Aniceto Monteiro (1907-1980)

António Aniceto Monteiro was born on 31 May 1907 in Moçamedes, Angola. He was a student at the Military School and at the Faculty of Sciences of Lisbon, from which he obtained a post-graduate degree in Mathematical Sciences in 1930. Shortly after completing his education, he received a scholarship from the National Education Board in order to study at the University of Paris, where he obtained the degree of Docteur és Sciences Mathématiques. His thesis was titled Sur l’additivité des noyaux de Fredholm and was supervised by Maurice Fréchet.

After his return from Paris, Aniceto Monteiro began a highly intensive intellectual activity, seeking to promote, in conjunction with his colleagues interested and involved in scientific activities, the presentation and publication of mathematical works. Together with Manuel Valadares (1904-1982), António da Silveira (1904-1985), Peres de Carvalho (1904-1989) and others, he founded the Núcleo de Matemática, Física e Química, which promoted several courses, conferences and publications. In 1937, in collaboration with Manuel Zaluar Nunes and José da Silva Paulo, he founded the Portugaliae Mathematica, the first Portuguese magazine dedicated exclusively to mathematical research. Three years later, he founded a research magazine Gazeta de Matemática in collaboration with Bento Caraça, J. da Silva Paulo, Hugo Ribeiro and Manuel Zaluar Nunes.

In 1940, he was one of the main driving forces behind the foundation of the Sociedade Portuguesa de Matemática, having been its first Secretary General between 1941 and 1942. In 1943, he founded the Junta de Investigação Matemática with Mira Fernandes and Ruy Luís Gomes. Between 1940 and 1943, he directed the work of the Centro de Estudos Matemáticos of the Instituto para a Alta Cultura. He received a scholarship from the National Education Board.

In 1945, he was forced to leave Portugal after his access to a university career was barred for political reasons. He moved to Brazil where he took up office at the National Faculty of Philosophy of the University of Brazil, currently the Federal University of Rio de Janeiro. He left Brazil in 1964, moving to Argentina, where he became a Professor at the University del Sur, Bahia Blanca.

He was a corresponding member of the Brazilian Academy of Letters and an honorary member of the Mathematics Union of Argentina. In 1978, he was awarded the Prémio Gulbenkian de Ciência e Tecnologia for his work Algèbres de Heyting Symétriques. He died on 29 October 1980 in Bahia Blanca, in Argentina. On 2 October 2000, the President of the Republic of Portugal awarded him posthumously the Grã-Cruz da Ordem Militar de Santiago e Espada.

Scientific Activity

After completing his PhD at the University of Paris, Monteiro returned to Lisbon where he developed an intense activity of mathematical research in Portugal, promoted publications dedicated to mathematics and organised several seminars. He created the magazines Portugaliae Mathematica, dedicated to research in mathematics, and Gazeta de Matemática, directed at students. He also created the Seminário de Análise Geral, the Centro de Estudos Matemáticos of the Instituto para a Alta Cultura and founded the Sociedade Portuguesa de Matemática.

Gazeta de Matemática “Journal of those applying for the aptitude test and of mathematics students of higher education establishments”

After the creation of the Núcleo de Matemática, Física e Química, the foundation of the Portugaliae Mathematica, of the Seminário de Análise Geral, of the Centro de Estudos Matemáticos de Lisboa, of the Sociedade Portuguesa de Matemática and of the Gazeta de Matemática in Lisbon, the Centro de Estudos Matemáticos do Porto was organised. To this effect, Aniceto Monteiro was invited by Ruy Luís Gomes to go to Oporto to explain how this had been achieved in Lisbon, collaborating in the organisation of the centre and drawing up the first work schedule of this Centre of Studies in October 1941. In November 1941, Aniceto Monteiro continued his regular collaboration with this centre with a conference under the title “Introduction to General Topology”. In 1942, he held a course in Oporto called “Introduction to the Notion of a Continuous Function”, which had a great repercussion with his lessons being published. He also held two conferences called “Finite Geometry” and “Finite Algebra and Analytical Geometry”, directed at a less specialised public. As a result of these activities, the students of the Faculty of Sciences of Oporto tried to found a Mathematics Club, an initiative which did not come into being due to a negative intervention of the Ministry of the Interior.

In October 1943, together with Ruy Luís Gomes and Mira Fernandes, he participated in the creation of the Junta de Investigação Matemática. The aim of the promoters of this Junta was to promote the development of mathematical research and to arouse an interest in mathematical research in young people. This Junta later managed to obtain financial support, making possible the hiring of Monteiro to stay in Oporto. During his stay, he participated in the organisation of the General Analysis Studies, structured into three fields: Modern Algebra, under the responsibility of António Almeida Costa, Measure and Integration, under the responsibility of Ruy Luís Gomes, and General Topology, under the responsibility of Aniceto Monteiro. These studies included colloquia and lessons, which made up a collection of publications called “Cadernos de Análise Geral”.

The Junta de Investigação Matemática later hired Aniceto Monteiro to remain in the city of Oporto and to continue with his activity of promoting mathematical research and of encouraging students interested in mathematical studies. He organised the General Analysis Studies organised into three fields: Modern Algebra, directed by António Almeida Costa, Measure and Integration, directed by Ruy Luís Gomes, and General Topology, under the responsibility of Aniceto Monteiro. These studies included colloquia and lessons, which made part of the collection called “Cadernos de Análise Geral”.

In 1945, he moved on to the National Faculty of Philosophy of the University of Brazil, today the Federal University of Rio de Janeiro. He developed research activities and conferences in the areas of General Topology, Hilbert Spaces, Functional Analysis, Ordered Series and Boolean Algebras and Lattices. Here he continued his activity of promoting mathematical research and encouraging and supporting students who wished to pursue this area of knowledge. While in Brazil, he started publishing a series of monographs called Notas de Matemática, editing six volumes. This series of publications was later continued by Leopoldo Nachbin, a former student of his. In 1949, pressured by the Portuguese embassy in Brazil, his four-year contract was not renewed and he left Brazil for Argentina.

Here Monteiro occupied the position of Mathematics Professor at the University of San Juan, where he started an intense activity of teaching, research and development of research projects and pair work. He directed research seminars in areas such as Boolean Algebra, Deductive Systems and Browder’s Algebras. He also became interested in certain practical problems, namely in hydrology directed towards irrigation.

He was the main driving force behind the creation of the Department of Scientific Research of this University in 1951. This department included an institute of mathematical research, which was set up in Mendoza. This institute congregated a group of mathematicians who played a crucial role in the development of mathematics in Argentina and in other Latin American countries. Although continuing his regular activity at the University of San Juan, Monteiro directed courses and seminars in the Department of Scientific Research, exchanging ideas and research problems with its members.

Together with M. Cotlar and E. Zarantonello, later joined by Julio Rey Pastor, in 1955 he started the publication of the Revista Matemática Cuyana.The Department of Scientific Research was subsequently dissolved after the military coup of 1956, which deposed General Perón, and its library was transferred to San Luiz. In the meantime, in July 1957, Monteiro moved to the University of Bahia Blanca, together with many of the old members of the Department of Scientific Research, where he founded a new institute of mathematical research. He later joined Ruy Luís Gomes, who in the meantime had moved away from Portugal for political reasons.

Shortly after establishing himself at the University of Bahia Blanca, Monteiro organised a meeting with the União Matemática Argentina and published its minutes, creating in this way a series of publications called Actas. He also started publishing research texts called Notas de Lógica Matemática and Notas de Algebra y Analisis, giving rise to an interchange of publications with specialised foreign magazines, thus enriching the collections of the institute’s library. Monteiro invited several renowned mathematicians to develop seminars and courses at this institute.

He launched a new series of publications, called Monografías de Matemática, distributed to all those involved in mathematical research. He also reformulated the post-graduate degree in Mathematics and made profound changes to the teaching of Mathematics in Argentina, which came to have a profound impact on the teaching in the faculties of science of this country.

At the end of the sixties, the first students entirely educated by the University del Sur drew up their PhD theses while the Mathematics Institute continued its activity with the collaboration of researchers from other Latin American countries.

In 1966, after a coup d’état, several faculties of the University of Buenos Aires were attacked by militaries who carried outacts of repression on students and teachers alike, which led to the resignation of many university teachers and to the closing down or paralysation of several research centres.

The University del Sur was not directly affected by this situation, thus becoming the main mathematical research centre of Argentina. The effects of the military regime became noticeable, however, in the reduction of the financing of teaching and research activities. Monteiro continued with his research work, presenting papers and travelling throughout Europe, visiting Romania, Paris, Belgium and England, where he contacted several researchers in his area.

After returning from Europe, Monteiro retired from the University of Bahia Blanca, having been its first professor emeritus. In 1974, the União Matemática Argentina bestowed on him an Honorary Fellowship. In the meantime, he continued to work in the institute. In March 1975, he was prevented from entering the University by representatives of the government, giving rise to a reaction of revolt throughout the Argentinean scientific community. The Conselho Nacional de Investigações Científicas e Técnicas of Buenos Aires invited Monteiro to form part of this institution, awarding him the highest existing degree. In the following years, several university teachers were pushed away from their positions and imprisoned, leading to the exile of many of them.

In 1977, Monteiro visited Portugal, at the invitation of the Instituto de Investigação Científica, corresponding in this way to the wishes of many colleagues and friends who wanted him to return after the re-establishment of the democratic regime on 25 April 1974. He remained in Portugal for two years, as a researcher at the Instituto de Investigação Científica, performing work in the Centro de Matemática e Aplicações Fundamentais of the University of Lisbon. In this research centre he created a line of research in Logic Algebra and presented several conferences, put forward research topics and offered guidance. This work led to the publication of several works in various magazines of the speciality and two PhD theses.

At the invitation of the Faculty of Sciences of the University of Oporto, he gave three conferences in July 1977 on “Álgebras de Boole cíclicas”, “Álgebras de Nelson finitas e lineares” and “Aritméticas dos filtros em espaços topológicos”. He also published a paper in the number dedicated to Aureliano Mira Fernandes in the magazine Técnica, of the Instituto Superior Técnico.

In 1978, he was awarded the Prémio Gulbenkian de Ciência e Tecnologia for the work Sur les Algèbres de Heyting Symétriques, written during his only period in Portugal after his exile.


António Monteiro’s scientific work comprehends more than 50 research papers. The list of these papers is included in annex.

Fernando Reis


MONTEIRO, Luiz F., “Contribuição Matemática do Professor Dr. António A. R. Monteiro”, in Um dia com o…Centro de Estudos Matemáticos do Porto, Actas, Porto, Centro de Matemática da Universidade do Porto, 2001.

Portugaliae Mathematica, 39, 1980. [número em homenagem a António Aniceto Monteiro]

DIONÍSIO, José Joaquim; OLIVEIRA, Augusto J. Franco de; “Matemáticos Portugueses”, in STRUIK, Dirk J., História Concisa das Matemáticas, 3.ª ed., Lisboa, Gradiva, 1997, pp. 383-388.


Uma curta viagem pela História da Matemática em Portugal – Teresa Monteiro

"Para a História da Sociedade Portuguesa de Matemática" – José Morgado

António Aniceto Monteiro

List of Publications

"Sur les noyaux additifs dans la théorie des équations intégrales", C. R. Acad. Sci. Paris, 198 (1934), 1737.

"Sur une classe de noyaux développables" C. R. Acad. Sci. Paris, 200 (1935), 2143.
"Sur l'additivité des noyaux de Fredholm", Thèse ès Sciences Math, Univ. de Paris, Portug. Math., 1 (1937-40), l-174. 4. Sur l'additivité dans un anneau, Portug. Math., 1 (1937-40), 289-292. 5.

(Com. H. Ribeiro) "Sur l'axiomatique des espaces (V)", Portug. Math., , (1937-40), 275-288.

"Caractérisation des espaces de Hausdorff au moyen de l'opération de dérivation, Portug. Math., 1 (1937-40), 333-339.

(Com A. Gibert) Os conjuntos mutuamente conexos e os fundamentos da topologia integral”, Las Ciencias, ano 7, nº 2 (1940).

Les ensembles fermés et les fondements de la topologie", Portug. Math., 2 (1941), 56-86.

La notion de fermeture et les axiomes de séparation", Portug. Math., 2 (1941), 290-298. (Avec H. RIBEIRO) L'opération de fermeture et ses invariants dans les systémes partiellement ordonnés, Portug. Math., 3 (1942), 171-184.

"Caractérisation de l'Opération de fermeture par un axiome", Portug. Math., 4, (1943-45), 158-160.

(Avec. H. Ribeiro) "La notion de fonction continue", Summa Brasiliensis Math., 1 (1945), 1-8.

"L'arithmétique des filtres premiers", C. R. Acad. Sci. Paris, 225 (1947), 846-848.

“Filtros e Ideais, I.” Notas de Matemática, n.° 2, Rio de Janeiro, (1948).

“Filtros e Ideais, II”. Notas de Matemática, nº 5 Rio de Janeiro (1948).

Réticulés distributifs de dimension linéaire n." C. R. Acad. Sci. Paris, 226, (1948), 1658-1660.

(Com M. Peixoto). Note On uniform continuity”, Proc. Inter. Congress of !Math., N.º 1 (1950), 385.

"L'Arithmétique des Filtres et les Espaces Topologiques", I Notas de Lógica Mat., Nº 29 (1974). Trabalho realizado em 1950 para o concurso organizado pela Soc. Math. de France em homenagem a M. Fréchet, cf. Bull. Soc. Math.France, 79 (1951), XXXIX-XL.

(Com M. Peixoto). "Le nombre de Lebesgue et la continuité uniforme", Portug. Math., 10 (1951), 105-113.

Les filtres des espaces compacts, Gaz. Mat., 50 (1951), 95-96.

Propriedades características de los filtros de un Algebra de Boole, Acta Cuyana de Ingenieria, 1 (1951), 1-7.

L'Arithmétique des Filtres et les Espaces Topologiques, Symp. sur les probl. math. étudiés en Amérique Latine, Villavicencio, Unesco, Montevideo (1954), 129-162.

Axiomes indépendents pour les algébres de Brouwer, Rev. Unión Mat Argentina, 17 (1955), 149-160

"Les ensembles ordonnés compacts", Rev. Mat. Cuyana, (1955), 187-194

(Com O. Varsavsky). Algebra's de Heyting monádicas, Actas de las X jornadas de la Union Mat. Arg., Bahía Blanca (1957), 52-59.

“Normalidad en las algebras de Heyting monádicas, Actas de las l Jornadas de la Union Mat. Arg., Bahía Blanca (1957), 50-51.

Algebras Monádicas, Conférences réalisées dans le «2.º Colóquio Brasileiro de Matemática», Poços de Caldas, 1959, Actas do segundo Colóquio Brasileiro de Matemática, São Paulo, Brasil, (1960) 33-52.

Matrices de Morgan caractéristiques pour le calcul propositionnel classique, Anais Acad. Brasileira Ciencias, 31 (1960), 1-7.

Linéarisation de la logique positive de Hilbert-Bernays, Rev. Unión Mat. Argentina, 20 (1962), 308-309.

(Com. D. Brignole). Caracterización de las Algebras de Nelson por igualdades, Rev. Unión Mat. Argentina, 79 (1962), 36.

(Com. L. Iturrioz). “Representación de las Algebras (le Tarski monádicas”, Rev. Unión Mat. Argentina, 19 (1962), 361.

“Construcción de las Algebras de Nelson finitas”, Rev. Unión Mat. Argentina, 19, (1962), 361.

“Algebras de Nelson semi-simples”, Rev. Unión Mat. Argentina, 21 (1963), 145-146.

Sur la définition des algébres de Lukasiewicz trivalentes, Bull. Math. Soc. Sci. Math. et Phys. R. P. Roumanie, Nouv. Série, 7 (1963), 1-13.

“Construction des algébres de Nelson finies”, Bull. Acad. Polonaise Sci., 11 (1963), 359-362.

“El cálculo proposicional trivalente de J. Lukasiewicz y la lógica clássica”, Rev. Unión Mat. Argentina, 22 (1964-65), 43-44.

“Relations between Lukasiewicz Three Valued Algebras and Monadic Boolean Algebras”, 1964 International Congress for Logic, Methodology and Philosophy of Sciences, Program and Abstracts, The Hebrew University, Jerusalem (1964), 16-17.

(Com. L. Iturrioz). “Calculo proposicional implicativo clássico con n varia bles proposicionales, Rev. Unión Mat. Argentina, 22 (1964-65), 146.

(Com. R. Cignoli). “Construcción geometrica de las algebras de Lukasiewicz trivalentes libres, Rear. Unión Mat. Argentina, 22 (1964-65), 152.

“Généralisación de un teorema de Sikorski sobre Algebras de Boole”, Rev. Unión flat. Argentina, 22 (1964-65), 151.

(Com. R. Cignoli). “Boolean elements in Lukasiewicz Algebras”, II, Proc. Japan Acad., 41 (1965), 676-680.

“Généralisation d'un théorème de Sikorski sur les Algébres de Boole, Bull. Sci. Math., 2ème Série, 89 (1965), 65-74.

“Algebras de Boole involutivas”, Rev. Unión Mat. Argentina, 23 (1966-68), 39.

(Com. I. Brignole). Caractérisation des Algébres (le Nelson par des égalités, I et II, Proc. Japan Acad., 43 (1967), 279-283.

"Construction des algébres de Lukasiewicz trivalentes clans les algébres de Boole monadiques, I, Math. Japonicae, 12 (1967), 1-23.

(Avec. L. MONTEIRO). Algebras de Stone con n generadores libres, Rev. Unión Mat. Argentina, 23 (1966-68), 201.

“Sobre un cláculo proposicional de Moisil”, Rev. Unión .Mat. Argentina, 23 (166-68), 2111.

“Generadores de Reticulados distributivos finitos”, Actas del Simpósio Panamericano de Matemática Aplicada, Buenos Aires (1968), 465.

(Com. O. Chateaubriand). Les Algébres de Morgan libres, Notas de Lógica Mat., N.° 26 (1969).

La semi-sinnplicité (les Algébres de Boole Topologiques et les systèmes déductifs, Rev. Unión Mat. .Argentina, 23 (1971), 417-448.

L'Arithmétique des Filtres et les Espaces Topologiques, II, Notas de Lógica Mat., N.° 30 (1974).

Séminaire sur les algèbres d'Heyting symmétriques, Notes polycopiées rédigées par A. Figallo (1974-75).

Algèbres de Boole cycliques”, Revue Roumaine Math. Pures Appli., 23 (1978), 71-76.

Conjuntos graduados de Zadeh”, Técnica (Revista de Engenharia, IST), 4.19-4.50 (1978), 11-34.

Les N-lattice linéaires”, Textos e Notas, CMAF, N.º 15 (1978), 11-19.

Les éléments réguliers d'un N-lattice, Anais Acad. Brasileira Ciencias, 54(1980), 653-656.

Sur les algèbres d'Heyting symmétriques, Portug. .Math., 39 (1980).

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