteiro moved to Argentina, where he lived for over thirty years until his death in 1980. Initially he joined the University of Cuyo; the doctoral dissertation of Antonio Diego, the first of a group of brilliant students he trained there, was later published in book form by Gauthier-Vil-lars in Paris. His passage through that university was also marked by the creation of the *Departamento de Investigaciones Científicas*, a mathematics research institute advocated by Rey Pastor, and a UNESCO-sponsored Latin American symposium on pure mathematics. At the time Monteiro continued working on lattice theory, trying to use the notion of filter, introduced by Henri Cartan in Paris in 1937, to discuss arithmetic properties of topological spaces. He was interested in finding mathematical objects that, in a general topological space, played a role analogous to that of integers in the field of real numbers. Early results were first communicated at the above mentioned UNESCO meeting, and in more detail in a long paper on the subject he sent to the Fréchet Jubilee in Paris, in 1950. Again through the influence of Rey Pastor, Monteiro was made director of the Mathematical Institute of a new *Universidad Nacional del Sur*, established in Bahía Blanca, Argentina, in 1955. In less than ten years his institute became one of the leading mathematical centers of Latin America, specializing in the modern chapters of mathematics. Through his work on lattice theory, in the 1950s Monteiro became interested in problems of the algebra of logic, a topic which would become the central focus of his research from the 1960s; he and his collaborators explored also its connections with theoretical computing.

In 1961 the *Universidad de Buenos Aires*, the largest university in Argentina, made him a visiting professor for a year, as part of an inducement to attract him to stay there on a more permanent basis. His lectures in Buenos Aires had a profound impact on young research students and resulted in the opening of new areas of research in mathematics at that university. At the end of his appointment Monteiro returned to his institute in Bahía Blanca.

By the 1970s Monteiro was already regarded in Argentina as one of its finest intellectuals. In 1969–1970 a fellowship from the National Research Council of Argentina enabled Monteiro to spend a year doing mathematics research in Europe. In 1972 he retired from the *Universidad Nacional del Sur*, which conferred on him, for the first time, the title of emeritus professor. In 1974 the *Unión Matemática Argentina* awarded him, as it had awarded Rey Pastor before him, the title of Honorary Fellow; this was in recognition of his original mathematical

research and of his singular contribution to its development in Argentina.

**A Brief Return to Lisbon** . When democracy returned to Portugal its science research council, the *Instituto Nacional de Investigação Científica*, invited Monteiro to return to Lisbon. He visited Portugal from 1977 to 1979, after a thirty-two year exile. In Lisbon he was awarded the prestigious Gulbenkian Prize for Science and Technology for 1978 for his work on multi-valued logic. He died in Bahía Blanca, after his return to Argentina, on 29 October 1980.

**Impact of Monteiro’s Mathematical Work** . The Portuguese government awarded him, posthumously, the Military Grand Cross of the Order of Saint James; the *Sociedade Portuguesa de Matemática* dedicated an entire volume of *Portugaliae Mathematica* to honor his memory. The International Congress of Mathematicians, in its 2006 meeting in Madrid, devoted a session to commemorating Monteiro’s centenary. His complete works, edited by Eduardo L. Ortiz and Alfredo Pereira Gomes, were published in 2007 by the Gulbenkian Foundation and the Humboldt Press, London, in an edition jointly sponsored by the Académie des Sciences, Paris, and the Academies of Science of Argentina, Brazil, Portugal, and Spain.

## BIBLIOGRAPHY

### WORKS BY MONTEIRO

*Sur l’additivité des noyaux de Fredholm*. (Thése présentée a la Faculté des Sciences de l’Université de Paris pour obtenir le Grade de Docteur ès-Sciences Mathématiques, [Série A, No. 1643, No. d’ordre: 2509]), Paris, 1936.

With Alfredo Pereira Gomes. *Introdução ao estudo da noção de função contínua*. Lisboa: Deposita’rio: Livraria Sa’da Costa, 1944.

“Sur l’arithmétique des filtres premiers.” *Comptes Rendus des Sceances de l’Académie des Sciences*, Paris, 225 (1947): 846–848.

“Filtros e ideais.” *Notas de Matemática* (1948): 1–57, 1–131. “L’arithmétique des filtres et les espaces topologiques.” In *Segundo Simposium de Matemáticas*. Buenos Aires: UNESCO, (1954): 129–162.

“Généralisation d’un théorème de R. Sikorski sur les algèbres de Boole.” *Bulletin des Sciences Mathématiques* 89 (1965): 65–74.

“Sur les algèbres de Heyting symétriques.” *Portugaliae Mathematica* 39 (1980): 1–237.

*The Works of António A. Monteiro*, 8 vols. Edited by Eduardo L. Ortiz and Alfredo Pereira Gomes. London: Humboldt Press and Lisbon: The Gulbenkian Foundation, 2007. This edition also contains a collection of manuscript notes left by Monteiro and edited by his son Prof. Luiz Monteiro with a group of his collaborators at the UNS’s Mathematical Institute.

### OTHER SOURCES

Cignoli, Roberto. “La obra matemática de António Monteiro.” In *II Encontro Luso-Brasileiro de Historia da Matemática*, edited by Sergio Nobre. São Paulo, Brazil, 1997. A clear account of Monteiro’s mathematical work.

Gomes, Alfredo Pereira. “O regreso de António Monteiro a Portugal de 1977 a 1979.” *Portugaliae Mathematica* 39 (1985): 33–41. Special issue in honor of António Monteiro.

Luís Gomes, Ruy and Luis Neves Real. “António Aniceto Monteiro e o C.E.M. do Porto (1941/1944).” *Portugaliae Mathematica* 39 (1985): 9–14. Special issue in honor of António Monteiro.

Monteiro, Luiz. “Profesor Dr. António A. R. Monteiro y su actividad en la Universidad Nacional del Sur.” In *II Encontro Luso-Brasileiro de Historia da Matemática*, edited by Sergio Nobre. São Paulo, Brazil, 1997.

Nachbin, Leopoldo. “The Influence of António A. Ribeiro Monteiro in the Development of Mathematics in Brazil.” *Portugaliae Mathematica* 39 (1985): 15–17. Special issue in honor of António Monteiro.

Ortiz, Eduardo L. “Professor Antonio Monteiro and Contemporary Mathematics in Argentina.” *Portugaliae Mathematica* 39 (1985): 19–32. Special issue in honor of António Monteiro.

_____. “Transferencias de Matemática Pura y Física Teórica de Portugal a Argentina en 1943–58: Beck, Monteiro y Ruy Gomes.” In *Um dia com o Centro de Estudos Matemáticos do Porto*, edited by Maria do Céu Silva, et al. Porto, Portugal: Centro de Matemática da Universidade do Porto, 2001.

_____. “António A. Monteiro and the Practice of Mathematics.” In *The Practice of Mathematics in Portugal*, edited by Luís Saraiva and Henrique Leitão. Coimbra, Portugal: Por ordem da Universidade, 2004. Monteiro’s ideas on mathematics research and education.

Ribeiro, Hugo. “Actuação de António Aniceto Monteiro em Lisboa entre 1939 e 1942.” *Portugaliae Mathematica* 39 (1985): 5–7. Special issue in honor of António Monteiro.

Silva da Silva, Circe Mary. “António Aniceto Ribeiro (1907–1980) no Brasil.” In *II Encontro Luso-Brasileiro de Historia da Matemática*, edited by Sergio Nobre. São Paulo, Brazil, 1997.

Sousa Amaral, Elza Maria Alves de. “António A. R. Monteiro— Um matemático Portugués no Brasil.” In *II Encontro LusoBrasileiro de Historia da Matemática*, edited by Sergio Nobre. São Paulo, Brazil: 1997.

*Eduardo L. Ortiz*

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**Monteiro, António A.**