The lectures that Nápoles Gándara 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.

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.

... the Department of Physics and Mathematics was located in the Palacio de Minería, home to the School of Engineers. The neighbourhood in the space of the two establishments was very fruitful. The professors in the Physics and Mathematics department were professors from the School of Engineering who had a special love for exact sciences. Those who were then dedicated to teaching these subjects had to give many hours of class every day to be able to collect a decent remuneration. There was no physics or mathematics institute, and the only income for them was from their teaching work.

It is worth mentioning about this book that, from its first edition, it became the text par excellence not only for the corresponding subject in the National Preparatory School but also for the first courses of this subject taught in faculties such as Engineering, Chemical Sciences and Sciences.

In 1944 I joined as a part-time connection the Instituto de Mathematicas at the National University of Mexico. This continued until 1966. At the Instituto I was as free as under my Princeton professorship. I conducted seminars in topology and differential equations, gave a couple of times a "volunteer" course on "general mathematical concepts" directed at beginners and, thanks to a good working library, was able to continue research.

In the 1960s, there was a shift in his research work, prompted, among other things, by a seminar organised at the Institute of Mathematics, in which José Adem and Félix Recillas participated, and in which the homological algebra book of Cartan and Eilenberg was studied. It was then that Vázquez began to study problems about projective modules and flat modules, and began to head towards the branch of categorical topology, of which he is one of the creators ... It is in this branch that his most important production is framed, especially highlighting the categorical conceptualisation of the connectedness property, which extends from geometric objects to arbitrary objects in a connection category. Of importance at this stage was his collaboration with the brilliant mathematician Graciela Salicrup, who died as a result of a tragic accident. She wrote her undergraduate thesis with Dr Vázquez and later began a joint research project with him, part of which gave rise to the thesis with which she obtained her doctorate. Their joint research continued for several years, yielding important results in connection theory.

... were among the first mathematicians who realised that certain topological concepts and constructions were best understood in the light of category theory. ... they analysed topological problems by means of categorical terms and methods, in many cases having first to develop the yet missing categorical machinery. For nearly a decade they produced roughly one joint paper per year, evincing a high sensitivity for suitable problems, and demonstrating great originality and skill. Their best papers of this period ... are prominent achievements in the newly emerging field of categorical topology. Unfortunately they published their results in a journal neither well known nor easily accessible in the non-Spanish speaking mathematical world. Thus, their work which otherwise would have had a considerable impact on categorical topologists - remained for a long time almost unknown, and several of their results had to be recovered independently by later investigators.

The truth is that he never dictated an agenda to us or pointed out long-term objectives. From the first day that I found myself in the student-teacher relationship with him, I learned topology; precisely the definition of this illustrated with examples. When he took us on trust, sometimes the most he would say to us when starting a topic was: "we're going to be in this as far as we go."

Many of us attended with the hope of seeing him, but his delicate health prevented him from going and his daughter Isabel attended in his place. A toast was made in his honour, music was played (there was a flute, and there was also a guitar), a pretty young lady sang old songs in French, speeches were made ... We never saw him again.

The Tecnológico de Monterrey Luis Elizondo Award for a Humanistic Outlook was established in 1967 with a personal contribution from Don Luis to Tecnológico de Monterrey. The award recognises prestigious researchers who have worked for the benefit of Mexico, as well as people and institutions who have devoted their humanitarian, fraternal work to their fellow human beings, have performed outstanding scientific and technological activity and carry out their philanthropic work in the Mexican community, all of whom have profiles similar to that of the Nuevo León philanthropist, Don Luis Elizondo.