09/08/2021

On the Science & Mathematics blog: António Aniceto Monteiro

Reproduction from the IMPA Science & Mathematics blog, from O Globo, coordinated by Claudio Landim.

Luis Saraiva – Professor in the Department of Mathematics at the Faculty of Sciences of the University of Lisbon and at the Inter-University Center for the History of Science and Technology.

A more complete perspective on anyone's actions implies taking into account the context in which they lived, the restrictions they faced, or, conversely, the favorable environment they encountered. In this sense, we can say that the mathematician António Aniceto Monteiro was a true giant in 20th-century science, and more specifically in mathematics. He lived through the turbulent post-World War I era, with the rise of fascism and Nazism in Europe, culminating in the Spanish Civil War (1936-1939) and World War II (1939-1945). In his country, he endured the initial period of a dictatorship that lasted from 1926 to 1974, a retrograde regime that placed the people under intense surveillance and repression. Even when he left for Brazil to live there, Monteiro continued to be monitored by the Portuguese political police.

He was educated in a university system whose sole purpose was to transmit knowledge to future public administration officials and future teachers. The university curriculum with regard to mathematics was outdated, had immense flaws, and mathematical research practically did not exist as an organized activity.

In his first quarterly report sent from Paris, where he was undertaking an internship that would lead to his doctorate, addressed to the National Education Board, the entity that subsidized his stay and to which he had to report periodically, he described in a worrying way the knowledge received by a graduate in Mathematical Sciences in Higher Education in Portugal:

"Ignorance of a vast amount of basic knowledge; encyclopedic education, resulting in a superficial understanding of all subjects studied; an almost complete absence of critical thinking; and a lack of initiation into research methods, resulting in zero interest in scientific investigation."

It was this serious state of affairs that Monteiro wanted to change when he completed his studies in Paris (1931-1936) and returned to Portugal, which happened after completing his doctorate under the guidance of the French mathematician Maurice Fréchet.

Upon returning to Portugal, Monteiro was the main driving force behind what became known as the "Generation of 40," which in ten years (1936-1945) changed the Portuguese mathematical landscape, creating in 1937 an international mathematical research journal, Portugaliae Mathematica, which still exists today, starting a mathematics dissemination journal in 1940, the Gazeta de Matemática, which also continues to be published [3], and founding the Portuguese Mathematical Society (SPM) in 1940. This group of mathematicians was constantly active in organizing various seminars on current mathematical topics and founded several research centers, creating conditions for the continuous development of mathematical research in Portugal on then-current topics.

Monteiro believed that the rebirth of mathematics in his country would only be possible if a fundamental current of interest in mathematics was created among secondary and university students. In this sense, and also as an attempt to overcome the university's resistance to proposals for curricular renewal by the new generation of mathematicians, and following the example of the United States in mobilizing youth and leading them to a practice that would develop a critical spirit geared towards research, Mathematics Clubs were created in 1942. Initially, the initiative was very successful; clubs were founded in several universities and colleges, but they were short-lived, as the government, fearful of anything that might acquire a critical spirit, spread the rumor that only communists participated in them, which was enough to make them disappear within a few years.

The dictatorship wanted to maintain strict control over the population, and with the victory of the Popular Front in the Spanish elections of February 1936, the regime panicked, feeling threatened by the presence of a progressive alliance in power in Spain, which included the socialists. It then tightened its control and enacted a decree obliging all those who wanted employment in the state to sign a declaration that essentially expressed support for the regime. Monteiro refused to sign this declaration, and consequently was unable to work for the state, specifically he could not be a university lecturer. Therefore, to earn a living, Monteiro gave private tutoring lessons. But the situation was far from ideal, and from a certain point onwards, Monteiro began to look for work opportunities outside of Portugal, with the help of foreign mathematicians.

An invitation from Brazil eventually arrived in September 1943, which he accepted, but the bureaucracies of the dictatorship delayed his departure by about a year and a half. He then left Portugal, accompanied by his wife Lídia, and their two sons, António and Luiz. He held the chair of Advanced Analysis at the National Faculty of Philosophy of the University of Brazil (FNFi), in Rio de Janeiro, the future UFRJ. At that time, his Department of Mathematics was the second best mathematics center in Brazil, the first being at the Faculty of Philosophy, Sciences and Letters of the University of São Paulo (FFCL). He signed a four-year contract, renewable. The Department of Mathematics at FNFi had important foreign visitors, such as Abraham Adrien Albert (1905-1972), Professor at the University of Chicago and future President of the American Mathematical Society in the 1965/66 biennium, and Marshall Harvey Stone (1903-1989), Professor at Harvard, President of the American Mathematical Society in 1943/44, and future President of the International Mathematical Union in the 1952-54 period. Monteiro gave several courses and seminars on topics such as General Topology, Hilbert Spaces, Functional Analysis, Boolean Algebras, and Lattices. He contacted important mathematicians who had recently arrived at FFCL, some already known from Paris, such as André Weil (1906-1998) and Jean Dieudonné (1906-1992), two fundamental members of the Bourbaki group.

Monteiro mentored several students during his time in Rio de Janeiro: Maria Laura Mouzinho (later Maria Laura Leite Lopes) (1917-2013) had Monteiro as her doctoral supervisor, becoming the second woman to obtain a doctorate in mathematics in Brazil (1949). The first was Marília Peixoto (1921-1961), when she passed the competitive examination for associate professor at the National School of Engineering [5] in 1948. Furthermore, she had a decisive influence on Leopoldo Nachbin (1922-1993), hired in 1947 as a professor at the FNFi, Maurício Peixoto (1921-2019), from the National School of Engineering, the only Brazilian mathematician with whom Monteiro has a joint article published in Portugaliae Mathematica, and Paulo Ribenboim (1928-), also hired for the FNFi in 1948. Nachbin was one of the greatest Brazilian mathematicians of the 20th century, being involved in the founding of the Brazilian Center for Physical Research in 1949, and in the founding of CNPq and CAPES in 1951. The first two Brazilian mathematicians to give plenary lectures at the International Congresses of Mathematicians were students of Monteiro: Leopoldo Nachbin in Stockholm, In 1962, and Maurício Peixoto in Vancouver in 1974. The two, along with Lélio Gama, were co-founders of the Institute of Pure and Applied Mathematics (IMPA) in 1952. Peixoto was president of CNPq, the Brazilian Academy of Sciences, and the Brazilian Mathematical Society. While in Argentina, Monteiro supervised the doctoral thesis of Mário Tourasse Teixeira (1925-1993), who defended his dissertation at the Faculty of Philosophy, Sciences and Letters of the University of São Paulo in 1965.

In 1945 and 1946, Monteiro was also a researcher at the Scientific and Technical Center of the Getúlio Vargas Foundation, and with Lélio Gama (1892-1981) he coordinated its Mathematics Center. He participated in the founding of the mathematical research journal Summa Brasiliensis Mathematicae, of which 2 volumes were published between 1946 and 1951: the first covers the period 1945/46, the second relates to the years 1947/51. These first two issues contain articles by Monteiro (with Hugo Ribeiro), Nachbin, Maria Laura, Paulo Ribenboim, Maurício Peixoto and Lélio Gama, but also by Paul Halmos (1916-2006), Jean Dieudonné (2), Abraham Albert (2), André Weil, Paul Erdös (1913-1996), Jacques Dixmier (1924-) and Oscar Zariski (1899-1986). After Monteiro's departure for Argentina, two more issues were published, no. 3, with articles from 1952 to 1956, and no. 4, relating to the period from 1957 to 1960.

In 1948 he began publishing Notas de Matemática (Notes on Mathematics), editing the first six volumes (1948/49), which included two of his own works, two by Nachbin, one by Maurício Peixoto, and one by José Abdelhay (1917-1996), a colleague of Monteiro in the Mathematics Department of the FNFi (National Faculty of Philosophy). From issue no. 7, with Monteiro already in Argentina, until issue no. 47 in 1972, Nachbin was the editor. From then on, the North Holland Publishing Company took over the Notas, although Nachbin remained the editor of the first issues.

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