Alberto Barajas Celis

Quick Info

17 July 1913
Mexico City, Mexico
3 July 2004
Mexico City, Mexico

Alberto Barajas played an important role in the development of mathematics in Mexico, both as a researcher and as a teacher. When the National University built the new University City campus, as director of the Faculty of Sciences he led the academic input into the design of the buildings and facilities for that Faculty.


Alberto Barajas was the son of Isidoro Barajas Manríquez (1883-1957) and Leonor Celis (born about 1883). Isidoro Barajas was born in Guanajuato, México on 4 April 1883 and he married Leonor in Mexico City on 1 May 1909. They had two children, Guadalupe Barajas Celis, born about 1912, and Alberto Barajas Celis, the subject of this biography.

Alberto Barajas loved mathematics from his years at primary school. He said mathematics [10]:-
... 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.
After studying at a high school, where he thought geometry was "the crowning glory of human creation," he entered the National Preparatory School in 1930. The Escuela Nacional Preparatoria had been founded in 1868 and belonged to the National Autonomous University of Mexico. In his first year of study at the school he was taught mathematics by Alfonso Nápoles Gándara [15]:-
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.
Barajas read in the newspapers that Alfonso Nápoles had been awarded a scholarship from the John Simon Guggenheim Memorial Foundation to study in the United States. A nervous and worried Nápoles told his students that the first year mathematics course would finish earlier than planned and the examination would be held in August so that he could begin his studies at the Massachusetts Institute of Technology. When Barajas began his second year studying at the Escuela Nacional Preparatoria he met his new mathematics teacher Sotero Prieto. Barajas wrote [15]:-
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.
He also spoke about having Sotero Prieto as his teacher of analytic geometry in the interview [10]:-
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.
After he fell in love with mathematics when at school, Barajas told his father he wanted to become a professional mathematician. When his father assumed that his son wanted to become an engineer, Barajas replied that he did not want to be an engineer who taught mathematics to engineers. He really wanted to be a professional mathematician. His father told him that he could never make a living as a professional mathematician, since it was not even a recognised career. It is doubtful that his father realised at this time that his son would become one of the people who would help create the career of professional mathematician in Mexico.

In 1932 Barajas graduated from the Escuela Nacional Preparatoria and enrolled for the degree in engineering at the National Autonomous University of Mexico. He chose engineering, not because he wanted to become and engineer, but simply because it was the degree with the most serious mathematics courses. He soon discovered that, although there were some excellent mathematics courses, there were also parts of the engineering syllabus that he did not enjoy [12]:-
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.
It was indeed a very bold decision when Barajas and Graef decided to become professional mathematicians since Mexico did not have a mathematics degree and there were not even Faculties of Science. Sotero Prieto, however, had already decided that Barajas was an exceptional talent and in 1934 asked him if he would like to teach a high school mathematics class. Barajas felt that he was being honoured and trusted by Sotero Prieto so he happily accepted [10]:-
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 ...
Barajas and Graef were fortunate in being able to study advanced mathematics courses since, in 1934, the rector of the National Autonomous University of Mexico, Manuel Gómez Morín, restructured the University and created the Faculty of Physical Sciences and Mathematics that included the School of Engineering, the School of Chemical Sciences and a Department of Physics and Mathematics. Barajas and Graef studied there and Graef describes what it was like in [8]:-
... 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 was head of the Department and he and Alfonso Nápoles gave advanced courses there. A tragedy occurred in 1935, however, when Sotero Prieto committed suicide. Barajas said [10]:-
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.
Having left engineering and committed himself to mathematics, Barajas could not graduate. There were, however, changes over the following few years. The School of Physical-Mathematical Sciences was created in 1936 to replace the Department of Physics and Mathematics. This school was headed by the engineer Ricardo Monges López (1886-1983) who had argued for it to be established. The school gained the right to award mathematics education degrees intended for those wanting to become school teachers. The Faculty of Sciences was created at the end of 1938 and it gained the right to award Master of Science degrees and Ph.D. degrees. The Faculty had a departmental structure and for each department there was a Research Institute, administratively independent but forming an academic unit. Researchers were assigned to the Institutes and classes were given at the Faculty. Barajas was appointed as Professor of Algebra in 1940 and he became one of the first to be awarded a Master's Degree in 1942. He wrote the thesis Invariantes Proyectivos en las Transformaciones Circulares and submitted it in August 1942. The thesis was examined on 18 August 1942 by Alfonso Nápoles, Carlos Graef and the engineer Bruno Mascanzoni. Barajas dedicate the thesis to his parents and to his sister. His sense of humour is there for all to see in the acknowledgement that he writes [4]:-
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.
Following the award of his Master's Degree, Barajas was appointed as an Investigator in the Institute of Mathematics.

It may seem surprising that Carlos Graef, who had been a fellow student with Barajas, was now examining his M.Sc. thesis. This, however, was natural since Graef had been awarded a fellowship by the John Simon Guggenheim Memorial Foundation and, after studying at the Massachusetts Institute of Technology, had been awarded a Ph.D. in 1940. Graef became deputy director of the Tonantzintla Observatory which was dedicated in February 1942. On 20 February 1942 George David Birkhoff gave a lecture at the Astrophysical Congress in Puebla, Mexico, at the congress held to inaugurate the Tonantzintla Astrophysical Observatory. He outlined his new theory of relativity at the Congress. This was important for Barajas since his research interests would turn to developing Birkhoff's theory.

In 1942 the Institute of Mathematics of the Universidad Nacional Autonoma de Mexico was created. This was for research in mathematics and initially it only had two members, Alfonso Nápoles who was Director of the Institute and Alberto Barajas. The First National Congress of Mathematics in Mexico was held in November 1942, organised by Alfonso Nápoles Gándara, Alberto Barajas and Francisco José Alvarez. At this Congress, a commission was set up consisting of the three organisers of the congress together with Carlos Graef, which was given the task of setting up the Mexican Mathematical Society. At the first meeting of the Society on 30 June 1943, Alfonso Nápoles Gándara was elected as the first president of the Society and Carlos Graef was elected the first vice-president.

After discussing Birkhoff's theory of gravitation with Birkhoff at the February 1942 Congress, Barajas began undertaking research on the topic. The meeting was important in another way, since Birkhoff encouraged Barajas to apply for a fellowship from the John Simon Guggenheim Memorial Foundation to enable him to go to Harvard and work with him there. Barajas published the paper Birkhoff's Theory of Gravitation and Einstein's Theory for Weak Fields in March 1944. His application for a Guggenheim fellowship was successful and he was awarded a fellowship for studies in the theory of gravitation for twelve months from 1 November 1944. Birkhoff had also invited Graef to lecture at Harvard in 1944-45 so both Barajas and Graef entered the United States at Brownsville, Texas on 30 October 1944 on a Pan American Airways flight on their way to Harvard. Even before they travelled to Harvard they were working with Manuel Sandoval Vallarta and Birkhoff, and published the four author paper On Birkhoff's new theory of gravitation submitted on 4 May 1944. The Abstract of the paper begins [3]:-
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.
Sadly, Birkhoff died only days after Barajas reached Cambridge, Massachusetts. Nevertheless, the work that Barajas did on Birkhoff's Theory of Gravitation led to him being awarded a Ph.D. by the Universidad Nacional Autónoma de México in 1947 for his thesis Teoría de las teorías de la gravitación . It is worth noting that Barajas became the director of the Faculty of Sciences in 1947 and so he signed his own examination report as director.

Universidad Nacional Autonoma de Mexico had been founded on a site in the centre of Mexico City and from the start of the 1930s it became clear that if the university was to continue to expand it required a much larger campus which would have to be on the outskirts of the city. In 1945 the University acquired land in the Coyoacán district in the southern part of Mexico City. A competition was set up for architects to present plans and the winners were Mario Pani and Enrique del Moral. These architects were not to design the buildings for the different faculties since each had an architect who was experienced in the particular needs of each area. Raúl Cacho was appointed as architect for the Faculty of Sciences and Barajas, as director of the Faculty of Sciences, was appointed by Salvador Zubirán, the rector of the university, to advise him. Raúl Cacho and Barajas had been classmates at high school which made their cooperation easier. The first task that faced Barajas was persuading everyone that the Faculty of Science, which was still a small unit, would grow rapidly and require a large site in the new University City. He quickly proved himself to be an outstanding negotiator.

Even before the construction work started, there was a crisis at the University. Students accused rector Zubirán and other school authorities of corruption, and demanded major reforms. A student strike led to students occupying buildings and soldiers were sent in which resulted in two students being killed. Zubirán resigned and the University City project looked to be in danger. Barajas, however, remained optimistic and said to Raúl Cacho [9]:-
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.
In the interview [10], Barajas said:-
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.
In the same interview, given in 1995, he was asked how he had combined the roles of teacher, researcher and administrator.
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.
In addition to his roles as teacher, researcher, and Director of the Faculty of Sciences at the Universidad Nacional Autonoma de Mexico, Barajas also served as Coordinator of Scientific Research and as a member of the Governing Board. He served on many Commissions, and we suggest that his most important contributions to these was as a member of the Commission for New Teaching Methods. He was named Professor Emeritus in 1976 and Doctor honoris causa in 1985.

Let us end with two quotes, the first from Víctor Neumann-Lara [14]:-
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.
Our second quote is from Javier Bracho and Luis Montejano [7]:-
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.
Finally a quote by Barajas himself [2]:-
There is only one area of human curiosity in which absolute truths are touched. Mathematicians know this happiness.

References (show)

  1. Alberto Barajas, John Simon Guggenheim Memorial Foundation.
  2. Aniversario luctuoso de Alberto Barajas Celis, RedEscolar (3 July 2021).
  3. A Barajas, G D Birkhoff, C Graef and M Sandoval Vallarta, On Birkhoff's New Theory of Gravitation, Physical Review 66 (1944), 138-143.
  4. A Barajas, Invariantes Proyectivos en las Transformaciones Circulares, Master's Thesis, Universidad Nacional Autonoma de Mexico (August 1942).
  5. A Barajas, "El conocimiento", Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  6. Biografía de Alberto Barajas, Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  7. J Bracho and L Montejano, Barajas: El Hacedor de Sueños, Instituto de Matemáticas de la Universidad Nacional Autónoma de México (June 1994).
  8. C Graef Fernández, Palabras Pronunciadas por el Dr Carlos Graef Fernandez Durante el Homenaje que le Rindio, La Sociedad Mexicana De Fisica, in J L Fernández Chapou and A Mondragón Ballesteros (eds.), Carlos Graef Fernández: Obra Científica (Universidad Autónoma Metropolitana, Mexico, 1993), 680-693.
  9. A Illanes, Alberto Barajas Celis en el centenario de su nacimiento, Miscelánea Matemática 58 (2014), 1-10.
  10. N Illescas, El milagro de las matemáticas: Entrevista a Alberto Barajas, Instituto de Matemáticas de la Universidad Nacional Autónoma de México (1995).
  11. A Jaidar, Entrevista a Alberto Barajas, Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  12. A Jaidar, La investigación matemática: entrevista a Alberto Barajas, Ciencias 27 (July-September 1992), 3-10.
  13. V Neumann-Lara, Alberto Barajas Celis (semblanza), Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  14. V Neumann-Lara, I Puga and S Macías (eds.), Alberto Barajas - su oratoria, sus matemáticas y sus enseñanzas (Sociedad Matemática Mexicana, México; Instituto de Matemáticas, UNAM, México, 2010).
  15. M Neumann and P Saavedra, Una conversación con Alberto Barajas, El Hacedor de Sueños, Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  16. M Neumann and P Saavedra, Una conversación con Alberto Barajas, El Hacedor de Sueños, Carta Informativa SMM (November 1996).
  17. G Zubieta Russi, Obituario de Alberto Barajas, Instituto de Matemáticas de la Universidad Nacional Autónoma de México.

Additional Resources (show)

Other websites about Alberto Barajas:

  1. MathSciNet Author profile
  2. zbMATH entry

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update June 2023