# Leopoldo Nachbin

### Quick Info

Recife, Pernambuco, Brazil

Rio de Janeiro, Brazil

**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.

### Biography

**Leopoldo Nachbin**was the son of Jacob Nachbin (1896-1936) and Léa Drechsler (known as Lotty). We should give a few details about the extraordinary career of Jacob Nachbin. Born into a Hassidic family in Ratshondzh, Poland, he was orphaned at an early age and raised by an uncle. He was in the Austrian army in World War I and eventually ended up in Budapest. There in 1918 he founded a Labour Zionist organisation but went to Zurich. He was exiled, went to Italy and then in early 1921, with his Austrian wife Léa and children, arrived in Pernambuco, Brazil. Leopoldo was born there in January 1922 and shortly after that Jacob and his wife split up. Jacob Nachbin set up a Jewish weekly newspaper and a Yiddish literary periodical in Rio de Janeiro. He began publishing books on the history of Jews in Portugal and Brazil and other Jewish related topics. Ilan Stavans writes [47]:-

I have come across various Yiddish publications he authored, including Der Letster fun di groyse Zakutos (The Last of the Great Zakutos, 1929), about the last in the dynasty of descendants of Abraham ben Samuel Zacuto, the 15th-century mathematician who served as astronomer in the court of Portugal's King Joao II.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. Jacob went to Mexico City in 1932 to undertake research on early Jews in the New World and worked on the Carvajal manuscript. 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. Reports about the missing manuscript and Jacob Nachbin [47]:-

... were read throughout the Yiddish-speaking world in Latin America, including in Recife, the sea-front capital in Brazil's northwestern state of Pernambuco. In Recife, another of Nachbin's wives, Léa Drechter, an Austrian Jew whom he had abandoned together with their child, found out about the robbery and also that he was now married to someone else. Nachbin had left her and had gone to Chicago, where he had reinvented himself as an academic.Let us note that Jacob Nachbin always denied stealing the manuscript which reappeared in 2016. It now appears probable that in fact he did not steal it. Jacob Nachbin went to Spain to fight against Franco and vanished, presumably killed in the fighting.

We have given these details about Leopoldo's father since, although he was not involved in his upbringing, the publicity about him clearly must have affected the young boy. Leopoldo was brought up by his mother and attended schools in Recife. At the Joao Barbalho School in Recife, he became a close friend of Clarice Lispector (1920-1977), a Ukrainian born Jew who came to Brazil with her family in 1922, and later became a famous novelist [21]:-

At the Joao Barbalho School in Recife, Leopoldo Nachbin and Clarice Lispector were just "the two impossibles of the class." The teacher separated them, but in vain: "Leopoldo and I just shouted across the room whatever we had to say to each other." Leopoldo became, besides her father, Clarice's first masculine protector, "and he did such a good job that for the rest of my life I have accepted and wanted masculine protection."Leopoldo and Clarice both then attended the Ginásio Pernambucano in Recife. 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. Ralph Raimi writes about Leopoldo's time at the Ginásio Pernambucano in Recife [41]:-

I asked him how the family managed when he was at High School; he merely said it was very hard, his mother worked very hard.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. This was a standard way of studying mathematics in Brazil at this time. In 1939 Nachbin enrolled at the National School of Engineering at the University of Brazil in Rio de Janeiro. Marília de Magalhaes Chaves and Maurício Peixoto were both his fellow students, all three beginning their studies in the same year. Peixoto said in the interview [37]:-

During the five years of the engineering course, Leopoldo and I were inseparable companions. ... Marília's influence was very strong during these "golden years" ... Both Marília Chaves and Leopoldo Nachbin were important influences in my becoming a mathematician. This in the sense of trying to live for and by mathematics.For his outstanding undergraduate performance, in 1942, Nachbin received the Licínio Cardoso Award, from the Licínio Cardoso Foundation. In 1943 he graduated with an engineering degree but he never intended to have a career as an engineer. Mathematics was always the subject for him and throughout his engineering course both he and Maurício Peixoto studied advanced mathematics together, often in the municipal library or at the university. Nachbin also attended lectures at the National Faculty of Philosophy at the University of Brazil by Luigi Sobrero and Gabriele Mammana. Luigi Sobrero (1909-1979) had been born in Turin, Italy, and was awarded an engineering degree from the University of Rome in 1931 and a mathematics degree two years later. Between 1939 and 1943 he was a visiting professor of theoretical physics at Rio de Janeiro. Gabriele Mammana (1893-1942) was also an Italian mathematician who had graduated from Pisa and then became Mauro Picone's assistant at the University of Catania. He taught in Livorno, Cagliari, Catania and Naples before teaching at the Federal University of Rio de Janeiro between 1939 and 1942. He was an analyst working on differential equations. 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*Ⓣ in 1941 while near the beginning of his engineering course. The paper, written in Portuguese, gives a generalisation of Arzelà's theorem. He writes in the paper:-

Arzelà's theorem ... naturally suggests the question: Is it possible to extend to differential equations of a more general type the preceding result on the differential equations of the very simple type mentioned?Nachbin's next paper was

It is with such an extension that I will deal with here. I was led to these considerations last year, when I dealt with the question, of educational interest, proposed to me by Professor G Mammana, of finding a proof, by elementary means, of the theorem of Arzelà; and it was under his promptings that I completed the wording of this note.

*Un estensione di un lemma di Dirichlet*Ⓣ 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. This certainly made his life difficult in gaining mathematics appointments. The Mathematics Department of the Faculdade Nacional de Filosofia of the University of Brazil hired the Portuguese mathematician António Aniceto Monteiro (1907-1980) in 1945 and he gave courses and seminars on ordered sets, lattices and Boolean algebras. Monteiro's undergraduate degree had been from the University of Lisbon followed by a Ph.D. from the Sorbonne with Maurice Fréchet as his advisor. Nachbin became interested in the topics Monteiro was teaching, and became a friend of Monteiro's. He writes in [28]:-

It suffices to express globally my indebtedness to Monteiro's influence when I was young and inexperienced, from the mathematical, psychological and political viewpoints, an occasion in which Monteiro granted me his valuable advice, protection and initiative ...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*Ⓣ and was successful in the competition.

Marshall Harvey Stone and Adrian Albert, both from Chicago, had came to Rio de Janeiro on a State Department programme as visiting professors in 1945. In January 1945 André Weil came to the University of São Paulo as a visiting professor. In 1946 and 1947 André Weil and Jean Dieudonné lectured at the University of São Paulo. Nachbin visited São Paulo and, through André Weil's lectures, became interested in uniform structures and topological vector spaces. Marshall Stone came again to Rio de Janeiro in 1947 and spent three months teaching a course on 'Rings of Continuous Functions'. 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. Both were eventually awarded a scholarship. Peixoto said [37]:-

It was a State Department grant, which cost us almost daily trips to Ministry of Foreign Affairs for about a year; the aid came from the Buenos Aires Convention, through which the American government gave scholarships to Latin Americans.Nachbin travelled to Chicago in October 1948. The scholarship lasted until September 1949 but he was able to spend a second year at Chicago funded by a scholarship from the Guggenheim Foundation. At Chicago, he met and attended lectures by André Weil, Jean Dieudonné, Marshall Harvey Stone and Laurent Schwartz. 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. He gave the talk

*On the continuity of positive linear transformations*on Saturday 2 September in the Analysis Section. After attending the Congress, he travelled to New York, departing from there on the ship

*Brazil*on 21 September 1950 and returned to Rio de Janeiro. Back at the University of Brazil he had no job, but the head of physics offered him a professorship in the Department of Physics which he accepted.

His outstanding contributions earned him election to the Brazilian Academy of Sciences as an associate member in 1948 and as a full member in 1950. Despite these distinctions, his career did not proceed smoothly. In 1950 the Faculdade Nacional de Filosofia of the University of Brazil advertised a competition for the Chair of Mathematical Analysis. Nachbin entered and submitted the thesis

*Topologia e Ordem*Ⓣ. He related the circumstances in the Preface to his book

*Topology and Order*(1965):-

In 1948 I published three notes in the Comptes Rendus de l'Académie des Sciences (Paris) containing results on the relationship between topological and order structures. In 1950 I also wrote a note along the same line for the Proceedings of the International Congress of Mathematicians Cambridge, Mass.). Most of these results were developed in a monograph entitled 'Topologia e ordem' which I wrote in Portuguese while I was at the University of Chicago and which was printed by the University of Chicago Press in 1950. This monograph was a thesis that I submitted to the Faculdade Nacional de Filosofia, Universidade do Brasil (Rio de Janeiro), in 1950, as a candidate for a vacant chair in analysis.For information about books by Nachbin, see THIS LINK.

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. Why would this happen? First let us note that 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. Perhaps he felt he would be shown up badly with such an excellent young mathematician in his department. Secondly we note that the Chair of Mathematical Analysis was at that time filled on a temporary basis by José Abdelhay (1917-1996) and he was in the competition. Abdelhay was an excellent teacher and had written a number of good research papers. 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. No quick solution was found and Jean Dieudonné, Charles Ehresmann and Laurent Schwartz, who were giving lecture courses at the University of Brazil in the summer of 1952, decided to write a letter attempting to resolve the situation. Their proposal was that both Abdelhay and Nachbin should be given chairs of Mathematical Analysis. Praising Nachbin, they wrote (see [45]):-

Brazil is fortunate to have today, in the person of Professor Leopoldo Nachbin, a young mathematician whose remarkable work has already attracted the attention of specialists throughout the world, and who, through his strong culture and dynamic personality would be particularly suitable for this training of the future Brazilian mathematical elite. By adding such a professor, the already very active nucleus of mathematicians of the Faculdade de Filosofia would further significantly strengthen the intensity of its efforts and the unity of action essential to their fruitful development.You can read a translation of their full letter at THIS LINK and you can read Halmos's account of the controversy at THIS LINK.

The letter appears not to have helped resolve the situation. In fact 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. He was one of the founders of the Brazilian Centre for Physical Research in 1948 and a founder and organiser of the Institute for Pure and Applied Mathematics in 1951. He continued his busy life visiting various institutions, being a Visiting Professor at the University of Montevideo, Uruguay, for one month in June and July 1953, and a Visiting Member of the Institute for Numerical Analysis, University of California, Los Angeles, USA from January to March 1954.

On 28 July 1956 Nachbin married Maria da Graça Mousinho (born 12 March 1928, in Recife, Pernambuco, Brazil). They had three children: André Nachbin, born on 8 August 1957 in Chicago, Illinois, USA; Léa Nachbin, born on 16 August 1961 in Rio de Janeiro, Brazil; and Luís Nachbin, born 30 July 1964 in Rochester, New York, USA. Nachbin and his wife travelled to Mexico where he was a Rockefeller Foundation Scholar at the Universidad Nacional Autónoma de México during August 1956. 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. He was then awarded a Guggenheim Foundation Scholarship which he held at the University of Chicago from August to December 1957 before moving to the Institute for Advanced Study at Princeton, New Jersey where he undertook research from January to September 1958.

In 1962, he received the Moinho Santista Award, from the Bunge Foundation. This award was given for outstanding research and Nachbin was the first to receive such an award in the area of mathematics. His friend Maurício Peixoto received the Moinho Santista Award in 1969. He visited Brandeis University, Waltham, Massachusetts, from December 1960 to March 1961 and accepted an invitation from Laurent Schwartz to the Sorbonne, Paris where he worked from October 1961 to September 1963. During this time in Paris, he went to the International Congress of Mathematicians in Stockholm from 15 August - 22 August 1962. He was an invited 30-minute speaker at the Congress and delivered the lecture

*Résultats récents et problèmes de nature algébrique en théorie de l'approximation*Ⓣ. The lecture begins:-

In this talk we will discuss some known results and some open problems in the theory of approximation of real, continuous or differentiable functions, in the case of algebras and modules of such functions. We will do this study either from the point of view of the theory of Weierstrass, therefore for the uniform convergence on any compact space, or from the more general point of view of the theory of Bernstein, that is to say of the weighted uniform convergence on not necessarily compact parts.Also he made a trip from Paris to Newcastle, England in April 1963 to visit Frank Bonsall. After his stay in Paris, Nachbin went to the University of Rochester in Rochester, New York, USA as a visiting professor. While there he was offered a full professorship and in September 1964 became a full professor at the University of Rochester. In 1967 he became George Eastman Professor of Mathematics at the University of Rochester, a chair specially created for him. He did not, however, give up his position at the University of Brazil in Rio de Janeiro and spent half of each year back in Brazil. Ralph Raimi writes [41]:-

Leopoldo brought graduate students from South America - and not only from Brazil - to Rochester; he brought former graduate students here as visiting professors. He got financing somehow to bring some of our Rochester students to Rio for a while, for he did spend a semester of most years in Rio.We have seen a little of the many travels that Nachbin made and Raimi make an interesting comment about this [41]:-

Leopoldo remembered everyone, and on each of his travels he must have sent dozens of cards of greeting, as if to gather the world together with these threads of communication. Threads of gossamer, perhaps, with nothing in the way of tensile strength; but unbreakable and unforgettable in their spiritual strength. 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. He did not give up his life of travel immediately, however, and in May 1981 he was a visiting professor at the Université de Paris VI.

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'. This theorem concerns the growth rates of analytic functions and appears first in his paper

*An extension of the notion of integral functions of the finite exponential type*(1944). We note that

*Mathematical Reviews*lists over 200 papers in which 'Nachbin's theorem' appears in the review text.

Let us end with a comment by Francisco Antonio Doria [6]:-

I first met Leopoldo in 1970. I was then a junior graduate student at the Brazilian Centre for Physical Research, and Leopoldo was going to give a talk on his latest findings about infinite-dimensional holomorphy. There used to be a tea before every colloquium, and I approached him during the tea as one would approach a demigod. I believe I even had a trembling voice when I asked him whether it would be worthwhile to attend his talk, as I knew very little about complex functions. He then gave me his first lesson: go there, he said; I always try to talk to the widest audience possible. "There is no point in giving a talk just to a small bunch of specialists, as one must interest everybody in every aspect of science." Later he made a comment that clarified that remark: "I believe it is my duty to advance as much as possible Brazilian science, and Brazilian mathematics. That's not easy, and I have suffered many misunderstandings because of my actions in the interest of our science."

### References (show)

- J A Barroso and A Nachbin (eds.),
*Leopoldo Nachbin (Portuguese)*(Universidade Federal do Rio de Janeiro, Rio de Janeiro, 1997). - D R Brown, Review: Topology and order, by Leopoldo Nachbin,
*Mathematical Reviews*MR0219042**(36 #2125)**. - J Danes, Review: Introduction to functional analysis: Banach spaces and differential calculus, by Leopoldo Nachbin,
*Mathematical Reviews***(82f:58002)**. - J Diestel, Review: Introduction to functional analysis: Banach spaces and differential calculus, by Leopoldo Nachbin,
*The American Mathematical Monthly***90**(8) (1983), 579-580. - J Dieudonné, Review: Integral de Haar, by Leopoldo Nachbin,
*Mathematical Reviews*MR0118802**(22 #9571)**. - F A Doria, Leopoldo Nachbin: some personal recollections,
*Contemporary Brazilian research in logic. Part I. Logique et Anal. (N.S.)***39**(153-154) (1996), 31-33. - J P Ferrier, Review: Weighted approximation, vector fibrations and algebras of operators, by Leopoldo Nachbin, Silvio Machado and Joao B Prolla,
*Mathematical Reviews***(52 #6434)**. - R L Gomes, Homage to Leopoldo Nachbin (Portuguese),
*Gaz. Mat. (Lisbon)***34**(35) (129-132) (1973/74), 7-11. - M Hervé, Review: Holomorphic functions, domains of holomorphy and local properties, by Leopoldo Nachbin,
*Mathematical Reviews*MR0274798**(43 #558)**. - R B Holmes, Review: Elements of approximation theory, by Leopoldo Nachbin,
*Mathematics of Computation***23**(106) (1969), 444-445. - J Horváth, The late works of Leopoldo Nachbin,
*Mat. Apl. Comput.***13**(3) (1994), 175-188. - J Horváth, The life and works of Leopoldo Nachbin, in
*Aspects of mathematics and its applications*(North-Holland Math. Library, 34, North-Holland, Amsterdam, 1986), 1-75. - J Korevaar, Review: Lectures on the theory of distributions, by Leopoldo Nachbin,
*Mathematical Reviews*MR0213868**(35 #4722)**. - Leopoldo Nachbin,
*Personalidades do Muro, UNIFEI*.

https://unifei.edu.br/personalidades-do-muro/extensao/leopoldo-nachbin/ - Leopoldo Nachbin,
*American Men & Women of Science*(R R Bowker, New Providence, NJ, 1992). - Leopoldo Nachbin,
*Who's Who in America*(Marquis Who's Who, Wilmette, IL, 1976). - Leopoldo Nachbin,
*Who's Who in Technology*(Gale Research, Detroit, 1995). - Leopoldo Nachbin,
*Who's Who in Technology Today*(Research Publications, J Dick Publishing, Lake Bluff, IL, 1984). - Leopoldo Nachbin,
*Who's Who in the World*(Marquis Who's Who, New Providence, NJ, 1992). - J Lesmes, J F Escobar, D Pareja, J J O'Connor and E F Robertson, Mathematical obituary: Leopoldo Nachbin (1922-1993), Ricardo Mañé (1948-1995), Morris Kline (1908-1992), John C Burkill (1900-1993) (Spanish),
*Lect. Mat.***16**(2) (1995) - B Moser,
*Why This World: A Biography of Clarice Lispector*(Oxford University Press, 2009). - J Mujica, A historical note about Leopoldo Nachbin (1922-1993) (Spanish),
*Cubo Mat. Educ.***1**(1999), 1-5. - J Mujica, Leopoldo Nachbin (1922-1993),
*Results Math.***25**(3-4) (1994), 195-197. - L Nachbin, Massera, one of the greatest mathematicians of Latin America of all times,
*Ciênc. Cultura***35**(7) (1983), 917-919. - L Nachbin, A glimpse at my career as a mathematician,
*Ciênc. Cultura***35**(1) (1983), 3-5. - L Nachbin, On the development of mathematics in Latin America (Portuguese),
*Ciênc. Cultura***33**(5) (1981), 649-651. - L Nachbin, The development of mathematical physics and related functional analysis, and its role in a developing country (Portuguese),
*Bol. Soc. Paran. Mat.*(2)**2**(1) (1981), 17-26. - L Nachbin, The influence of António A Ribeiro Monteiro in the development of mathematics in Brazil. Special issue in honor of António Monteiro,
*Portugal. Math.***39**(1-4) (1980), xv-xvii. - L Nachbin, Aspects of the recent development of functional analysis in Brazil (Portuguese),
*Ciênc. Cultura***32**(4) (1980), 409-412. - L Nachbin, Aspects of the recent development of functional analysis in Brazil (Portuguese),
*Bol, Soc. Paran. Mat.*(2)**1**(2) (1980), 49-57. - L Nachbin, The development of mathematical physics and related functional analysis, and its role in a developing country (Portuguese),
*Ciênc. Cultura***31**(9) (1979), 1001-1004. - L Nachbin, A look at approximation theory, in
*Approximation theory and functional analysis, Proc. Internat. Sympos. Approximation Theory, Univ. Estadual de Campinas, Campinas, 1977*(North-Holland Math. Stud., 35, North-Holland - L Nachbin, Brazil's mathematical requirements (Portuguese),
*Gaz. Mat. (Lisbon)***34**(35) (129-132) (1973/74), 1-5. - L Nachbin, Aspects of the recent development of mathematics in Brazil (Portuguese),
*Soc. Parana. Mat. Anuário***3**(1956), 28-41. - Ph Novaerraz, Review: Uniformité d'holomorphie et type exponentiel, by Leopoldo Nachbin,
*Mathematical Reviews***(52 #6425)**. - J C Oxtoby, Review: The Haar integral, by Leopoldo Nachbin,
*The American Mathematical Monthly***73**(8) (1966), 918. - M M Peixoto, Maurício Matos Peixoto, in
*J Palis, C Camacho and E L Lima, (eds.), IMPA 50 anos*(IMPA, Rio de Janeiro, 2003), 240-250. - C Pereira, Leopoldo Nachbin, an excellent twentieth-century Brazilian mathematician (Portuguese),
*Rev. Bras. Hist. Mat.***17**(34) (2017), 73-81. - R R Phelps, Review: Elements of approximation theory, by Leopoldo Nachbin,
*Mathematical Reviews*MR0208228**(34 #8038)**. - J B Prolla, Dedication in memoriam Leopoldo Nachbin (1922-1993), in Approximation, probability, and related fields, Santa Barbara, CA, 1993 (Plenum, New York
- R A Raimi, Leopoldo Nachbin 1922-1993,
*University of Rochester*(12 May 1993).

https://people.math.rochester.edu/faculty/rarm/leopoldo.html - V Rita da Costa, Interview of Cândido Lima da Silva Dias,
*Science Today*(November 1997).

http://www.canalciencia.ibict.br/notaveis/livros/candido_lima_da_silva_dias_45.html - J Sebastiao e Silva, Review: Distributions and partial differential equations, by Leopoldo Nachbin,
*Mathematical Reviews*MR0124599**(23 #A1911)**. - C P da Silva, The work of the mathematician Leopoldo Nachbin (1922-1993) from FNFi,
*Rev. Bras. Hist. Mat*.**19**(38) (2019), 83-103. - C P da Silva,
*Início e Consolidação da Pesquisa em Matemática no Brasil*(São Paulo, 2022). - C L da Silva Dias, C S Hönig and L A da Justa Medeiros, Leopoldo Nachbin,
*Computational and Applied Mathematics***13**(3) (1994), 173-174. - I Stavans,
*The Return of Carvajal: A Mystery*(Pennsylvania State University Press, 2019). - Trajetória de Leopoldo Nachbin foi marcada por ineditismos,
*Instituto de Matemática Pura e Aplicada*(31 January 2022).

https://impa.br/en_US/noticias/leopoldo-nachbin-teve-trajetoria-marcada-por-ineditismos/ - Yankev Nakhbin (Jacob Nachbin),
*Yiddish Leksikon*(2017).

http://yleksikon.blogspot.com/2017/12/yankev-nakhbin-jacob-nachbin.html

### Additional Resources (show)

Other pages about Leopoldo Nachbin:

Other websites about Leopoldo Nachbin:

### Honours (show)

Honours awarded to Leopoldo Nachbin

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update November 2022

Last Update November 2022