In 1961 the Cinvestav (Centro de Investigación y de Estudios Avanzados) was founded following need for a formal school for graduates of the IPN (Instituto Politécnico Nacional). However, it was created as an institution independent of the IPN due to the efforts of Arturo Rosenblueth, its first director. From the outset Dr. Rosenblueth set himself the task of ending the multiemployment which was characteristic of academia at that time, furnishing decent salaries to the personnel. Among the guidelines of the new institution, he established first-class research and the highest level of teaching at the Master's and doctorate level.
Mathematics was one of the first departments with which the Center began its activities. Its creation responded to the need for, in the words of José Adem, "mathematical research to radiate its beneficial effect on the other branches of science." The Department of Mathematics began its work in the buildings of the IPN; two years later it moved to the upper floor it was to occupy for about 32 years. Its first Chairman was José Ádem, recognized among one of the most eminent Latin American mathematicians. His research had placed him on the frontiers of algebraic topology. There could not have been a better beginning. Ádem had graduated from the National Engineering School and had done graduate study in mathematics in the Faculty of Sciences of the U.N.A.M. (1946-1948). He earned his doctorate at Princeton University in 1948 under Norman Steenrod, at a time when it was necessary to go abroad to continue with graduate studies. He returned to México in 1953 as teacher and researcher of the IMATE (Institute of Mathematics of the U.N.A.M). His doctoral thesis was one of the most important works in algebraic topology of the 1950's, now recognized as the golden age of algebraic topology. The Adem relations, his main contribution, belong forever to the history of mathematics of the 20th century.
In 1960, Ádem tried to have Carlos Ímaz and Samuel Gitler, who recently earned their doctorate abroad, accepted to work in the IMATE. However, both were rejected. This was one of the main reasons which led him to seek new options for young Mexican mathematicians. Thus in 1961 Carlos Ímaz and Samuel Gitler became the first associate professors hired by the Mathematics Departent, and Francisco Tomás Pons, who had begun his doctoral thesis independently, entered as an instructor.
In those days, in the 1960's, algebraic topology was at its peak, and one of the most important questions was the immersion and embedding problem of manifolds in Euclidean spaces. José Ádem y Samuel Gitler obtained results which promptly positioned them at the forefront of this field. Since publication in mathematics is quite slow (in general, it takes at least a year to produce an article and another for it to appear in print), researchers of the Mathematics Department began an intense exchange of letters (as email had not yet appeared) with a large number of topologists who had studied this problem and invited them to visit the Cinvestav, succeeding in having almost all of the important topologists come to Mexico.
In 1961 the ESFM (Escuela Superior de Física y Matemáticas of the IPN) was created, with professors and students of the Cinvestav. The ESFM would come to be the most important source of students for the Mathematics Department, which at that time had five excellent and enthusiastic Master's students: Silvia de Neymet de Christ and Manuel Meda Vidal (Mexican), Francisco Oliva y Óscar Valdivia (Peruvian), and José Luis Arraut (Colombian); four of them shortly obtained their doctorate.
The first international visit was by Francois Bruhat, an eminent French algebraist who helped Francisco Tomás polish his research results. After four months, the first doctoral student of the the Department and the first doctoral graduate of the Cinvestav was Francisco Tomás, under Bruhat's direction. In 1963, Zdeneck Vorel of the Czechoslovakia Academy of Sciences joined the Department, and began a very intensive and fruitful collaboration with Carlos Ímaz in differential equations and analysis. That summer, four distinguished professors arrived as visitors to the Cinvestav: B. Durork in number theory, P. A. Griffiths in algebraic geometry, J. J. Kohn and M. Kuranishi in complex analysis.
Francisco Tomás Pons
First graduate of the Department of Mathematics
With this academic faculty, a Master's and doctoral program in mathematics similar to the best universities in the world was prepared for the first time in Mexico. In a few years, not only were highest-level courses offered, but students recieved their Master's and doctorate with theses which were competitive with those of older universities of much greater tradition.
In 1964 Arturo Fregoso in álgebra and Peter Seibert in differential equations joined as associate professors. That summer four professors visited the Cinvestav, among them I.M. Singer y D.C. Spencer.
Dr. Guillermo Restrepo joined in 1965 to strengthen the area of analysis. That summer five professors visited the Cinvestav, among them K. Borsak, M. Mahowald, and E. Spanier in the area of algebraic topology.
The Department's faculty grew in 1966 with Carlos Perelló in the area of dynamical systems and José Luis Arraut, one of the first doctorates of the Cinvestav, in differential geometry. That summer N.E. Steenrod and B. Sanderson in topolgy and J. Hale in differential equations arrived as visitors. Also, four students finished their Master's, among them Juan José Rivaud and Eugenio Filloy, and three students received their doctorate.
In 1967, M. Mahowald, E. Spanier, and C.T.C. Wall came as visiting professors, the latter as an exchange professor with the London Royal Society. Also, Samuel Peder and Byron Drachman joined as associate professors.
The events of 1968 greatly affected the personnel of the Department of Mathematics to the extent that the intensity of research was reduced and almost paralyzed. However, exchange activities were kept up and J. Milgram was hired as a visiting professor.
In 1969, K.Y. Lam arrived at the Cinvestav as a visiting professor, and Adalberto García-Máynez in point-set topology and Enrique Ramírez de Arellano in complex analysis joined the faculty.
Warren Ambrose and Richard Griego came as visiting professors in 1970. During the summer E. P. Peterson, E. H. Brown, R. Sezarba and W. Browder joined as well.
In the summer of 1971, the Department of Mathematics organized the II Latin American School of Mathematics (ELAM), with the presence of Raoul Bott, William Browder, Albrecht Dold, Louis Nirenberg, Joseph J. Kohn, Ioan James, and Samuel Gitler as teachers. Forty 40 U.S. students, 30 Latin Americans and 30 Mexicans attended. Many of these students began to excel as mathematicians about 10 years later.
José Ádem was Department Chairman until 1971.
In 1971, the Department of Mathematics had a faculty of nine professors, six of them full-time professors: Ádem, Gitler, Feder and García-Máynez in topology, Ímaz and Perelló in differential equations, and three associates: Ramírez de Arellano (complex analysis), Filloy (differential topology), Rivaud (analysis).