Félix Recillas Juarez

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27 January 1918
San Mateo Atenco, Mexico
15 January 2010
Mexico City, Mexico

Félix Recillas was a Mexican mathematician who was awarded a Ph.D. by Princeton advised by Chevalley and made a major contribution to building successful mathematical research schools in Mexico.


Félix Recillas was the son of Félix Recillas and Herminia Juárez. He had three brothers, Agustin, Vicente and Felipe who were quite a lot older than he was. The family lived in San Mateo Atenco, on the east side of Toluca. Félix's father was a minor civil servant in the government of the Mexican President José de la Cruz Porfirio Díaz before the Mexican revolution of 1910. This presented problems when the revolution broke out and many members of the community joined the Zapatistas, set up by Emiliano Zapata, or the Carrancistas, followers of Venustiano Carranza. Another revolutionary Pancho Villa at first supported the Carrancistas but later broke away and formed the Villistas. These different revolutionary groups fought each other but Felix's father, who had collected taxes for Porfirio's government, was seen as 'the enemy' by them all. When men from San Mateo Atenco joined one of the revolutionary groups and later returned home they would show their enmity to Félix's father. He had to hide among the fishing nets in the lagoon when they came looking for him. When Félix was three months old, his mother became so worried by the situation that she insisted that the family move to Mexico City.

In the interview [7] Recillas spoke of his early years in Mexico City:-
We came to live in a vacant lot where there were some shacks, near the General Hospital. At the age of two my father vanished, got lost in the big city, left and never came back. My mother returned to the village, where they had some pieces of land that they continued to cultivate, and I stayed with my older brothers. They started working in spinning and weaving factories, later they became drivers, all very hard-working. I never left the district of Doctores, where I spent my childhood and adolescence in an environment of blacksmiths, carpenters and drivers.
As we indicated above, Félix's brothers were much older than he was and, by the time he was attending primary school, his brothers were married. This led to another problem for the young boy when religious tensions became a major issue. Plutarco Elías Calles was the Mexican president from December 1924 to November 1928. Calles, who was an atheist, decided to try to end the power of the Roman Catholic Church in Mexico with the imposition of anticlerical laws in June 1926. Catholic organisations and individuals resisted the imposition of the law with an economic boycott against the government. Catholic teachers in state schools refused to teach. One of Félix's sister-in-laws was a staunch Roman Catholic and, through her influence, Félix was not allowed to attend primary school for between one and two years. He was therefore older than the other children in his class when, at the age of fifteen, he entered Secondary School No. 17 in 1933.

Recillas was fortunate in having some exceptional teachers at the Secondary School. The head of mathematics was Alfonso Nápoles Gándara who taught elementary algebra in the first year [7]:-
Nápoles had a great personality and walked with an air of great dignity through the central courtyard.
In the same interview, he spoke about his literature teacher:-
Julio Torri was my literature teacher. When Torri got to the classroom, he was met by a mob of crazy people, who were fighting and yelling, and he would sit very dignified at the desk, he would open his book and wait until everyone calmed down.
The school invited Alberto Barajas to give a trigonometry course during the vacation so that the pupils might progress faster. He gave a course which went as far as spherical trigonometry and Recillas was so impressed that he knew at that stage that he wanted to study more mathematics. Completing the examinations, Recillas qualified to enter the National Preparatory School which was only one block away from Secondary School No. 17.

Life now became exciting but chaotic for Recillas. Barajas suggested that a way for Recillas to learn more mathematics was to enrol at the Chemical Sciences High School and attend the mathematics classes given there by Carlos Graef. He did so and took classes on analytical geometry and calculus. Graef realised he had an enthusiastic and very able student and suggested that they walk together each day from San Idelfonso to the School of Construction Engineers. Recillas said [7]:-
Graef was very jocular, cheerful, and a great athlete. On walks he would talk to me about his mathematical friends and the history of mathematics. He taught me vector calculus by chatting.
After a year Graef advised Recillas to enrol for a bachelor's degree engineering in the School of Engineering Sciences rather than spend a second year at the high school. That would give him the opportunity to learn more advanced mathematics. What Recillas chose to do, however, was to enrol for a second year at the high school but hardly ever attend. Instead he took some mathematics classes given by Graef and some given by Nápoles Gandara. It was an exciting time for the young man who now met with students who came from a very different cultural environment. Not only did he learn more advanced mathematics but he learned about literature and music. In 1938 Graef was awarded a Guggenheim scholarship and left for the United States in July of that year. Recillas did not have the financial support to continue with his education and decided he had to find employment.

Now twenty years old, Recillas got a job as a surveyor in Michoacán. He enjoyed working outdoors but that work ended and then he had to work in the central office from 8:00 to 14:00. He was bored with the work and hated the discipline so he became depressed. In 1940 he heard that Graef had returned to Mexico, so he went to see him and told him that he wanted to continue studying mathematics. At this time Graef had become involved in astronomy. While he had been studying for a Ph.D. at Harvard, Graef had met Luis Enrique Erro (1897-1955). Erro was an amateur Mexican astronomer who became a member of the administration in 1940 tasked with building an observatory in Tonantzintla, Puebla. This site has particularly favourable atmospheric conditions for an observatory. Erro had asked Graef if he would be the founding deputy director of the Observatory project. Graef now saw the possibility for Recillas to go to Harvard by having him join the Tonantzintla Observatory project. Recillas replied that he did not know anything about astronomy, but Graef said if he went to Harvard saying he wanted to learn astronomy, he could attend all the mathematics courses he wanted. With support from Erro and Graef, Recillas was awarded a scholarship to study astronomy at Harvard and began his studies in January 1941.

Recillas spent the summer of 1941 learning observational tasks at the Harvard Observatory. In his spare time he read the book An Introduction to the Study of Stellar Structure by Subrahmanyan Chandrasekhar. Recillas thought that learning German would be useful to him and the astronomy postdoctoral student Paris Pishmish offered to help him. Although Turkish, she spoke perfect German. It had been her favourite foreign language at school and she had perfected it when studying for a Ph.D. in Istanbul advised by Finlay Freundlich. Recillas and Pishmish married around the end of 1941. They had two children Elsa Recillas Pishmish (born 1942) and Roberto Sevín Recillas-Pishmish (born 1943). We will give some details about these children's careers later in this biography.

The fact that he had read Chandrasekhar's book, meant that Recillas could start graduate studies at Harvard. He took physics courses but continued his passion for mathematics by attending algebra courses by Garrett Birkhoff and Oscar Zariski. It was Manuel Sandoval Vallarta, who had been Graef's thesis advisor, who suggested that Recillas continue his interest in mathematics in this way. He was at Harvard, however, as part of the programme for setting up the Tonantzintla Observatory and in 1942 his studies had to be cut short when he was told to return to Mexico and bring with him the 28 inch Schmidt camera which had been built in the Harvard College Observatory shops with optics provided by PerkinElmer. With a colleague, Recillas drove a truck with the Schmidt camera from Boston to the Mexican border where a professional group took over and continued the journey to the Tonantzintla Observatory. The Observatory was officially opened in February 1942 and an Astrophysical Congress was held in Puebla to inaugurate the Tonantzintla Astrophysical Observatory. Both Recillas and his wife Paris attended the Congress and Recillas presented a paper on radiation transport in stellar atmospheres.

Chandrasekhar attended the Astrophysical Congress and was impressed by Recillas's paper. After returning, he wrote to Erro suggesting that Recillas might come to Chicago to work with him and said he could arrange a scholarship and make the travel arrangements. Although Recillas was now officially an astronomer at the Tonantzintla Observatory, mathematics was still his real love and he made the 100 km journey to Mexico City every week to attend the topology seminar in the Mathematics Institute organised by Roberto Vázquez.

The First National Congress of Mathematics was held in Saltillo, Coahuila, 1-7 November 1942. It was organised by Alfonso Nápoles Gándara, Alberto Barajas and Francisco José Alvarez. Recillas attended the Congress and while there he spoke with Solomon Lefschetz telling him that he was interested in studying more mathematics. Lefschetz asked him what area of mathematics interested him and Recillas replied that he was fond of algebra and had read An Introduction to Abstract Algebra by Cyrus C MacDuffee. Lefschetz told him that MacDuffee's book was useless as an introduction to research and said he could arrange a scholarship for Recillas to study for a Ph.D. at Princeton supervised by Claude Chevalley. Chevalley had been on a visit to the Institute for Advanced Study at Princeton when World War II broke out and chose to remain there throughout the duration of the war. When Recillas went to the topology seminar in Mexico City in the week after the Congress, Lefschetz told him that his scholarship for Princeton had been arranged.

Recillas had begun astronomy research and had published the joint paper [17] with Edith Jones Woodward (1914-2002). Woodward worked at Harvard College Observatory and had published A study of four W Ursae Majoris stars in 1942. Their joint paper begins:-
The variability of U Pegasi was discovered by Chandler in 1894. Visual observations established the fact that it was a short period variable and subsequent observations have shown it to be an eclipsing binary of W Ursae Majoris type, with a period of about 0.375 days. ... The present study was undertaken with the purpose of investigating the constancy of the period of U Pegasi and determining an accurate light curve for the star.
While waiting to go to Princeton, Recillas continue to work at the Tonantzintla Observatory but was a founding member of the Mexican Mathematical Society, being present at the first meeting on 30 June 1943. He was on the Tonantzintla Observatory expedition to Peru organised by Luis Enrique Erro to observe the eclipse of 25 January 1944. They set up their instruments west of Chiclayo in the school grounds of Centro Escolar 221. Visibility was good and they were able to take several photographs. Recillas' own account is in [18].

In 1944 Recillas resigned his position at the Observatory, but his wife continued to hold a post there. On 28 October 1944 Recillas entered the United States on his way to the Graduate School at Princeton. He gives the following personal details: Height, 5ft 7in; Complexion, dark; Hair, black; Eyes, brown; Scar under chin. His Mexican address is 17 Sur 709, Pueblo, Mexico and his wife continued to live there. He said [7]:-
With the money that Luis Enrique Erro gave me to go to Chicago and with the scholarship that Solomon Lefschetz gave me, I was able to pay for my first year in Princeton. After that year I passed the examinations and they gave me a scholarship from the Rockefeller Foundation to finish my doctorate.
Recillas' wife, Paris Pishmish de Recillas, worked at the Tonantzintla Observatory until January 1946 when she went to study at the Princeton University Observatory, joining her husband.

At Princeton, Recillas was advised by Claude Chevalley and wrote the thesis Extension of a theorem of Hilbert to formal power series. He was awarded a Ph.D. by Princeton in 1948. The theorem of Hilbert referred to in the title of the thesis is Hilbert's syzygy theorem, a fundamental theorem about polynomial rings over fields proved in 1890. The theorem is important in algebraic geometry. An Abstract of the thesis can be read in [19].

Returning to Mexico in 1948, Recillas became a researcher at the Institute of Mathematics of the Universidad Nacional Autónoma de México (UNAM) and a professor in the Faculty of Sciences of the UNAM. In [7] he spoke about the Institute of Mathematics at that time:-
Although I was received with kindness and courtesy, the academic atmosphere was disillusioned. The splendid works of Graef and Barajas had been left behind and there was an atmosphere of depression, there was no confidence that theorems could be proved. The responsibility for the mathematical work was carried out by Roberto Vázquez, who asked me to organise a course or, failing that, a seminar on algebraic topology. I agreed to do the seminar on the condition that José Adem was invited to participate. We read the book 'Algebraic Topology' by Professor Lefschetz. The first chapter we read was relatively easy, because it had been written by Chevalley, but the subsequent chapters, written by Lefschetz in the style of the old French school, proved really difficult. But facing the challenge with humility and a deep critical spirit allowed us to achieve our purpose.
He was invited to Princeton for a semester as a visiting professor in 1950. While he was there, Claude Chevalley suggested that he spend a year in Paris at the Henri Cartan Seminar at the École Normale Supérieure. His wife and children flew from Mexico City on 12 November 1951 and, joining up with Recillas, the whole family flew to Paris on 16 November 1951. Recillas returned after the year in Paris sailing from Le Havre to New York, arriving there on 9 November 1952. He returned for a second visit to Paris, leaving Mexico City on 10 November 1953 and returning on 10 March 1954.

In 1956 Recillas was one of the organisers of the Symposium Internacional de Topología Algebraica held at the UNAM. Many leading topologists attended this meeting including Michael Atiyah, Samuel Eilenberg, Peter Hilton, Friedrich Hirzebruch, Witold Hurewicz, Ioan James, Solomon Lefschetz, John Milnor, Hans Samelson, Stephen Smale, Norman Steenrod and René Thom.

He was one of the editors of the conference Proceedings which has the following Preface [1]:-
The International Symposium on Algebraic Topology was held in Mexico at Ciudad Universitaria in August 1956, at the initiative of a group of researchers from the Institute of Mathematics of the National University, the National Institute of Scientific Research and the Mexican Mathematical Society, with the cooperation of various men of science from foreign academies. This scientific event was carried out with the moral and economic support of the Federal Government of our Republic, and the cooperation of some national institutions ... and foreign institutions, the American Mathematical Society, the Rockefeller Foundation, and UNESCO, to whom we publicly give our most sincere thanks.
Recillas received several further invitations, being in Princeton in 1957 and then back to Paris as a visiting professor from March to June 1959. He was also invited to spend time as a visiting professor at the Henri Poincaré Institute in Paris in 1962 and at the University of Heidelberg in Germany in 1965.

Félix Recillas and Paris Pishmish were divorced and Recillas married Minerva Targa; they had one son Félix Recillas Targa.

Recillas published a number of papers including: On prime ideals in generalized semilocal rings (Spanish) (1953); Hilbert's function in semilocal rings (Spanish) (1954); On the formulas of Peterson and Stein (Spanish) (1961); and Specializations of local complete rings (Spanish) (1961). He was the Director of the Faculty of Sciences of the UNAM from 1982 to 1986.

Having continued to work at the Institute of Mathematics into his nineties, Recillas died a few days short of his 92nd birthday. He left instructions that his collection of 1953 books be donated to the library of the Institute. This was fitting since it had been largely through the efforts of Recillas that the Institute library was started. When the books were received in April 2014, Javier Bracho, a former director of the Institute, said [14]:-
By opening one of these books and noting that it was donated by one of the most important researchers the country has had in the field of mathematics, students can find out who Recillas Juárez was and what he has meant to the Institute. Dr Recillas Juárez was very important in the development of Mexican mathematics and he had a special interest all his life in books on this science. He had a really precious and very well selected collection. It is a great honour to be chosen to host this collection.
The collection contains books published in English, French, German, Spanish, Italian, and Portuguese.

Let us give a few details of Recillas' three children. Elsa Recillas Pishmish (born 1942) was awarded a physics degree by the UNAM in 1968, a Master's Degree in Astronomy by the University of Sussex, England, in 1971, a Master's Degree in Physics from UNAM in 1983 and a Ph.D. from the UNAM in 1988. She became a professor in the Mexican National Institute of Astrophysics, Optics and Electronics. She married the astronomer Carlos Cruz-González, and their daughter Irene Cruz-González also became an astronomer. Sevín Recillas-Pishmish (born in Puebla in 1943) was awarded a Bachelor's Degree in Mathematics from the Faculty of Sciences of the UNAM in 1964, and then went to Brandeis University in the United States where he received a Master's Degree in 1967 and a Ph.D. for his thesis A relation between curves of genus 3 and curves of genus 4 in 1970. MathSciNet lists 27 papers by Sevín Recillas-Pishmish all on algebraic geometry. He died in 2005. Félix Recillas Targa studied biology at the UNAM (1982-85), then studied for a biochemistry Ph.D. at the University of Paris (1988-1993). He became a researcher at the Institute of Cellular Physiology of the UNAM in 1990.

Finally, let us quote some thoughts about Recillas. Raymundo Bautista writes [3]:-
Félix Recillas shared with the mathematicians of his generation the dream of building mathematics schools in Mexico with international impact. He always had a piece of advice, a word of encouragement, towards those he believed to be interested in research in mathematics. He was a tireless propagandist for those mathematical topics that he saw as central, he organised seminars, lent books, got whoever he saw interested in a topic of his interest invitations to international schools or congresses. We will remember him with gratitude and affection.
His son Félix Recillas Targa, spoke about his father [9]:-
He was extremely honest, quite a gentleman, but he had a strong, tough character ... He was very strict academically, but his human part was very good with people ... He never forced us to be scientists but he gave us the example ... he was doing mathematics at his desk, at home. He told us that we had to be very humble about science.
Enrique Ramirez de Arellano writes [13]:-
When the scientific culture of a country is in formation, the paths that the sciences will follow will be regulated by their founders, and not only the paths, but also the ambitions, illusions and above all the audacity to set goals, apparently utopian, for the development of these sciences. In the case of Mexican mathematics, Félix Recillas is one of the first to raise such goals, apparently illusory in our environment regarding the development of mathematics. He insisted "You have to study the great contemporary mathematical schools" and he gave importance to modern algebraic geometry, Lie groups, the teachings of Weil, Grothendieck, Mumford, Tate and many more. He encouraged a new generation to study algebraic groups, automorphic forms, analysis of locally compact groups, and many other topics that were beginning to have relevance. He was the one who made students aware of the Langlands' program of uniting various branches of mathematics and of the importance of not artificially subdividing mathematics into mutually alien branches. The development of modern mathematics in Mexico is largely due to the tenacious work of Félix Recillas. We can never thank him enough for his efforts.

References (show)

  1. J Adem, A Barajas, S Lefschetz, E Lluis, A Nápoles Gándera, F Recillas, G Torres and R Vázquez, Roberto (eds.), Symposium Internacional de Topología Algebraica. La Universidad Nacional Autónoma de México y la UNESCO (1958).
  2. A Barajas and F Recillas, Facultad de Ciencias, Revista de la Universidad de México (618-619) (2002), 82-86.
  3. R Bautista, Félix Recillas Juarez (1918-2010), Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  4. Breve biografía de Félix Recillas, Instituto de Matemáticas de la Universidad Nacional Autónoma de México.
  5. F Bulnes, Integral Geometry Methods in the Geometrical Langlands Program (Scientific Research Publishing, 2016).
  6. F Bulnes, Orbital Integrals on Reductive Lie Groups and Their Algebras (IntechOpen, 2013).
  7. M Neumann, Una conversación con Féliz Recillas Juárez a sus 80 años, Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México (21 January 1998).
  8. M Neumann, Una conversación con Féliz Recillas Juárez a sus 80 años, Carta Informativa SMM 16 (March 1998).
  9. A Ortiz, Dr Félix Recillas Juarez. Entre las matemáticas y la astronomía, Instituto de Matemáticas de la Universidad Nacional Autónoma de México (18 February 2010).
  10. Paris Pishmish, The Boston Globe (23 March 1939), 8.
  11. Paris Pishmish Mexican Astronomer, Astronomía Astrónomos Universo (20 February 2021).
  12. C Prieto de Castro, Félix Recillas, Boletín Departmento de Matemáticas (2015), 2-4.
  13. E Ramirez de Arellano, Semblanza del Dr Félix Recillas,
  14. C Ramírez Torres, El legado de Félix Recillas. Juárez a los estudiantes de Matemáticas, ZonaFrancaMX (30 April 2014).
  15. C Ramírez Torres, El legado de Félix Recillas. Juárez a los estudiantes de Matemáticas, ZonaFrancaMX (30 April 2014).
  16. Recillas family, ancestry.com
  17. F Recillas and E Jones Woodward, A study of the eclipsing binary U Pegasi, BD +15'4915, Astronomical Journal 51 (1945), 101-103.
  18. F Recillas, Mexican Eclipse Expedition, Sky and Telescope (May 1944).
  19. F Recillas, Abstract, F Recillas, Extension of a theorem of Hilbert to formal power series, Dissertation Abstracts 15 (University Microfilms, 1955), 840.
  20. Videos del Homenaje a Félix Recillas Juárez, Instituto de Matemáticas de la Universidad Nacional Autónoma de México (21 Mat 2015).

Additional Resources (show)

Other websites about Félix Recillas:

  1. Mathematical Genealogy Project
  2. MathSciNet Author profile

Cross-references (show)

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