Gilberto Francisco Loibel

Quick Info

24 May 1932
São Paulo, Brazil
13 November 2013
São Paulo, Brazil

Gilberto Francisco Loibel was a Brazilian mathematician who played a major role in the development of mathematical sciences in Brazil. He supervised 19 Master's dissertations and 8 Doctoral theses.


Gilberto Francisco Loibel was the son of Franz Loibel and Gertrud Loibel Reyar who were both chemical engineers. Franz Loibel, born in Germany on 30 July 1891, married Gertrud Reyar, born in Germany in about 1894. They worked in Magdeburg, Germany where their first child Gerda Angelica Loibel was born on 13 January 1928. Maria Aparecida Sores Ruas writes [11]:-
Gilberto Francisco Loibel was the son of Franz Loibel and Gertrudes Loibel Reyar, German chemical engineers who came to São Paulo in 1929, during the crisis in Europe. His only sister, Angelica, was born in Germany a few years earlier. The family returned to Germany in 1939, shortly before the outbreak of World War II, which took place in September of the same year. The family returned to Brazil in 1947.
In fact Dr Gertrud Loibel (age 36) and Gerda Angelica Loibel (age 2) sailed from Hamburg, Germany, to Brazil on the ship General Osorio leaving on 3 April 1930. They give their final destination as Santos, São Paulo, Brazil. Dr Franz Loibel had travelled to Santos, São Paulo, before his wife and daughter. He sailed from Hamburg to Brazil, with final destination Santos, São Paulo, on the ship the Antonio Delfino leaving Hamburg on 22 August 1929. After the family spent the years of World War II in Germany, Franz Loibel and Gerda Angelica Loibel returned from Germany to Rio de Janeiro, Brazil arriving on 27 May 1948. We have not found the dates on which Gertrud and Gilberto returned to Brazil from Germany after the end of World War II but assume they travelled around a couple of months after Franz and Gerda.

Gilberto's primary education was in Germany and he also began his secondary education there. This was during World War II when conditions were extremely difficult. After the family returned to Brazil in 1948, he attended the Instituto de Educação in Jundiaí, São Paulo. This school began as an independent school in around 1930 but became a State school in September 1945. When Gilberto attended, it was actually named Colégio Estadual e Escola Normal of Jundiaí, only adopting the name Instituto de Educação in 1953.

While at this college, Loibel met Izette Alves Coelho; they became close friends and later married. Coelho had been born in Botucatu, Brazil on 18 December 1932. Loibel completed his studies at the college in 1951 and, in the following year, he was ranked first in the entrance examination for the bachelor's degree in Mathematics at the Faculty of Philosophy, Sciences and Letters of the University of São Paulo. Let us give a little background to the Department of Mathematics at the University of São Paulo.

The University of São Paulo was founded in 1934 and professors were brought to São Paulo from France, Italy and Germany. The first mathematics professor that was brought was Luigi Fantappiè who travelled to Brazil from Italy in 1933. Cândido Silva Dias began studying mathematics at the Polytechnic School in 1932 and became one of Fantappiè's first students. In 1934 Omar Catunda was appointed as Fantappiè's assistant and they collaborated on starting up the Mathematics Subsection of the Faculty of Philosophy, Sciences and Letters at the University of São Paulo with Fantappiè as its head. It later became the Institute of Mathematics and Statistics. Cândido Silva Dias was appointed as Fantappiè's assistant in 1937 and taught in the Mathematics Department for 54 years retiring in 1990. In 1945 Elza Furtado Gomide became Catunda's assistant and, a couple of years later, she took over teaching Catunda's Mathematical Analysis course. One of the students taking this course was Carlos Benjamin de Lyra, who was an undergraduate between 1946 and 1950. Luiz Henrique Jacy Monteiro was also an important figure, having been an undergraduate at the University of São Paulo, then awarded his doctorate by university in 1951, and Leopoldo Nachbin, although in the Department of Physics at São Paulo at this time, was another outstanding mathematician.

While studying mathematics at the University of São Paulo, Loibel was taught by Omar Catunda, Elza Gomide and Cândido Silva Dias among others. He graduated from the Faculdade de Filosofia, Ciências e Letras of São Paulo with a bachelor's degree in Mathematics in 1955. In August 1956 he was appointed as an Instructor in Geometry at the Department of Mathematics of the School of Engineering of São Carlos, University of São Paulo. Occupying the Chair of Geometry at São Carlos was combinatorial topologist Achille Bassi who was [8]:-
... born in Italy, and arrived in Brazil in 1939 at the invitation of the Brazilian government to teach at the National Faculty of Philosophy, part of the University of Brazil, located in Rio de Janeiro. He went through other Brazilian educational institutions until, in 1953, he received an invitation to organise the Department of Mathematics at the School of Engineering of São Carlos, University of São Paulo. In this institution, he also taught, and supervised undergraduate and graduate students ...
We obtain more information about the Department of Mathematics at São Carlos from [5]:-
The organisation of the Department of Mathematics was under the responsibility of Professor Achille Bassi, who endeavoured to acquire a bibliographic collection and hire qualified researchers to form a research centre in Mathematics. In this way, the Department was created with post-graduate courses. Professor Achille Bassi's determination to create an excellent library gave rise to one of the best libraries in the country in the area of Mathematics ... The Department of Mathematics was then formed by professors Achille Bassi, Jauréz Cecconi and Ubaldo Richard and some engineers who came from the Polytechnic School on a part-time basis ... Professor Jaurez Cecconi was an analyst. His research papers on Calculus of Variations and Optimisation were published between 1951 and 1985, mainly in Italian journals. Professor Ubaldo Richard was also an analyst. His research papers on Differential Equations and Integral Equations were published between 1940 and 1982, mainly in Italian journals.
Loibel began undertaking research for a Ph.D., advised by Achille Bassi and took postgraduate courses taught by Bassi, Jauréz Cecconi and Ubaldo Richard. He also regularly attended postgraduate seminars run by Carlos Benjamin de Lyra, at the Faculty of Philosophy, Sciences and Letters at the University of São Paulo and attended the Algebraic Geometry Seminars at the same institution run by Luiz Henrique Jacy Monteiro. During this period, Loibel married Izette Alves Coelho in 1958. She became a mathematician writing the Master's Thesis Curvas planas e aplicações excelentes in 1970 which she submitted to the Universidade de São Paulo, São Carlos. Gilberto and Izette Loibel had several children including Selene Maria Coelho Loibel. Selene wrote the Master's thesis Uso de métodos Bayesianos para modelos com pontos de mudança in 1998. She dedicates the thesis "To my parents, Izette and Gilberto and to my son Diog." She became a professor of statistics at the Universidade Estadual Paulista.

In 1959 Loibel was awarded a doctorate for his thesis Sobre Quase Grupos Topológicos e Espaços com Multiplicação . In fact he had published the paper Sobre Quase Grupos Topológicos in 1958 which consisted of the first three chapters of his thesis. Reviewing this paper, Federico Sioson writes [12]:-
This paper constitutes the first three of the four chapters of the author's doctoral thesis. The first of these is an exposition of well-known results in (algebraic) quasi-groups ... A quasi-group with a multiplicative identity is a loop. The remaining two chapters are devoted to a development of certain fundamental notions, adaptations from topological groups, for topological quasi-groups. A topological quasi-group [loop] is a quasi-group [loop] endowed with a topology under which its operations are continuous; or what amounts to the same thing, a topological space which admits a compatible quasi-group [loop] structure. ... The main theorems of the second chapter include (1) the observation that a topological space which admits a quasi-group structure also admits a loop structure, (2) a characterisation of the notion of a fundamental system of neighbourhoods of the identity of a Hausdorff loop, (3) a homomorphism theorem for topological loops, and (4) a necessary condition for two topological loops to be locally isomorphic.
Also in 1959 he published the paper Multiplications on products of spheres. J Frank Adams writes [1]:-
The author studies continuous multiplications with identity defined on a Cartesian product of spheres. He determines when such multiplications exist; when they exist, he classifies them in terms of homotopy groups of spheres. He then states, for example, that a homotopy-commutative product can exist only on a product of circles.
In 1960 Loibel was promoted to Assistant to the Chair of Geometry at São Carlos. He was awarded a CAPES scholarship to support a postdoctoral internship at the University of California, Berkeley, USA. CAPES is a Foundation within the Ministry of Education in Brazil whose central purpose is to coordinate efforts to improve the quality of Brazil's faculty and staff in higher education through grant programmes. CAPES is particularly concerned with the training of doctoral and postdoctoral candidates. Loibel and his wife left São Paulo and arrived in New York on 25 September 1960 on their way to Berkeley.

Loibel's host at Berkeley was Edwin Spanier who had been appointed to Berkeley one year earlier and had begun building up a strong group working in geometry and topology by several appointments of topologists. During the visit, Loibel had contact with leading topologists and geometers. He attended Topology Seminars, in conjunction with Stanford University, took a Differential Geometry course given by Shiing-shen Chern and a 'Stratified Sets' course given by René Thom. Loibel remained in Berkeley until 1962 when he returned to Brazil and was promoted to Regent Professor in the Department of Mathematics in the São Carlos School of Engineering and became Head of Mathematics. He organised a Topology Seminar in the Department which studied topics such as the Theory of Homotopy and Fibres according to Jean-Pierre Serre, Multilinear Algebra and Differentiable Manifolds, and Cellular Complexes. He also set up a research group on Singularities in his department.

In 1962 he published Über topologische Lösungssysteme . Karl Heinrich Hofmann writes in the review [6]:-
The systems mentioned in the title are topological spaces with a continuous multiplication with left unit such that the equation xa = b is continuously uniquely solvable for x. Some general (and, on the whole, superficial) features of topological group theory carry over to these structures, e.g., the standard statements about substructures, continuous and open homomorphisms, separation properties, and connectivity. (For example, the closure of a subsystem is a subsystem. Open subsystems are closed. Connected systems are generated by each neighbourhood of the left unit, etc.) A useful observation (even in the case of groups) is this: If a system S is such that every 1-1 continuous map of S×SS \times S onto itself is a homeomorphism, then the continuity of multiplication implies the continuity of the solution, and conversely (the condition is satisfied if S is compact or is a manifold). A general notion of uniformity is introduced to fit the purpose of invariantly uniformising a system. Most of the results in the theory of covering structures are flexible enough to hold for the systems considered. However, an example is given of a system on the 2-torus which is covered by a system on the plane but is not covered by any system on the cylinder.
In 1965 Loibel ended his time as Head of Mathematics and from October 1965 to July 1966 he was a Visiting Professor at the Universidad Central de Venezuela. There he supervised the work of two students working for the equivalent of a Master's Degree.

Before going to Venezuela he attended the Fifth Brazilian Mathematics Colloquium was held from 4 - 24 July 1965 in the city of Poços de Caldas. The coordinator of the Colloquium was Luiz Henrique Jacy Monteiro, two postgraduate courses were given, and five advanced courses were given including 'Obstruction Theory' by Edwin Spanier and 'Diophantine Approximation' by Serge Lang. The Sixth Brazilian Mathematics Colloquium was held from 2 - 22 July 1967, also in the city of Poços de Caldas, and again the coordinator of the Colloquium was Luiz Henrique Jacy Monteiro. Loibel gave a postgraduate course on 'Singularities' and postdoctoral courses were given by Leopoldo Nachbin and Israel Herstein. The Seventh Brazilian Mathematics Colloquium, 6 - 26 July 1969, was again held in Poços de Calda. Loibel was the coordinator of this Colloquium and among courses given we mention 'Fundamental Group and Covering' by Carlos Benjamin de Lyra, 'Galois Theory' by Jacy Monteiro and 'Invariant Subspaces' by Paul Halmos. During this Colloquium, the Brazilian Mathematical Society was founded. The meeting to found the Society was attended by 162 mathematicians and was chaired by Loibel. The course on Singularities that Loibel taught at the Sixth Brazilian Mathematics Colloquium in 1967 was written up as the book Singularidades das aplicações diferenciáveis and published by the Instituto Nacional de Matemática Pura e Aplicada (IMPA).

As we saw above, the Mathematics Department of the University of São Paulo at São Carlos had been set up in 1953 by Achille Bassi as part of the São Carlos Engineering School. Loibel had worked in that Department from 1956 but there were problems caused by the fact that it was part of an engineering school. Loibel said [3]:-
... we were suffocated inside the São Carlos School of Engineering, obviously because the important thing was engineering. Mathematics and numerical analysis were in the background, they were suffocated inside. The issue was not only related to funding for staff and laboratories, but also for the library.
For further details of this interview, see THIS LINK.

In 1970 the Computational Science and Statistics Department was set up, also in the São Carlos School of Engineering, but in 1971 the Mathematical Science Institute of São Carlos (ICMC) was founded by joining together the Mathematics Department and the Computation Science and Statistics Department, making them independent of the Engineering School. Maria Aparecida Sores Ruas, a professor at the University of São Paulo who had been a student of Loibel's, wrote [11]:-
Together with a small group of pioneering professors, Loibel played a fundamental role in the creation and consolidation of the then Institute of Mathematical Sciences of São Carlos.
There had been different views on the creation of the Institute [8]:-
According to Gilberto Francisco Loibel, at that time there were groups of professors who sympathised with various different positions regarding the creation of an Institute. Some of them, including Professor Loibel, defended the idea of bringing together the Basic Sciences in a single Institute separate from the Engineering School. However, this was not the position that the head of the Mathematics Department defended, as he was thinking of creating an Institute solely for his area.
Ruas gave further details of Loibel's contributions in [9]. She said that:-
... in addition to being the person who introduced the Theory of Singularities in Brazil, Loibel was the founder of the Grupo de Singularidades de São Carlos. He supervised the first master's and doctoral students in this area, mainly from 1970 to 1985. Many of the dissertations and theses supervised by Loibel were pioneers in the topics covered, thanks to the supervisor's brilliance. He was one of the most brilliant mathematicians I ever met ...
On 11 January 1971 Loibel was elected to the Brazilian Academy of Sciences. From 1971 to 1976, Loibel coordinated the Graduate Programme in Mathematics at São Carlo. He became a full professor at the ICMC in 1981 defending his thesis L-Equivalência e Bordismo Ambiental de Subvariedades on 4 September 1981. He was a founding member of the Academia de Ciências do Estado de São Paulo (ACIESP) when it was founded on 8 October 1974. This Academy organises scientific meetings, publishes books and proceedings of meetings, supports the Mathematical Olympiads, and supports students through scholarships. In this Academy he was elected several times as a representative of the Mathematics area on its Board of Directors and was Regional Director of ACIESP in the city of São Carlos. He was regional coordinator of the 1st Brazilian Mathematics Olympiad and 2nd Brazilian Mathematics Olympiad which took place in 1979 and 1980. He was vice-director of the ICMC from 1982 to 1986. He was also coordinator, in 1988, of the 11th Mathematics Olympiad of the State of São Paulo, an event that was sponsored by the ACIESP. He retired from the ICMC in São Carlos in 1987.

After retiring from São Carlos, he was a professor at the Institute of Geosciences and Exact Sciences at the Rio Claro campus of the University of São Paulo from 1987 to 2002.

The Federal Institute of Mato Grosso do Sul has its main campus in Campo Grande and nine other campuses, one of which is in Coxim. On 9 - 10 April 2013 a Mathematics Colloquium was held which was open to the community. The lecture "What does a mathematician do?" was given by Gilberto Francisco Loibel while the final talk about the outlook for young researchers in mathematics was given by his wife Izette Alves Coelho Loibel [2]:-
The sum of the couple's experience, is a career of seventy years. Gilberto even presided over the founding meeting of the Brazilian Society of Mathematics, in 1969, and is a founding member of the Academy of Sciences of the State of São Paulo. The two were part of the construction process for research in the city of São Carlos, in the interior of São Paulo. "In addition to promoting and encouraging academic activity in Coxim, the colloquium aims to share the experience of the two speakers on how to create an academic culture for a city," emphasises Professor Tadeu Cândido, coordinator of the event.
One year after Loibel died, the ICMC inaugurated a space in his honour [7]:-
The Institute of Mathematics and Computer Sciences (ICMC) of the University of São Paulo, in São Carlos, inaugurated the Professor Loibel hyperspace on 20 November 2014, located in the opening of the Achille Bassi Library. The tribute took place one year after the death of Professor Gilberto Francisco Loibel, one of the main drivers of the study and research environment in mathematics in the interior of the State of São Paulo.

References (show)

  1. J F Adams, Review: Multiplications on products of spheres, by Gilberto Francisco Loibel, Mathematical Reviews MR0107237 (21 #5962).
  2. Câmpus Coxim do IFMS promove evento sobre matemática, ediçaoms (8 April 2013).
  3. Entrevista com o professor Gilberto Loibel, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (29 May 2012).
  4. Gilberto Francisco Loibel, Academia Brasileira de Ciências.
  5. Histórico, Departamento de Matemática, São Carlo.
  6. K H Hofmann, Review: Über topologische Lösungssysteme, by Gilberto Francisco Loibel, Mathematical Reviews MR0142680 (26 #249).
  7. ICMC inaugura espaço em homenagem ao professor Gilberto Francisco Loibel Universidade de São Paulo (27 November 2014).
  8. A Leme da Silva and P Z Táboas, A Contribuição de Achille Bassi como Gestor da Matemática no Brasil, Universidade Estadual Paulista.
  9. Morre professor do ICMC que trouxe para o Brasil a Teoria de Singularidades, Universidade de São Paulo (18 November 2013).
  10. C Pereira da Silva, Início e consolidação da pesquisa em matemática no Brasil (Edgard Blücher, 2022).
  11. M A S Ruas, Professor Loibel - contribuição acadêmico-científica, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo (2014),
  12. F M Sioson, Review: On topological quasi-groups (Portuguese), by Gilberto Francisco Loibel, Mathematical Reviews MR0177054 (31 #1318).
  13. Três docentes do ICMC receberão título de Professor Emérito, Universidade de São Paulo (14 April 2015).
  14. Various details of the Loibel family,

Additional Resources (show)

Honours (show)

Honours awarded to Gilberto Loibel

  1. Speaker at the Brazilian Mathematics Colloquium 1963

Written by J J O'Connor and E F Robertson
Last Update November 2022