**Leopoldo Nachbin** was an outstanding Brazilian mathematician who spent time as a Visiting Professor at many of the top institutions worldwide. He worked on ordered systems, topology, topological vector spaces, approximation theory, harmonic analysis, and infinite-dimensional holomorphy.

- We should give a few details about the extraordinary career of Jacob Nachbin.
- Jacob Nachbin set up a Jewish weekly newspaper and a Yiddish literary periodical in Rio de Janeiro.
- Around 1930-1931 Jacob Nachbin went to the United States and held chairs at the Northwestern University, in Evanston, Illinois and the New Mexico State University in Las Cruces.
- The manuscript vanished, Jacob Nachbin was accused of stealing it, spent three months in prison before being released for lack of evidence and was deported to the United States.
- Nachbin had left her and had gone to Chicago, where he had reinvented himself as an academic.
- Jacob Nachbin always denied stealing the manuscript which reappeared in 2016.
- Jacob Nachbin went to Spain to fight against Franco and vanished, presumably killed in the fighting.
- At this school, Leopoldo was taught by Luís de Barros Freire (1896-1963), a civil engineer and professor at the Escola Politécnica de Pernambuco who had won the chair of mathematics at the Escola Normal de Pernambuco in 1919 and had taught physics and mathematics at several high schools in Recife.
- It was Luís Freire who brought out Nachbin's passion for mathematics and encouraged him to go to Rio de Janeiro and study for an engineering degree.
- In 1939 Nachbin enrolled at the National School of Engineering at the University of Brazil in Rio de Janeiro.
- Both Marília Chaves and Leopoldo Nachbin were important influences in my becoming a mathematician.
- For his outstanding undergraduate performance, in 1942, Nachbin received the Licínio Cardoso Award, from the Licínio Cardoso Foundation.
- Nachbin also attended lectures at the National Faculty of Philosophy at the University of Brazil by Luigi Sobrero and Gabriele Mammana.
- In addition to attending courses by Sobrero and Mammana, Nachbin spent much time in a deep private study of the works of Jean Dieudonné and Laurent Schwartz.
- Remarkably, Nachbin published his first paper Sobre a permutabilidade entre operações de passagem ao limite e de integraçao de equações diferenciais Ⓣ(On the interchangeability between crossing the limit and integrating differential equations operations) in 1941 while near the beginning of his engineering course.
- Nachbin's next paper was Un estensione di un lemma di Dirichlet Ⓣ(An extension of a Dirichlet lemma) written in Italian and published in 1942; this paper on harmonic analysis was sponsored by Sobrero.
- If the reader is a little surprised that Nachbin's second paper was written in Italian, let us say they will be more surprised to learn that between 1942 and 1946 he wrote papers in Portuguese, Spanish, Italian, English and French.
- Despite a remarkable publication record in mathematics from a young age, Nachbin had an engineering degree and no mathematics degree.
- Nachbin became interested in the topics Monteiro was teaching, and became a friend of Monteiro's.
- In 1947, supported by Monteiro, Nachbin was hired by the Mathematics Department on a one year contract.
- Towards the end of 1947, Monteiro suggested Nachbin enter the competition for the position of docent in Mathematical Analysis.
- Nachbin submitted the dissertation Combinaçao de topologias pseudo-metrisáveis e metrisáveis Ⓣ(Combination of pseudo-metrizable and merisable topologies) and was successful in the competition.
- Nachbin visited São Paulo and, through André Weil's lectures, became interested in uniform structures and topological vector spaces.
- Nachbin attended this course and through it became interested in the theory of approximation.
- Nachbin, together with his friend Maurício Peixoto, decided to try to obtain a Buenos Aires Convention scholarship to study at Chicago.
- Nachbin travelled to Chicago in October 1948.
- While he was in Chicago, the head of mathematics at the University of Brazil, José da Rocha Lagoa, did not renew Nachbin's position in the Mathematics Department.
- Nachbin was offered a position in Chicago but turned it down since he wanted to work in Brazil and help develop mathematics there.
- Nachbin attended the International Congress of Mathematicians at Cambridge, Massachussetts from 30 August to 6 September 1950.
- Nachbin entered and submitted the thesis Topologia e Ordem Ⓣ(Topology and order).
- There was now a campaign by supporters of the head of mathematics, José da Rocha Lagoa, to prevent Nachbin being a candidate for the chair.
- If Nachbin were a candidate, it is almost impossible that he would not have been appointed.
- So our question should be: "Why did Lagoa not want Nachbin in the Chair of Mathematical Analysis at the University of Brazil?" Let us suggest two possible reasons, both of which may have contributed.
- It is clear that Lagoa was a second rate research mathematician compared to Nachbin, we can only find two papers by Lagoa, both on the structure of the Department of Mathematics in the University of Brazil.
- He was not up to Nachbin's extremely his standards as a researcher, but nevertheless, was a valuable member of the Mathematics Department.
- The argument presented against Nachbin being a candidate was that he had an engineering degree.
- Their proposal was that both Abdelhay and Nachbin should be given chairs of Mathematical Analysis.
- It is almost unbelievable that the argument, with professors on both sides, went on for 22 years and only in 1972 was the competition held and Nachbin appointed.
- Nachbin, even before 1952, was making a strong impression both in terms of his research and in terms of building research facilities in Brazil.
- They then travelled to the University of Chicago, Illinois, USA where Nachbin continued to hold his Rockefeller Foundation Scholarship from September 1956 to July 1957.
- This award was given for outstanding research and Nachbin was the first to receive such an award in the area of mathematics.
- After his stay in Paris, Nachbin went to the University of Rochester in Rochester, New York, USA as a visiting professor.
- They said very little, these cards, but they were gentle as Leopoldo himself was gentle, they were kind as he was kind, and they were part of the social fabric of our trade, the structure that contains all mathematicians and not just the handful of specialists that each of us is naturally linked to in our working life.
- Nachbin continued to hold the chair at the University of Rochester until December 1980 when he retired.
- We have mentioned above several honours that Nachbin received but let us mention a few more: in 1969 he became a corresponding member of the Lisbon Academy of Sciences; in 1970 he was awarded a medal from the University of Liege; in June 1973 he received an honorary doctorate from the Federal University of Pernambuco; in 1982 he received the Bernardo Houssay Science Prize from the Organization of American States; and in 1983 he was elected a member of the newly-founded Latin American Academy of Sciences.
- Finally, his name is well-known today through 'Nachbin's theorem'.
- We note that Mathematical Reviews lists over 200 papers in which 'Nachbin's theorem' appears in the review text.

Born 7 January 1922, Recife, Pernambuco, Brazil. Died 3 April 1993, Rio de Janeiro, Brazil.

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Origin Brazil

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive