... 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.

In the 1930s, I had a pupil by the name of Alphonso Napoles. He was very good in tensor calculus, and overall. Then he went to Mexico and soon became an outstanding member of the mathematics faculty at the Autonomous University in Mexico City. He became head of the department. Then he invited me to come to Mexico, which I did in 1934, at the time that I had a sabbatical. Included in the invitation was also an invitation by Manuel Sandoval Vallarta, who had returned to Mexico and became a very big shot in the scientific side of the government. I was in Mexico for six weeks in 1934, which was one of the great experiences of my life. The absolute differences between the Spanish and Indian cultures of Mexico and the Northern European culture of the United States was for me overwhelming. So I never forgot the deep impression I got of Mexico in those days. I was received very friendly. I was one of the very first outside lecturers in Mexico, and my pupils and colleagues showed me around. They showed me the pyramids and all kinds of things, and the colonial monuments and the nature. It was a very grand time. I'll never forget it.

Graef and Nápoles Gándara were my mathematics teachers. With such teachers my vocation was further defined. Graef was a nice man, a very good teacher and a man of great human qualities. His laughter in the first yard could be heard as far as the third yard of the Preparatory School. ... Graef was our geometry teacher ...

Appointed for studies of the theory of probability and mathematical theory of statistics; tenure, twelve months from September 17, 1938.

... was in effect until February, 1940, and in March of the same year the President of Mexico, General Lázaro Cárdenas, awarded me a stipend to finish my doctoral studies. I received a stipend from the Universidad Nacional de México during all my residence in the United States, as well as scholarships from Massachusetts Institute of Technology for three terms.

This thesis deals with the orbits traced by a charged particle moving in the magnetic field of a dipole, on a rotating meridian plane following the particle.
...
We use the geometrical method of attack to find properties of the orbits. The transformation of the dynamical problem into a geometrical one is done by the introduction of the characteristic surface, i.e. the surface whose geodesics have the same differential equation as the trajectories. The passing from the dynamical equations of motion to the geometrical equation of the geodesics is essentially an elimination of the time. The meridian plane is a conformal image of the characteristic surface, so that properties of the geodesics on the latter can be translated into properties of orbits on the former.

We found that the characteristic surface has singular points which correspond to the boundary between allowed and forbidden regions in the meridian plane. The curvature of the surface is proved to be everywhere positive.

This work, in the opinion of the famous topologist Solomon Lefschetz, was notable for the very original way of attacking a problem of differential equations in three dimensions, to the best of his knowledge, for the first time. One main result, that all periodic trajectories intersect the magnetic equator, was verified years later when the Van Allen bands, the cosmic ray death belts that surround the Earth, were discovered, so important to astronauts.

... the people who had committed to the director Luis Enrique Erro to translate foreign scientific papers for some reason did not arrive on time and Erro had asked Graef to help him in the emergency by taking care of the translation. G D Birkhoff spoke in English as the first speaker and Graef listened attentively without interrupting him. At the end of the presentation, he made a very precise synthesis of the work, underlining the most interesting conclusions, inserting witty comments and expanding explanations on graphs and diagrams. After a few hours of this unexpected way of translating, Harlow Shapley, could not contain himself and interrupted the session to say: "We are amazed at the transformation that a work undergoes when Graef translates it into Spanish. It becomes brighter and more understandable; as if the translator knew the article better than the author."

On Tuesday evening, Dr Carlos Graef Fernández, President of the Society, delivered an invited popular expository lecture on "Space, Time, Gravitation", and on Wednesday evening Manuel Sandoval Vallarta gave another invited lecture on "The Relation Between Cosmic Rays and Radio Waves Emitted by the Sun". Both were attended by capacity audiences of about 200 which filled the 17th century lecture hall to overflowing.

When the faculties and schools of the National Autonomous University of Mexico were moved from their old sites in the City to their magnificent building in the Ciudad Universitaria in 1952, many new values were gained, but some very dear and appreciable values were also lost. For reasons of historical development, the faculties and schools moved to Ciudad Universitaria as intellectual islands, as they had been in Mexico City. There had been very little academic contact between one campus and another due to their different geographical location in the City. In this way the university dependencies went to their new city. Each one moved as an island. In the scree the links that had not existed in the centre were not established. Some university students hoped that by being all together in the Ciudad Universitaria a greater spiritual contact would be fostered; that the courses of the same subjects that are taught in different schools could be a bond of intellectual union. For example, we dreamed that all university students who had to acquire knowledge of analytical geometry would take that course in a Mathematics Department and have students from very different faculties as companions, all listening to the professional mathematician who taught them. The inertia of tradition was an insurmountable obstacle for this system that would have achieved a spiritual rapprochement among all university students. In many university structures around the world, including in the United States and Europe, this happens on a daily basis. When moving to Ciudad Universitaria, the link between the Faculty of Sciences and the Faculty of Engineering was lost.

Dr Graef distinguished himself as a great teacher. His classes mainly revolved around differential calculus, analytical geometry, and classical mechanics. He also gave courses on relativity, both special and general, on classical field theory, and on gravitation. Although he was aware of the achievements of modern physics - that based on quantum theory - he was, so to speak, a classical physicist. In his classes, he poured out enthusiasm and emotion when referring to the achievements of the human intellect in his explanations about space, time and the movement of bodies, which caused his students to continue studying what he pointed out. His expositions were very clear because he had the gift of communicating complex ideas in a simple way, for which he used analogies and metaphors based on everyday knowledge. He took advantage of his vast culture to exemplify his statements and told stories and anecdotes to support his teachings. He had a great sense of humour and liked to chat with the students, never missing a joke with which he was the first to laugh. His permanent attitude was to preach the charm of scientific knowledge and to enthuse everyone to take a look at it.

With Graef's death, Mexico loses one of its great teachers, researchers, and organisers; but there are many seeds that he sowed and that will continue fighting to magnify the University and our Country, which he loved so much.

Galileo said that the world is an open book; only that it is written in mathematical characters. For Dr Graef it was easy to read them and, furthermore, when he described them they became luminous.

Above all Graef had a warm and enthusiastic personality, and he was always willing to help students with homework problems or to discuss physics with colleagues. Listening to his class made one feel that physics was a beautiful and enjoyable science, worth being part of. Probably his best obituary was an anonymous note that appeared on the wall outside his classroom the day his death became known, written on a student's piece of paper: "Graef we loved you, we will miss you."