# Cândido Lima da Silva Dias

### Born: 31 December 1913 in Mococa, São Paulo, Brazil

Died: 15 September 1998 in São Paulo, São Paulo, Brazil

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**Cândido Silva Dias**was a Brazilian mathematician who was the son of Gabriel Antonio da Silva Dias, an electrician engineer who graduated from Escola Politécnica of São Paulo in 1905, and Adília Lima da Silva Dias, a housewife.

Since his childhood he used to play with numbers because his father was an engineer and he enjoyed stimulating Silva Dias to do mathematics. As a result of this time playing with numbers, Silva Dias had an early start with arithmetic. When he started studying at primary school, doing mathematics was something that he found very easy to do. He studied at Barão de Monte Santo Primary School only a hundred metres from his house. The school was well organized with good teachers. After primary school he went to the capital, São Paulo, and started studying at Franco Brasileiro High School which was very liberal and had accessible teachers. Teachers and also the students had the possibility to live at the school, and this was where Silva Dias boarded. He enrolled at Escola Politécnica of São Paulo in February 1932 and studied there until the year of 1934 receiving the surveyor diploma. In the same year he still enrolled in the Mathematics course of the College of Philosophy Science and Languages of the University of São Paulo.

You can read about Silva Dias's own description of his change to mathematics in the interview he gave in 1997 at THIS LINK.

Soon after his graduation he was appointed as second scientific assistant to the Italian mathematician Luiggi Fantappiè and his role was working with exercises of Mathematical Analysis. Afterwards he was promoted to first category scientific assistant working with both theory and exercises in the following year. In 1937, in a Mathematics Seminar, he studied and presented the theory of algebras as developed by Gaetano Scorza. In the same seminar in 1938, he presented the theory of continuous groups applied to differential equations. During his summer vacation of 1938-39, Silva Dias presented a course on Mathematical Analysis which some engineers had requested.

Silva Dias married Odila Leite Ribeiro in 1937; they had four children: Cândido Leite da Silva Dias (born 1938), now retired, Maria Odila Leite da Silva (born 1940), a University Professor now retired, Guilherme Leite da Silva Dias (born 1942), a University Professor now retired, and Pedro Leite da Silva Dias, a University Professor.

In the beginning of 1939, he was in charge of the course in Mathematical Analysis which was part of the first year of the mathematics course. He was appointed to this position by Fantappiè and the Secretary of Education. Silva Dias remained in this position until 1941. In February 1939 he participated in the examination board for the entrance examinations of the first year of the engineering course at Escola Politécnica. He also took part in examination boards in 1942, 1943 and 1945.

By a decree of 21 January 1942 he was appointed to teach the subject Higher Analysis in the mathematics and physics courses in the Faculty of Philosophy, Science and Letters of the University of São Paulo. In July 1942, he presented his work entitled "About the concept of the analytic functional" to the Brazilian Academy of Sciences, which was published in its

*Annals*. In November of the same year, he defended his doctoral thesis according to the regulation of the Faculty of Philosophy, Science and Letters (FFCL) at the University of São Paulo and was awarded the mark ten. In 1943 he started teaching Complements of Geometry and Higher Geometry. In August 1943 Silva Dias took part in the examining board for the doctoral examinations of the graduate Benedito Castrucci (1909-1995). On 6 July 1943 Silva Dias presented the work "Application of the theory of the analytical functionals to the study of a solution for a differential equation of infinite order" to the Brazilian Academy of Sciences, communicated by Francisco de Oliveira Castro, which was published in its

*Annals*. In 1945 he became active in the foundation of the Mathematical Society of São Paulo in which he was elected vice-president. In the same year he attended the classes of Oscar Zariski (on Algebraic Geometry) and André Weil (on Differential Forms, de Rham's Theorems, and Hilbert spaces). He also attended Professor André Weil's college courses in 1946 and 1947 as well as professor Jean Delsarte's college extension courses in 1949 and 1950.

In 1946 Silva Dias was appointed professor of infinitesimal calculus at the newly founded College of Industrial Engineering. In 1947 he was hired to teach Complements of Geometry and Higher Geometry in the Faculty of Philosophy, Science and Letters of the University of São Paulo. During the winter vacation, he participated in a conference and gave a lecture on the Theory of Proportion. In February 1948 he went to the United States due to the fact that he won a one-year scholarship from Guggenheim Foundation. He was nominated for the scholarship by professors André Weil, Jean Dieudonné and Marshall Stone. In March 1948 he was nominated Research Fellow in Mathematics by the University of Harvard and he also studied with professor Henri Cartan attending the course given by him on Algebraic Topology. In the same year

*Theorems of Existence in Differential Equations*was published. In July 1948 Silva Dias was transferred to the University of Chicago and was nominated "Research Associate" in the mathematics department. In this university he worked with professor André Weil and he participated in two conferences on Integral and Relative Geometry in Shiing-shen Chern's work, one being Integral Geometry in Klein's spaces and another on the Theory of Analytical Functional of Fantappiè. He also attended the courses: Algebraic Topology with professors Edwin Spanier and Saunders Mac Lane, Banach's spaces with professor Irving Segal and Integral Geometry with Professor Luis Santaló. In the early April 1949, he went to Princeton in New Jersey, where he was nominated as a member of the Institute for Advanced Study. Silva Dias attended a seminar on "Fiber Spaces" with Professor Shiing-shen Chern and conferences with Professor Norman Steenrod on Algebraic Topology. He undertook some research on non-linear analytic functionals and started some research that would be useful for his thesis that he presented in a contest afterwards.

In December 1949, Cândido was elected President of the Mathematical Society of São Paulo. On this occasion he gave an address on the Teaching of College Mathematics in the USA, particularly at the University of Chicago. In November 1949 he participated in the doctoral examining board at the University of São Paulo specifically that of Paulus Pompéia (1911-1993). In August 1950, Silva Dias returned to the United States to represent Brazil together with Professor Leopoldo Nachbin at the Union Conference that discussed the statutes of an International Union of Mathematics that had just been founded. Soon after, he participated in the International Congress of Mathematicians which was held in Harvard. In November 1950, he was elected President of the Mathematical Society of São Paulo and presented his work on non-linear analytic functionals at the Second Annual Reunion congress of the Brazilian Society for the Science which was held in Curitiba, Paraná, Brazil. In April and December of the same year he participated in the doctoral examining board of professors Edison Farah and Luiz Henrique Jacy Monteiro.

In June 1951, Silva Dias presented his work on analytic functional structure to the Brazilian Academy of Sciences. In July of the same year, he was invited for the position of director of research of the mathematical research sector of the National Council for Scientific and Technological Development (CNPq). During his period of office the Institute of Applied and Pure Mathematics was founded.

In 1960, he participated in the foundation of the Institute of Mathematical Research of the University of São Paulo (USP), of which he was appointed as the director. In addition, he was the director of the Faculty of Architecture and Urbanism at the University of São Paulo. In 1962, he became member of the Council of the National Council for Scientific and Technological Development. In 1970, he was nominated director of the Institute of Mathematics of USP, constituted by the reform of the university in 1969.

He retired from the University of São Paulo in 1978 and in the following year he became professor of the Institute of Mathematics of the Federal University of São Carlos and thereafter retiring in 1990.

For information about Silva Dias's career, his interaction with the Bourbaki mathematicians and much more, see THIS LINK.

**Article by:** Paulo Cesar Xavier Duarte.

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