# Elon Lages Lima

### Quick Info

Maceió, Alagoas, Brazil

Rio de Janeiro, Brazil

**Elon Lima**was a Brazilian mathematician who is famed as the most famous mathematics textbook writer in the Portuguese language. He also made important research contributions in topology and was a major contributor to the Brazilian Mathematics Colloquium between 1961 and 1983.

### Biography

**Elon Lima**was the son of Manoel de Albuquerque Lima (1883-1970) and Adelaide Lages (1889-1960). We note that Manoel, Elon's father, is sometimes known as Manuel. He [24]:-

... was a merchant; he had a grocery store that sold everything: from bread to shaving equipment, from wine to bananas.Elon's mother, Adelaide, was a housewife. Elon was brought up in Maceió, a coastal city and capital of the State of Alagoas. He had a sister who was two years older than him and who played an important part in his development. He attended the Colégio Batista Alagoano which had been founded in 1922 and approved by the Baptist Church. At this time he was a friend of Manfredo Perdigão do Carmo (1928-2018) who would later become his colleague at the Institute of Pure and Applied Mathematics in Rio de Janeiro. Elon said that Manfredo, who attended a Marist brothers school in Maceió, was the intellectual of their group of friends. Elon played ball, swam, and played button football while Manfredo drew. At the Colégio Batista Alagoano, Elon was taught mathematics by Benedito de Morais who, according to Elon, was never a great mathematician but was an exceptional teacher.

Lima spent two years at the Colégio Estadual in Maceió, where he took the scientific course together with his friend Manfredo do Carmo. Since there was no higher education, other than a Law school with did not interest him, in Maceió he decided to join the Army and, when seventeen, entered the Escola de Cadetes in Fortaleza. His time at this school, however, did not go well. The physics teacher kept making mistakes and Lima always corrected him. The physics teacher was not pleased at being corrected by a pupil and told Lima to leave the Escola de Cadetes as soon as possible. He left after a year but did receive a reservist certificate. Ari de Sá Cavalcante, who taught Lima at the Escola de Cadetes, had taken over the management of Ginásio Farias Brito, in Fortaleza, in 1941, where he was also a teacher. He was delighted to have Lima teach at the Ginásio Farias Brito and within two months of leaving the Escola de Cadetes, he was teaching Mathematics, Science, Geography, Portuguese and other subjects there. At this time he thought that he wanted a literary career as a writer, poet, or journalist. Soon after he arrived at the Ginásio Farias Brito, however, the mathematics teacher left and Ari de Sá Cavalcante invited Lima to become the mathematics teacher. He now became a mathematics teacher despite never having completed his high school studies.

It had been the influence of Lima's sister that helped him do particularly well in mathematics. He said in the interview [16]:-

I have a sister, two years older than me, who was an excellent student, in everything she did she was better, although she was incredibly modest and in particular she was an excellent student of mathematics and was a student of the same teacher as me. And she inspired me because she taught her classmates at home and I attended those classes. So when it was my turn to study those things at school, I had already learned them at home.Lima realised that if he was to be a mathematics teacher he should learn more about the topic. After he had taught for a year, Ari de Sá Cavalcante told him there was a contest for a teacher at the Colégio Estadual in Ceará. Lima thought that the fact that he had not finished high school would prevent him from entering the competition but it did not. He was one of ten candidates who entered the competition and came out top. Now aged nineteen, he took up the job in Ceará and, in addition, enrolled to study mathematics at the Catholic Faculty of Philosophy of Ceará, a night school run by Marist brothers. This, Lima said, was very poor but every vacation he returned to his home town of Maceió and there became part of a little group. His friend Manfredo do Carmo was at this time studying engineering in Recife, but he returned to Maceió every vacation. In Maceió, Lima met Newton Braga, a physicist who was studying at the Centro Brasileiro de Pesquisas Físicas (CBPF) in Rio de Janeiro but also returned to Maceió at the vacations. The three managed to get a room at the Colégio Estadual de Alagoa where they could study mathematics during the vacations.

Newton Braga encouraged Lima to apply for a scholarship from CNPq which was successful. Having been accepted to study mathematics at the National Faculty of Philosophy, Sciences and Letters at the University of Brazil, in March 1952 he went to Rio de Janeiro. There he came into contact with Maurício Peixoto and Leopoldo Nachbin who both worked at the CBPF and at the University of Brazil. In October of 1952, the IMPA, the Institute of Pure and Applied Mathematics, was created, situated at this time in the CBPF. Lima was awarded a Bachelor's Degree in Mathematics from the University of Brazil in December 1953. Both Peixoto and Nachbin had studied for their doctorate at the University of Chicago and they suggested that Lima should study there for his doctorate. They wrote to Irving Kaplansky who quickly agreed to accept Lima. Harry Miller Jr, the director of the Rockefeller Foundation, was at the CBPF and Nachbin recommended Lima for a scholarship. After an interview, he was awarded the scholarship and was set to begin his studies at Chicago in September 1954. Before going, he spent the first half of 1954 teaching the course 'Topologia dos Espaços Metricos' at the Faculty of Philosophy, Sciences and Letters which he wrote up as a mimeographed booklet and was published in Nachbin's "Notes of Mathematics" series. Jacques Riguet writes [27]:-

This is the first part of the general topology course given by the author as part of his teaching of higher geometry during the year 1954 for 2nd and 3rd year mathematics students at the Faculty of Philosophy of Rio de Janeiro. This presentation, clear and precise, interspersed with examples and exercises, follows Nicolas Bourbaki fairly closely and can constitute an excellent introduction to the latter's treatise on general topology.On 14 July 1954, Lima married Valdece, a daughter of Antonio Gonçalves de Magalhães and Maria de Lourdes Pessoa e Sá. Elon and Valdece Lima had five children, all girls. In August 1954 Lima and his wife sailed from Santos, Brazil on the SS

*Argentina*, departing on 9 August, arriving in New York on 23 August. The record of the voyage shows that Valdece was four years younger than her husband. The day after they arrived they read in a newspaper that the Brazilian president, Getúlio Vargas, had committed suicide.

Lima arrived in Chicago thinking he would undertake research for his doctorate in Functional Analysis, Nachbin's speciality. Nachbin suggested that one of Paul Halmos, Irving Kaplansky or Irving Segal would supervise him but when he arrived he discovered that all three had lost interest in that subject. He had expected to begin work on his Ph.D. immediately, but Chicago insisted that he study first for a Master's Degree. Kaplansky was his advisor for this degree.

In 1955, Lima received the Edna M Allen Award from Chicago and he explained in [24] how that happened:-

There were in Chicago the Senior Maths Club and the Junior Maths Club, one for teachers and one for students, and each organised a series of lectures on Wednesdays. One week the lecture was given by a researcher, the following week by a student; at the Junior Maths Club, the student who gave the best lecture of the year won this prize. When I arrived, I was asked if I wanted to give a talk; I did and won the prize. Then I was elected president of the Junior Maths Club.In May 1955 Lima took both a written and an oral examination in five subjects for his Master's Degree and was then able to continue to study for his Ph.D. The Rockefeller Foundation grant only funded him for two years, then he was able to obtain a CNPq grant for the rest of his studies at Chicago. Finances were very tight, with his first daughter born in 1955. After realising that functional analysis was not a good topic for his Ph.D. in Chicago, Lima began studying algebraic topology. While studying for his Master's Degree, he read the mimeographed notes taken by students who had attended a course given by Edwin Spanier and then Lima undertook research advised by Spanier. He sat the oral examination for his doctoral thesis

*Duality and Postnikov Invariants*in December 1958; he had submitted the thesis on 17 October 1958

*.*The thesis contains the following Acknowledgement:-

I would like to express my gratitude to Professor E H Spanier for his generous help and encouragement during the preparation of this thesis.In his thesis Lima introduced the notion of the spectrum of topological space which generalises cohomology theory. This idea has led to many advances by numerous mathematicians. The examiners praised the high quality of Lima's thesis at his oral but a strange problem between Saunders Mac Lane and Lima almost stopped him graduating with his doctorate; for Lima's account, see THIS LINK.

Back at the IMPA in Rio de Janeiro, Lima was an assistant researcher paid through a scholarship. By now he had two daughters and the scholarship did not cover the rent of his apartment so it was impossible to continue but to allow him to continue to work there he was promoted to a senior researcher so getting a larger scholarship. We mentioned above Lima's original intention to have a literary career. He explained how this led to him writing mathematics books [16]:-

... my intention since I was a boy was to be a writer. I wrote a lot of nonsense, like poetry and short stories. I had a huge notebook with the rubbish I wrote. When I finished my PhD, I reread everything, saw that it was second-rate stuff, and then I tore it up and threw it away. So I decided to write about mathematics, because I was always concerned with helping to create a group of people in Brazil who were very competent in mathematics. And so I started writing books because I thought and still think that books are the best way for you to develop and disseminate knowledge.The third Brazilian Mathematics Colloquium was held at University of Ceará in July 1961. Lima was the organiser of the Colloquium and delivered the course

*Topologia Diferencial*Ⓣ. He contributed several other courses to the Brazilian Mathematics Colloquium over the following years, in 1969, 1973, 1975, 1977 and 1987.

In the 1960s, Lima spent time at different institutions in the United States. He made a short visit to the University of California, Berkeley in 1960. A Guggenheim Fellowship allowed him to spend from August 1962 to September 1963 at the Institute for Advanced Study at Princeton [24]:-

... there are no classes there, only 6 seminars - and a fabulous working environment, with a huge library. There are a hundred houses for visiting members, where I lived that year, attending seminars and doing research; twice a month I went to New York to talk to Steve Smale, who worked at Columbia University. When the year ended, the Guggenheim Foundation renewed my scholarship for another 12 months, which is unusual. So I went to Columbia University and lived in New York; when my period was about to end, I received an invitation to stay at the University. I also had offers from the University of Massachusetts and later from the University of Maryland. I turned them all down and went back to Brazil, but not to IMPA, because I decided to accept an invitation from the University of Brasília.Lima's American colleagues could not understand why he decided to return to Brazil when he had offers of positions in the United States. There had been a military coup in Brazil in April 1964 and it was unclear whether universities would be able to continue to operate. Lima's invitation had come from Zeferino Vaz, the rector of the University of Brasília, who said Lima had been recommended to him by Nachbin and several others. Lima was honoured to have received the invitation and, rather reluctantly because of uncertainty over the military coup, accepted the offer leaving the United States in August 1964 to take up his new position. The director of the Institute of Mathematics at the University of Brasília was Nachbin, but since he did not come to the Institute, Lima was effectively the director. He spent a year there undertaking research and delivering courses but by the middle of 1965 the position had deteriorated. The military regime began to decide on whether they approved appointments of professors. There was a mass resignation of staff from the university.

After leaving the University of Brasília, Lima went with his family to Ceará where he lived for a while without a job. Then he received an invitation to spend six months at the University of Rochester which he gladly accepted. He left his family in Ceará and went to Rochester, New York, where he lived with Moisés Nussenzweig, a Brazilian professor of physics who had left the CBPF in Rio de Janeiro because of persecution by the military dictatorship. After the six months at Rochester Lima was invited, with his family, to spend a year at the University of California, at Berkeley which he did, returning to the IMPA in Brazil early in 1968.

Nachbin was recognised as the outstanding mathematician at the IMPA but Lima and others were not happy with the direction he was taking it. In an attempt to improve the tense situation, Lima accepted an invitation from the Pontifical Catholic University of Rio de Janeiro spending the first half of 1969 there. Lima was then invited back to the IMPA as director and he accepted. This was the first of three spells he spent as director, 1969-71, 1979-80, and 1989-93. When asked in the 2001 interview [4] about the status of the IMPA, Lima replied:-

I think that the IMPA is unique at a world level, not in the sense of being exceptional. It is unique because it is a first world institute in a third world country. It is an institution that, for various reasons, has managed to maintain itself and reach an excellent level, despite never having had an exceptional position or any privilege within the scheme of scientific policy in Brazil. For some time the IMPA was more famous, more respected, outside than inside Brazil. Today this is no longer true. However, its scientific prestige is not reflected, for example, in the prestige of professors who have very low salaries, even in comparison with the salaries of Brazilian federal universities. IMPA salaries are lower and some privileges that teachers have, we don't have. We are not considered teachers. Although it is an institution accredited by the Ministry of Education to offer Master's and Doctoral degrees, the members are not professors, they are researchers.Although Lima made some deep and important research contributions, his greatest achievement was as an author of textbooks. He wrote books at secondary school level, at undergraduate level and at postgraduate level. Let us quote from Paulo Araújo [1]:-

Elon Lages Lima is the author of the best mathematics textbooks that, over the last forty years, have been written in Portuguese. His books in the Projecto Euclides and Matemática Universitaria collections, successively republished by IMPA (National Institute of Pure and Applied Mathematics, Rio de Janeiro, Brazil), not only contributed to the learning of generations of students, but also conveyed to them a taste for elegant exposition, lucid and orderly maths topics. It is worth naming some of these books: in the Projecto Euclides collection, the two-volume Analysis Course (the first one already has eleven editions) and the text on Metric Spaces; and, in the Matemática Universitaria collection, the Linear Algebra manual, where, through its exquisite exposition and original perspective, Elon manages to breathe new life into a subject that the profusion of textbooks has trivialised to the point of irrelevance. Both Metric Spaces and Linear Algebra won the Jabuti Prize awarded by the Brazilian Book Chamber for the best science book published in that country in the respective year (1978 and 1996).More information about 28 of Lima's books, see THIS LINK.

To fulfil his vocation as a writer, Elon has written assiduously, always about mathematics. After the university manuals, in recent years he dedicated his attention to secondary education (equivalent to our secondary education), directing an improvement course for teachers that has been running at IMPA since 1990 and launching, as support for the course, a collection of books, Meu Professor de Matemática, which now has 19 titles, 12 of which he authored (alone or in partnership). They are elementary books, which clarify and deepen the curricular themes of mathematics of this teaching level; their value and usefulness, however, far transcend the immediate purpose for which they were written: any professor or student of mathematics, in any country or educational level, could read them with pleasure and profit (if the language were not an obstacle).

The above quote details the two Jabuti Prizes that Lima was awarded. He received several other honours: an honorary degree from the Federal University of Ceará in 1989 and full membership of The World Academy of Sciences in the same year; the Anísio Teixeira Award from the Ministry of Education in 1991; the National Order of Scientific Merit in the Class of the Grand Cross from the President of the Republic in 2000; an honorary degree from the Pontifical Catholic University of Peru in 2001; and honorary degrees from the Federal University of Campinas and the Federal University of Bahia, both in 2003.

After Lima's first marriage ended, he married Carolina Celano in the 1990s. She was the head librarian at the IMPA. Lima died of pneumonia and at his funeral a mass was celebrated by Paul Schweitzer, a mathematician who received his doctorate from Princeton in 1962 and eight years later became a priest. Schweitzer was a friend who taught at the Pontifical Catholic University in Rio de Janeiro. Lima was buried at the Cemitério da Penitência, in Caju, Rio de Janeiro.

### References (show)

- P V Araújo, Matemática e Ensino, de Elon Lages Lima,
*Gazeta de Matemática, Rio de Janeiro***148**(2005), 44-46. - C Camacho (ed.),
*Elon Lima - Selected Papers*(Springer, 2020). - Ciência perde Elon Lages Lima,
*Diario de Pernambuco*(8 May 2017).

http://www.impresso.diariodepernambuco.com.br/noticia/cadernos/brasil/2017/05/ciencia-perde-elon-lages-lima.html - F J Craveiro de Carvalho, Diálogo em Janeiro com Elon Lages Lima,
*Gazeta de Matemática, Rio de Janeiro***140**(2001), 5-16. - Dies at Rio the mathematician Elon Lages Lima,
*Instituto de Matemática Pura e Aplicada*(10 May 2017).

https://impa.br/en_US/noticias/morre-no-rio-o-matematico-elon-lages-lima-ex-diretor-do-impa-aos-87-anos/ - Editors, Review: Análise geométrica, by Elon Lages Lima,
*Mathematical Reviews*MR0393373**(52 #14183)**. - Editors, Review: Curso de análise. Vol. 1, by Elon Lages Lima,
*Mathematical Reviews*MR0654861**(83h:26002a)**. - Editors, Review: Curso de análise. Vol. 1, by Elon Lages Lima,
*Mathematical Reviews*MR0654861**(83h:26002a)**. - Editors, Review: Espaços métricos, by Elon Lages Lima,
*Mathematical Reviews*MR0654506**(83d:54001)**. - Editors, Review: Introducción a la cohomología de deRham, by Elon Lages Lima,
*Mathematical Reviews*MR2008501. - Editors, Review: Fundamental Groups and Covering Spaces, by Elon Lages Lima,
*Mathematical Reviews*MR2000701**(2005c:57001)**. - Elon Lages Lima,
*Brazilian Academy of Sciences*.

https://www.abc.org.br/membro/elon-lages-lima/ - Elon Lages Lima,
*John Simon Guggenheim Memorial Foundation*.

https://www.gf.org/fellows/all-fellows/elon-lages-lima/ - Elon Lages Lima,
*Ordem Nacional do Mérito Científico*.

https://web.archive.org/web/20080511075931/http://www.abc.org.br/sjbic/curriculo.asp?consulta=elima - Elon Lages Lima, Produção Técnico-Científica,
*Instituto de Matemática Pura e Aplicada.*

https://impa.br/wp-content/scriptLattes/membro-6383153340652483.html - Entrevista com o prof Elon Lima,
*Assiciação Nacional dos Professores de Matemática na Educação Básica*.

https://anpmat.org.br/cafe-com-a-anpmat/entrevista-com-o-prof-elon-lima - B Esteves, Mestre De Mestres: Elon Lages Lima e o estabelecimento de uma cultura matemática no Brasil,
*piauí***129**(June 2017).

https://piaui.folha.uol.com.br/materia/mestre-de-mestres/ - Há um ano, a Matemática perdia Elon Lages Lima,
*Instituto de Matemática Pura e Aplicada*(7 May 2018). - Interview with Elon Lages Lima is part of FGV's Oral History program archive,
*Fundação Getulio Vargas*(10 May 2017).

https://portal.fgv.br/en/news/interview-elon-lages-lima-part-fgvs-oral-history-program-archive - W S Massey, Review: Introdução ás variedades diferenciáveis, by Elon Lages Lima,
*Mathematical Reviews*MR0155332**(27 #5266)**. - Mathematician Elon Lages Lima, former director of IMPA, dies in Rio at the age of 87,
*facebook*(7 May 2017).

https://m.facebook.com/IMPABR/photos/morre-no-rio-o-matemático-elon-lages-lima-ex-diretor-do-impa-aos-87-anosum-dos-m/638161016384507/ - P Maynard, Review: Fundamental Groups and Covering Spaces, by Elon Lages Lima,
*The Mathematical Gazette***88**(512) (2004), 359-360. - R Padilha, Matemático alagoano reconhecido nacionalmente morre aos 87 anos no Rio,
*Portal Gazetaweb.com*(17 April 2020). - M M Peixoto, Review: Cálculo tensorial, by Elon Lages Lima,
*Mathematical Reviews*MR0196644**(33 #4831)**. - M M Peixoto, Review: Cálculo tensorial, by Elon Lages Lima,
*Mathematical Reviews*MR0196644**(33 #4831)**. - Revista Piauí: O matemático que deu profundidade à superfície,
*Instituto de Matemática Pura e Aplicada.*

https://impa.br/en_US/noticias/o-matematico-que-deu-profundidade-a-superficie/ - J Riguet, Review: Topologia dos espaços métricos, by Elon Lages Lima,
*Mathematical Reviews*MR0077109**(17,991b)**. - A M Rodrigues, Review: Introdução à topologia diferencial, by Elon Lages Lima,
*Mathematical Reviews*MR0159341**(28 #2558)**. - R E Stong, Review: Variedades diferenciáveis, by Elon Lages Lima,
*Mathematical Reviews*MR0526597**(80i:57001)**. - T Torres, Morre professor Honoris Causa da UnB Elon Lages Lima,
*University of Brasília*(8 May 2017).

https://www.noticias.unb.br/76-institucional/1489-morre-professor-honoris-causa-da-unb-elon-lages-lima - S Veloso, Elon Lages Lima recebe título de professor honoris causa,
*UnB Notícias, University of Brazil*(26 October 2016).

### Additional Resources (show)

Other pages about Elon Lima:

Other websites about Elon Lima:

### Honours (show)

Honours awarded to Elon Lima

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update February 2023

Last Update February 2023