# Alfonso Nápoles Gándara

### Quick Info

Cuernavaca, Morelos, Mexico

Mexico City, Mexico

**Alfonso Nápoles Gándara**was the first Mexican mathematician to be awarded a Guggenheim fellowship. He was director of the Institute of Mathematics of the Universidad Nacional Autónoma de México and president of the Mexican Mathematical Society for many years.

### Biography

**Alfonso Nápoles**had the full name of

**Alfonso Antonio de Jesús Nápoles Gándara**but was usually known as

**Alfonso Nápoles Gándara**. He was the son of José Antonio Nápoles León (born 1864) and Josefa Gándara Ayala (born 1868). Antonio Nápoles, the son of Francisco Nápoles and Maria Narcisa Leon, married Josefa Gándara, the daughter of Hesíquio Gándara and Felipa Ayala, in Cuernavaca, Morelos, Mexico on 22 May 1891. They had five children: María Esther Nápoles Gándara (born 22 April 1892); Francisco Antonio Nápoles Gándara (born 14 January 1895); Alfonso Nápoles Gándara (born 14 October 1897), the subject of this biography; Margarita Asunción Nápoles Gándara (born 20 July 1899); and Carlos Nápoles Gándara (born 4 November 1901), All five children were born in Cuernavaca, the main city of the state of Morelos, situated about 60 km due south of Mexico City.

**Alfonso Nápoles was baptised on 28 October 1897 in the Church of Sagrario in Cuernavaca.**

Alfonso entered the National Preparatory School in 1910. This school, originally a Jesuit College in the centre of Mexico City, was taken over by the government in 1868 and brought pupils up to the standard required for entering the Universidad Nacional Autónoma de México. Alfonso began his studies there at a difficult time for the Mexican Revolution began in the year he entered. In his home city of Cuernavaca, Emiliano Zapata Salazar (1879-1919) was the main leader of the Mexican Revolution in the State of Morelos and led the revolutionaries known as the Zapatistas. The Mexican Revolution, essentially a civil war with foreign involvement (particularly from the United States), lasted from 1910 to 1920. Tragedy struck the Nápoles family on 20 July 1912 when Francisco Nápoles, Alfonso's elder brother, was one of 82 people killed when a train going from Cuernavaca was attacked by the Zapatistas between the stations of "Cima" and "Fierro del Toro", on the slopes of Ajusco. Alfonso completed his studies at the National Preparatory School in 1915 and in 1916 entered the National School of Engineers, part of the Universidad Nacional Autónoma de México.

While a student at the National Preparatory School, Nápoles fell in love with mathematics. It was his mathematics teacher Sotero Prieto who inspired him. After he began studying at the National School of Engineers he was again taught mathematics by Sotero Prieto and Nápoles knew that he wanted a career teaching mathematics. In 1920 he began teaching mathematics in secondary schools in Mexico City while continuing to study at the Universidad Nacional Autónoma de México. In 1921 he became a professor of mathematics in the National School of Engineers. From 1923 he took courses in the School of Advanced Studies where he took courses such as Philosophy taught by Antonio Caso, Adolescent Psychology taught by Ezequiel Chávez, Educational Philosophy also taught by Ezequiel Chávez, School Organisation taught by Moisés Sáez, and Mathematics taught by Sotero Prieto. Nápoles taught at the National Preparatory School becoming head of mathematics there in 1926. Alberto Barajas entered the National Preparatory School in 1930 and had Nápoles as his mathematics teacher. Barajas writes [23]:-

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.The course that Barajas was taking with Nápoles was, however, cut short [11]:-

One day we began to notice him nervous and worried, then he announced that the course would have to be shortened and the final examination would be in August. From the newspapers we learned the cause of his concern: he had just been awarded a Guggenheim fellowship to pursue higher studies at the Massachusetts Institute of Technology. He was the first Mexican mathematician to obtain such an honour. From that moment, our respect for him took a quantum leap.Nápoles applied for the John Simon Guggenheim Memorial Foundation fellowship since he had been advised and encouraged to do so by Sotero Prieto. The award of the fellowship is reported in [20]:-

The Committee of Selection in Mexico for the John Simon Guggenheim Memorial Foundation takes great pleasure in announcing that, upon its nomination and recommendation, the Trustees of the Foundation have appointed Mr Alfonso Nápoles Gándara and Dr Arturo Rosenblueth Stearns to the first Latin American Fellowships granted by the Foundation in Mexico. The Committee of Selection in Mexico ... received some 50 applications for the two fellowships offered by the Guggenheim Foundation for the year 1930. These applications came from various States of the Republic and represented almost every field of intellectual endeavour. The attainments and plans for study of many of the applicants were of the highest type and the committee was able to make its final selections only after a great deal of difficult study and comparison. After a careful consideration of each case, however, the committee was unanimous in the opinion that the greatest contributions, in line with the purposes of the Foundation, would be made by Doctor Rosenblueth and Mr Nápoles.More detail of Nápoles' proposed plans are given in [21]:-

The object of Doctor Nápoles' fellowship will be to permit him to engage in a study of higher mathematics in the Massachusetts Institute of Technology and to pursue further study in the principles of pedagogy and methods of teaching mathematics in secondary schools. Doctor Nápoles has had many years' experience as teacher of mathematics in the secondary schools of Mexico City and is at present professor of that subject in the College of Engineering of the National University of Mexico.José Adem spoke about this in his speech [18]:-

Highly impressed with the large number of innovative courses that he found at the Massachusetts Institute of Technology and at Harvard University, many of them never before studied in Mexico, Nápoles Gándara set himself the goal of learning as many subjects as possible in order to bring them to our country. In just 18 months and through an extraordinary effort, he managed to internalise himself in a large number of topics, including Mathematical Analysis, Differential Geometry, Tensor Calculus, Fourier Series and the Theory of Functions. The lectures that he gave upon his return became the main basis for training a group of young higher mathematics teachers, which would later constitute the physical-mathematical faculty of our Faculty of Sciences.From September 1930 to January 1932 Nápoles studied fourteen graduate level courses at the Massachusetts Institute of Technology including Differential Geometry, Tensor Calculus (Absolute Differential Calculus), Riemannian Geometry, Differential Equations (advanced course), Fourier Series, Calculus of Variations, Probability Theory, Real Variable Functions, Algebraic and Projective Geometry. He also took courses on Functions of Complex Variables and Mathematics Teaching Methods at Harvard University.

José Adem said in his speech [18]:-

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.Nápoles himself recognised the importance of the Section of Mathematics and Theoretical Physics and wrote [26]:-

It was an escape valve for some distinguished professors and students in the exact sciences. Like an oasis in the aridity of the environment. There they were able to present some original research papers in physics and mathematics, and develop several topics of higher study in both disciplines. A new, promising era for physics and mathematics was beginning.While at the Massachusetts Institute of Technology, Nápoles had become friends with Dirk Struik. Realising the importance of foreign contacts for those researching in the Section of Mathematics and Theoretical Physics, Nápoles requested the Ministry of Education Public to invite Struik to visit Mexico. This was an important move for up until that time no leading foreign mathematicians had gone to Mexico. Struik visited in 1934 and gave lectures on tensor calculus and probability theory to the Antonio Alzate Academy of Sciences.

Sotero Prieto, who had taught and inspired Nápoles, was undoubtedly the leading mathematician in Mexico at this time but tragically he committed suicide on 22 May 1935. This meant that, for thirty years from 1935 to 1965, Nápoles became the leading figure in Mexican mathematics. It was through the efforts of Nápoles that, towards the end of 1938, the Faculty of Sciences was created in the Universidad Nacional Autónoma de México. Also through his efforts, the Institute of Mathematics was founded on 30 June 1942. He was appointed as its first director and remained the director from 1942 to 1966 although during 1964 Roberto Vázquez acted as Director for a few months while Nápoles was on sabbatical leave.

The Institute of Mathematics began to operate in the Palacio de Minería, in the historic centre of Mexico City. The building also housed the National School of Engineers and the recently founded Faculty of Sciences. The Institute was subdivided into three areas: Pure Mathematics, led by by Alberto Barajas and Roberto Vázquez, Applied Mathematics, led by Carlos Graef, and Logic and Fundamentals led by Francisco Zubieta. These four young researchers and the director Alfonso Nápoles were the only members of the Institute's academic staff when it was founded. One of the most important functions of the Institute under Nápoles' leadership was the bringing of foreign mathematicians to work and lecture there. Particularly important for Mexican mathematics was the many visits of George D Birkhoff and Solomon Lefschetz between 1944 and 1966.

Although Nápoles was the leading Mexican mathematician from 1935, he had no mathematics degrees. In 1939, he obtained a master's degree in Physical Sciences and Mathematics, awarded by the Ministry of Education. In 1940 he was awarded a doctorate in mathematics conferred by the National Autonomous University of Mexico. It is worth noting that Nápoles did not want to receive the doctorate but in the end accepted it feeling that it was good for Mexican mathematics. The doctoral diploma is dated 28 November 1940. Manuela Garín was involved in finding and restoring the diploma after the death of Nápoles and a ceremony was held in celebration, see [12].

The First National Congress of Mathematics was held in the city of Saltillo, Mexico, 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 from 1943 to 1945. Nápoles was President of the Mexican Mathematical Society from its founding in 1943 until 1955, and then again from 1957 to 1961. In 1961 he was made an Honorary President for Life.

Alfonso Nápoles married Guadalupe Salazar Espinosa de Los Monteros on 22 December 1948 in Mexico City. Guadalupe, the daughter of Mariano Salazar and Guadalupe Espinosa de Los Montero, had been born in Puebla, Mexico, on 18 March 1900. They had one son, Alfonso Nápoles Salazar, who became an architect and a Professor of Architecture at the Universidad Nacional Autónoma de México.

Santiago Ramirez writes in [26]:-

Nápoles published little, had few disciples, his life has an anticlimactic taste, there are no great deeds, there are no great acts of heroism. It was a thankless job: organising, raising money, convincing the authorities of the time that mathematics existed. In a way, life, the long life of Nápoles, had a taste of sadness, of loneliness, of an inner conviction that is proof against any bureaucratic obstacle that might arise, an inner conviction that one day we would be here as we are today.Although he published little, Nápoles did publish three volumes of the book

*Algebra elemental para escuelas secundarias*Ⓣ which was very popular and ran to several editions.

Nápoles received a number of honours for his outstanding contributions to Mexican mathematics. In 1953 the Autonomous University of the State of Morelos awarded him an honorary doctorate, in 1956 the Benito Juárez Autonomous University of Oaxaca awarded him an extraordinary professorship and in 1965 he received the distinction of emeritus researcher from the National Autonomous University of Mexico. He was awarded a prize by the National University in 1987 for his Teaching in Exact Sciences.

Let us end by quoting Nápoles' own thoughts about mathematics as given in [3]:-

... mathematics is a very abstract science and difficult; being difficult in general is not very attractive for the students. [However] mathematics exercises the mind and helps the student to reason and decide correctly. But not everyone realises this. Know to foresee and foresee to act. The one who is going to act must foresee, but in order to foresee, one must know. A person who studies mathematics, due to its structure and practice of logic, acquires greater abilities to predict than those who do not study it. Those who study mathematics are taught to reason correctly, for that is its main purpose. As I have told my students: it doesn't matter if you forget the name of the theorem and what it consists of; but by studying it they understood and exercised reasoning. It is an intellectual exercise that when it is done it leaves its mark.

### References (show)

- J Adem, A Barajas, S Lefschetz, E Lluis, A Nápoles Gándera, F Recillas, G Torres and R Vázquez (eds.)
*Symposium Internacional de Topología Algebraica*(La Universidad Nacional Autónoma de México y la UNESCO, 1958). - Alfonso Nápoles Gándara: Docencia en Ciencias Exacta,
*Centro de Ciencias Matemáticas, National Autonomous University of Mexico*.

https://www.matmor.unam.mx/~muciray/smm/60/alfonso3.html - Alfonso Nápoles Gándara: Docencia en Ciencias Exacta, in
*Nuestros Maestros***4**(Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México, 1998), 110-112. - Alfonso Nápoles Gándara,
*Geneanet*.

https://gw.geneanet.org/sanchiz?n=napoles+gandara&oc=&p=alfonso - Alfonso Nápoles Gándara 1897 - 1992 México,
*Instituto de Matemáticas de la Universidad Nacional Autónoma de México.*

https://matematicos.matem.unam.mx/matematicos-i-p/matematicos-n/alfonso-napoles-gandara/631-alfonso-napoles-gandara-1897-1992-mexico - Alfonso Nápoles Gándara,
*John Simon Guggenheim Memorial Foundation*.

https://www.gf.org/fellows/alfonso-napoles-gandara/ - Alfonso Nápoles Gándara,
*Prabook*.

https://prabook.com/web/alfonso.napoles_gandara/1114517 - A Barajas, Alfonso Nápoles Gándara,
*Centro de Ciencias Matemáticas, National Autonomous University of Mexico*.

https://www.matmor.unam.mx/~muciray/smm/60/alfonso2.html - A Barajas, Alfonso Nápoles Gándara, in
*Nuestros Maestros***1**(Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México, 1992). - A Barajas, Alfonso Nápoles Gándara,
*El Irracional***16**(February 1993), 1-3. - A Barajas, Alfonso Nápoles Gándara,
*Revista de Cultura Científica, Facultad ee Ciencias, Universidad Nacional Autónoma De México*.

https://www.revistacienciasunam.com/en/106-revistas/revista-ciencias-53/926-alberto-barajas.html - Ceremonia de entrega del diploma de Doctorado del profesor Nápoles Gándara,
*Instituto de Matemáticas de la Universidad Nacional Autónoma de México.*

https://www.matem.unam.mx/acerca-de/noticias/ceremonia-de-entrega-del-diploma-de-doctorado-del-profesor-napoles-gandara - F Del Río Haza,
*Destellos del cosmos. Ensayo biográfico sobre Manuel Sandoval Vallarta*(El Colegio Nacional, 2020). - J Flores and N Blazquez Graf (eds.),
*Ciencia, tecnología y género en Iberoamérica*(Universidad Nacional Autónoma de México, Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidades, 2005). - Fondo de Cultura Económica,
*México, setenta y cinco años de revolución: Educación, cultura y communicación*(Fondo de Cultura Económica, 1988). - M Garín and M G Lomelí, Alfonso Nápoles Gándara,
*Instituto de Matemáticas de la Universidad Nacional Autónoma de México.*

https://matematicos.matem.unam.mx/matematicos-i-p/matematicos-n/alfonso-napoles-gandara/630-alfonso-napoles-gandara-a-barajas - N Illescas, El milagro de las matemáticas: Entrevista a Alberto Barajas,
*Instituto de Matemáticas de la Universidad Nacional Autónoma de México*(1995)*.*

https://paginas.matem.unam.mx/matematicos/matematicos-a-g/matematicos-b/barajas-alberto/1496-el-milagro-de-las-matematicas - José Adem: Ciencias Exactas. Mathematico,
*El Colegio Nacional*.

https://colnal.mx/integrantes/jose-adem/ - J Justin Castro and J A Garza (eds.),
*Technocratic Visions. Engineers, Technology, and Society in Mexico*(University of Pittsburgh Press, 2022). - Latin American Exchange Fellowships of the Guggenheim Foundation, in
*Bulletin of the Pan American Union***64**(1930), 447-451. - Mexico. Award of the Guggenheim Foundation Fellowship, in
*Bulletin of the Pan American Union***64**(1930), 970. - Nápoles family,
*ancestry.com*. - M Neumann and P Saavedra, Una conversación con Alberto Barajas, El Hacedor de Sueños,
*Instituto de Matemáticas de la Universidad Nacional Autónoma de México.*

https://paginas.matem.unam.mx/matematicos/matematicos-a-g/matematicos-b/barajas-alberto/214-una-conversacion-con-alberto-barajas-el-hacedor-de-suenos - C Prieto de Castro, Sotero Prieto Rodríguez,
*Miscelánea Matemática***57**(2013) 123-128. - S Ramirez, Alfonso Nápoles Gándara: A 100 años de su nacimiento,
*Centro de Ciencias Matemáticas, National Autonomous University of Mexico*.

https://www.matmor.unam.mx/~muciray/smm/60/alfonso.html - S Ramirez, Alfonso Nápoles Gándara: A 100 años de su nacimiento,
*Carta Informativa Sociedad Matemática Mexicana***15**(November 1997), 4-5. - Y Rodríguez González, Alfonso Nápoles Gándara, forjador de un destino matemático, Revista de Divulgación Científico-Tecnológica del Gobierno del Estado de Morelos.

https://www.revistahypatia.org/conociendo-a-revista-23.html - P Saavedra and M Neumann, Una pionera de la Matemática en México,
*Centro de Ciencias Matemáticas, UNAM*(February 1997).

https://www.matmor.unam.mx/~muciray/smm/60/manuela.html - Semblanza de Alfonso Nápoles Gándara,
*Instituto de Matemáticas de la Universidad Nacional Autónoma de México.*

https://matematicos.matem.unam.mx/matematicos-i-p/matematicos-n/alfonso-napoles-gandara/629-semblanza-de-alfonso-napoles-gandara

### Additional Resources (show)

Other websites about Alfonso Nápoles Gándara:

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Written by J J O'Connor and E F Robertson

Last Update June 2023

Last Update June 2023