... gave me the psychological security that no other subject gave me. In all the other subjects it was the authority that told me what I had to do, except in mathematics where they say: this is so because it can't be otherwise, because human reason has its limits and its rules, because not even God can change it. Letting the professor know that he was wrong, that my calculations were correct, gave me great security and it happened frequently; that fair game of mathematics, the one where there is no authoritarianism but the one who is right is the one who triumphs.

He was a very good presenter, very well organised. I always attended his class with great pleasure. ... Nápoles walked very straight, very fast and I don't think I've ever met anyone who managed the blackboard area like he did. Simply by attending his class one learned what was needed. He compared very favourably with the mathematics teachers I had been given in high school.

He was a genius of oral teaching; even the humblest themes were given a magical touch. In the tense atmosphere of his class, we youngsters practiced the energetic sport of mental precision.

I fell in love with his great strength, his enthusiasm. With his presence he communicated his passion for mathematics. He was a magnificent presenter, he knew how to capture the attention of his listeners to a point that almost hurt; how tense his classes were and he did not let us lose attention for a moment. His ability to develop the topics has been, in my experience, incomparable. He not only knew how to teach, he knew how to guide us so that we could discover what he wanted to convey to us. When I left high school I was under the impression that I had invented analytic geometry.

At the same time there were subjects that did not arouse my enthusiasm. Surveying practices, for example, taught me that seeing the sun rise makes birds happy but not human beings. It was then that I began to dream of a school for mathematics. That year I met Carlos Graef who was studying to be a petroleum engineer. In 1934 we decided to dedicate ourselves professionally to mathematics.

Sotero bet blindly and entrusted me with a very rebellious group of very intelligent and mischievous boys who inspired fear in me, but who became my friends ...

... 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.

Sotero Prieto committed suicide in 1935, for us it was a terrible blow, he had given us classes a week before, very lucid, very calm and, at Easter, when I arrived at the School of Engineering, they informed me of his death. We felt helpless but not discouraged, we decided to go ahead with Nápoles Gándara and shortly after he took charge of the courses.

I want to publicly thank all my teachers. To the gentlemen of the jury Dr Alfonso Nápoles Gandara, Dr Carlos Graef and Ing. Bruno Mascanzoni, I express my special gratitude because you were kind enough to approve this thesis, despite having read it. Your benevolence will grant me, I hope, the pleasant title of Master of Mathematical Sciences.

It is pointed out in the first place: (1) in Birkhoff's gravitational theory based on "flat" space-time, the "red shift" is accounted for by the energy change of the photon as it travels from the emitting body, whereas the photon plays no especial role in the Einstein theory; (2) the solution of the problem of two or more bodies is feasible in the new theory because of its simpler character. Four comments of H Weyl concerning the Birkhoff theory are discussed, and it is concluded that these are to be taken with much reserve.

Despite the tragedy, University City is going to have to be built ... I propose that we continue working on the project as if Subirán were still the rector. There will come a day when the work will restart and at that moment we will be ready.

I kept seeing Cacho for two years every third day to finish the project at the Faculty of Sciences. When Miguel Alemán became president, he appointed Carlos Lazo manager of University City, he called all the groups of architects to submit sketches. When he asked me: "what progress is there for the Faculty of Sciences? When can you start building?" I could say we already had the plans for the buildings and all the detailed schedules for the construction. ... All of us scientists feel as if we had won the lottery. Having a school specially designed to teach, the blackboards were the finest that could be achieved at that time, because mathematicians only have one work instrument, which is the blackboard. Therefore the best in the world were needed, but these were very expensive. Well, I said buy them, and they brought those precious blackboards for the Faculty of Sciences.

Since 1934 I began to teach at the University, so I have already completed more than sixty years as a teacher. I have considered that to be a teacher in the University is the highest honour. Every time I go to teach I think that it is the prize that they have given me for being a mathematician by profession, structurally and genetically. I accepted the administrative tasks because I thought I had more experience, because I had become more interested in the problems, in the study plans, in the difficulties to which we subject students, in the lack of space. I had thought about all of that more than any of my friends and I was sure that if given the chance I could do it. I think I did, I think I achieved momentum that lasts. ... As a witness of the Mexican mathematical movement, I am extremely surprised that in a few years mathematics and physics gave wonderful results and that fundamentally it is the National University that carries out the most important research in the country ... It also has another aspect that does not appear when evaluations are made: it is a very passionate institution. In other universities the passion that ours inspires in us is not noticeable. It is a centre of affection, we are all in love with the University, it is a fact. In other countries they respect them a lot, they are very happy in them, but I don't see that they arouse the passion of love.

Alberto Barajas is a key piece in the Mexican mathematical edifice. As a professor of Geometry and Number Theory in the Faculty of Sciences of our University, he has contributed decisively, over more than fifty years, to forming a solid nucleus of Mexican mathematicians. During those years he has engendered a multitude of ideas that have been crystallising in the expansion and enrichment of the Mexican mathematical environment, our University and the country. His elegant style of exposing geometry is already a classic model in our environment. Where Barajas inhales, the atmosphere widens, becomes richer and more breathable because he is, above all, a builder of space. It is no coincidence that he was captivated by the Theory of Gravitation and by Geometry, fields in which he carried out his main works of mathematical creation.

Barajas' brilliance, clarity and lucidity in the classroom extends to his public speaking. In the ancestral art of oral literature it is out of the ordinary. He manages the tones, the rhythms, the images, the emphasis, the nuances, the humour and something else that only he knows, to generate those very strange and almost magical moments in which a direct and two-way communication is established between an expressly sensitive audience and a speaker who improvises with virtuosity. Anyone who, moreover, has had the privilege of conversing with him, knows that the generosity and intellectual honesty that is manifested in each of his works and in each of his words comes from deep within, comes from an almost timeless human being for being so committed to his present and for being so deeply human; he gives the impression of being in an open and direct line with Prometheus himself.

There is only one area of human curiosity in which absolute truths are touched. Mathematicians know this happiness.