José Adem's admittance speech to El Colegio Nacional

On 14 June 1960 José Adem became a member of El Colegio Nacional which is a public institution dedicated to the dissemination of scientific, artistic and humanistic culture. He gave the following admittance speech on the history of the mathematical movement in Mexico which was printed as a pamphlet by El Colegio Nacional in 2012.

José Adem Chaín: Admittance speech to El Colegio Nacional (14 June 1960).

A history of the mathematical movement in Mexico to 1960.

I arrive today with deep emotion to this welcoming House. My election as a Member of the National College has been the most pleasant and profound of surprises. Surprise not only for me, but also for my mathematical colleagues, with whom I have been so actively and fruitfully linked in recent years. The nature of our work apparently closes some doors that are more accessible to other specialists, but this does not mean that there is not a decided interest among us in everything related to culture in general and the development of our country. I take the great honour that is now given to me as both an award and an encouragement to a team of scientific workers of which I am a part.

My admission to the National College means, in this way, not so much a prize awarded for the work of an individual person; rather, it represents the recognition obtained for the hard, persevering and quiet work of the mathematicians who have emerged in Mexico in recent decades.

In expressing gratitude for the high distinction granted to me, I do not do so in a personal capacity; I do so on behalf of my colleagues, to whom I owe so much and with whom I identify not only the purpose of advancing the Mexican mathematical contribution, but also that of intervening with all our strength and enthusiasm for the progress of science in our country.

I feel a bit like a fish out of water tonight. If I were allowed to operate in my own milieu, I would prefer to use the blackboard, and express in the peculiar language of the mathematician some of the ideas or themes on which I work. But I consider that, even if this were easier for me, it would create certain obvious difficulties within a non-specialised public. Allow me then to jump out of my own milieu, and attempt a succinct and incomplete history of the mathematical movement in our country.

The current structure of the National University, as is well known, was started by Justo Sierra in 1910. In that same year, he founded the School of Advanced Studies, in order to provide higher education in sciences and arts to graduates of high schools and professionals. The dominant tendencies at that time directed him towards philosophy, letters and biology.

In those years and until 1932, mathematical activities were reduced to teaching, mainly, at the National Preparatory School and at the National School of Engineers.

From this period, the most distinguished professor is undoubtedly Sotero Prieto, a highly talented self-taught mathematician who managed to awaken in a group of professors and students great concern and enthusiasm for research and the study of higher mathematics, in an environment hitherto unfavourable for its development.

Higher mathematics classes were not taught and, as exceptional cases, we can mention a conference on Analytical Functions, in 1912, and a winter course on Kinematic Geometry and Relativity, in 1924, offered by Sotero Prieto at the School of Advanced Studies.

There was great confusion about the trends in contemporary mathematics, the existence of specialised journals was ignored or, simply, their level was too high for there to be interest in them. He desperately rummaged through books, trying to find a way to the top and it seemed inaccessible, giving the impression of needing superhuman efforts to reach it. It was the insurmountable wall of the mathematical production of several centuries, through which it was a question of traversing rough paths, taken at random. There was a lack of orienting guides that indicated the quick shortcuts that rapidly lead to the frontier of knowledge.

One of Sotero Prieto's most enthusiastic colleagues was Alfonso Nápoles Gándara, who in 1920 began as a mathematics teacher. Ten years later, in 1930, he is chosen, together with Arturo Rosenblueth, as one of the first two fellows of the Guggenheim Foundation in Latin America.

Highly impressed with the large number of innovative courses that he found at the Massachusetts Institute of Technology and at Harvard University, many of them never before studied in Mexico, Nápoles Gándara set himself the goal of learning as many subjects as possible in order to bring them to our country. In just 18 months and through an extraordinary effort, he managed to internalise himself in a large number of topics, including Mathematical Analysis, Differential Geometry, Tensor Calculus, Fourier Series and the Theory of Functions.

The lectures that he gave upon his return became the main basis for training a group of young higher mathematics teachers who would later constitute the physical-mathematical faculty of our Faculty of Sciences.

The effort of Nápoles Gándara did not fall in a vacuum. At the National University of Mexico, and thanks to the great cultural vision of one of the founding members of the National College, Maestro Antonio Caso, the Science Section was founded in 1932 within the Faculty of Philosophy and Letters, the Science Section that operated for three years, and where the classes of Rational Mechanics and History of Mathematics were taught by Sotero Prieto, Introduction to Mathematical Analysis and Differential Geometry by Nápoles Gándara, and Introduction to Theoretical Physics by Alfredo Baños, Jr. These were the first higher Mathematics courses to be offered on a regular basis.

In 1935 the Faculty of Physical and Mathematical Sciences, as it was then called, was created, made up of the following three sections: the School of Physical and Mathematical Sciences, the National School of Engineers and the National School of Chemical Sciences. In the School of Sciences studies were offered leading to qualifications for science teachers and Master degrees in Physics and Mathematics. In this way, linked to the needs of the Schools of Engineering and Chemistry, the School of Physical and Mathematical Sciences operated for four years.

Once again it was Antonio Caso who insisted on the need to recognise the intrinsic importance of pure studies in the different branches of science. In a speech he gave on 12 October 1938, at the Bolívar Amphitheatre of the National Preparatory School, he said that it was a shame that the National University of Mexico did not have a Faculty of Sciences. It was partly due to his criticism that, at the end of 1938, the Faculty of Sciences was created at our University, which began to function in 1939 with the structure it currently has: Department of Mathematics, Department of Physics and Department of Biology.

Parallel to teaching, research began to be organised when in 1932, and at the initiative of a group headed by Sotera Prieto, Nápoles Gándara, Jorge Quijano and Mariano Hernández, the Section of Mathematics and Theoretical Physics was formed at the Antonio Alzate National Academy of Sciences. The weekly sessions that were held for several years were one of the first stimuli received by mathematical research in Mexico. Several professors participated in this mathematical seminar, as well as a group of distinguished students of Sotera Prieto and Nápoles Gándara.

Manuel Sandoval Vallarta, the first Mexican physicist who managed to win a scientific name abroad, a professor at the Massachusetts Institute of Technology at the time, was a counsellor and active participant at the Alzate Seminar every summer. It was in this seminar, in 1934, where for the first time in Mexico a foreign mathematician, Dirk J Struik, also from the Massachusetts Institute of Technology, was invited to develop a series of lectures on modern mathematics.

In 1935, the death of Sotera Prieto painfully surprised his colleagues and students. His wisely planted seed had germinated, the tree was beginning to blossom, progress could not be stopped. In 1939, when the Faculty of Sciences, the Institute of Physics, and later the Institute of Mathematics were founded, the work of the old Alzate Seminary was transferred to these new institutions.

It was at this time that Luis Enrique Erro, founder of the Tonantzintla Astrophysical Observatory, stood out as a great promoter of science in Mexico. To inaugurate the Observatory, he organised the International Astrophysics Congress that was held in Tonantzintla, Puebla, on 16 February 1942. In addition to Mexican specialists, a host of first-rate foreign scientists participated in this event. This Congress produced great benefits in our scientific environment. The recently created Institute of Mathematics received the sympathy, support and help of several of those attending the Congress. In this regard, G D Birkhoff and H Shapley deserve special mention.

Inspired by the Congress of Astrophysics, the members of the Institute of Mathematics organised, with great success, the First National Congress of Mathematics, held in the city of Saltillo in November 1942.

One of the proposals of the Saltillo Congress was the following:
The First National Congress of Mathematics unanimously approves the creation of the Mexican Mathematical Society, with the main purposes of maintaining interest in mathematical research and seeking the union and cooperation of professors of exact sciences, and of Mexican professionals and intellectuals, to achieve the progress of this science in our country.
Shortly after, in Mexico City, on 30 June 1943, the Mexican Mathematical Society was founded, initially consisting of 131 founding members.

Since its foundation, the Society has been concerned with improving and modernising the teaching of mathematics in our country, which is still deficient today, mainly in elementary, secondary and high schools.

With the double purpose of stimulating interest in research and trying to raise the scientific level of provincial universities, the Society has organised assemblies and congresses, such as those held in Cuernavaca, Guanajuato, Toluca, Guadalajara, Monterrey, Veracruz, San Luis Potosí, Hermosillo, Oaxaca, Jalapa and Mexicali.

The Society maintains two periodical publications: the Revista Matemática, dedicated to the diffusion and dissemination of mathematical ideas, and the Bulletin of the Mexican Mathematical Society, devoted to the publication of research papers.

In 1960, with barely 18 years of work, for its part, the Institute of Mathematics has managed to organise and direct, on a professional basis, mathematical research in our country. Its team of researchers currently covers a broad mathematical front, such as that made up of mathematical logic, algebraic geometry, topology, analysis, differential geometry, differential equations, probabilities and statistics.

A specialised library, indispensable for the researcher, has been formed, with nearly 5,000 volumes of mathematical works and several complete collections of journals. In addition, journals published by other research centres are periodically received.

The research works carried out by the members of the Institute have been published in the Bulletin of the Mexican Mathematical Society and in several foreign journals. Some of the researchers have managed to carry out very important work, contributing notably to the progress of contemporary mathematics.

Highly meritorious work of the Institute was the organisation of two scientific events of the first magnitude, held in the University City: the International Symposium of Algebraic Topology, which took place in August 1956, and the International Symposium of Ordinary Differential Equations, which took place in September 1959. Both events had great repercussions and the most outstanding foreign specialists participated, along with the Mexican researchers.

Thanks to the cultural exchange programmes with the Government of France and Government of the United States, every summer the Institute receives visits from distinguished mathematicians from these countries.

Thus, in 1944, the eminent mathematician Solomon Lefschetz, from Princeton University, arrived in Mexico. Enthusiastic about the idea of creating an important research centre in our country, Lefschetz has been a great promoter of mathematics in Mexico ever since. Retiring from Princeton University in 1954, and putting aside offers from many other universities, he entered our Institute of Mathematics as one of its researchers.

Lefschetz is responsible, in large part, for the training of several of the Institute's researchers. Some of them began their research under his direction, others were sent, thanks to his efforts, to important centres where they conducted their research studies. It is difficult to find a young researcher in Mexico who has not received his generous help. I am obviously one of the beneficiaries.

Although I began my professional studies at the National School of Engineers, it was in the professorships of maestro Alfonso Nápoles Gándara where I discovered my true vocation. In this way, when I finished my studies at the Faculty of Sciences in 1945, I attended the graduate courses and seminars offered at that time for several years. I remember the great influence that Roberto Vázquez's courses, the Topology seminar organised by Vázquez and Recillas, Enrique Valle's modern Algebra seminar, and Francisco Zubieta's Mathematical Logic seminar had on my formation.

During the visit that Lefschetz made to the Institute in the summer of 1949, I told him of my desire to go abroad for my doctorate. Days after his return to the United States, I received an offer from Princeton University, which I immediately accepted.
In September of that same year, upon my arrival at Princeton, I began my research in algebraic topology under the direction of N E Steenrod. The preparation that was in Mexico was satisfactory.

The great progress achieved in the last 20 years is indisputable. The mathematics hobbyist has been replaced by the professional researcher. But we are still far from the final goal: to form in Mexico one of the main mathematical research centres that radiates its beneficial influence on all other branches of science, technology, and education. Such is the effort in which we are committed.

Last Updated June 2023