# Samuel Carlos Gitler Hammer

### Quick Info

Cuauhtémoc, Mexico City, Mexico

Mexico City, Mexico

**Samuel Gitler**was a Mexican mathematician who made outstanding contributions to algebraic topology. He played a major role in leading algebraic research groups in Mexico City and at the University of Rochester, New York.

### Biography

**Samuel Gitler**was the son of Moises Gitler Hammer (born in Czestochowa, Poland on 1 April 1907) and his wife Mariem. Moises (whose name sometimes appears as Mojzesz) and Mariem Gitler (whose name sometimes appears as Miriam) were Polish Jews who married in Poland and, together with their parents, they emigrated to Mexico in 1933. Mariem was pregnant with their first child when they left Poland and Samuel Gitler, the subject of this biography, was born in Mexico City soon after they reached Mexico. Their second child, Mario Gitler, was born on 11 February 1937 also in Mexico City. Samuel's mother, however [15]:-

... passed away when he was a few years old. His childhood was spent in the Bohemian atmosphere of his grandparents' house.Let us note at this point that there is detailed, but completely incorrect, information about Samuel Gitler's family on ancestry.com where he has been assigned to the wrong Gitler family.

Samuel attended primary school in Mexico City. When he was thirteen years old his father sent him to San Antonio, Texas, USA, to attend Junior High School. He flew from Mexico City to San Antonio, Texas, on American Airlines, arriving in San Antonio on 9 September 1946. He returned to Mexico City for Christmas 1946, returning to San Antonio, Texas on American Airlines on 6 January 1947. Back in Mexico City over the summer vacation, he returned again to San Antonio on 5 September 1947. It was at the Junior High School in San Antonio that Samuel first found his talent and love of mathematics. Although his English was poor, the mathematics teacher would praise him in front of the class, telling the other students that he was better than any of them at mathematics even if he struggled to speak English.

Back in Mexico City for Christmas 1947, he began his studies at Escuela Nacional Preparatoria in January 1948. This school, the oldest and one of the most prestigious senior high schools in Mexico, belonged to the National Autonomous University of Mexico (UNAM). At Escuela Nacional Preparatoria, Gitler was taught by Eli Eduardo de Gortari (1918-1991). Gortari had studied engineering at the UNAM, then became a sanitary engineer but continued to study mathematics and philosophy which led to him becoming a teacher and professor. He quickly saw the mathematical potential in young Gitler and began to teach him introductory material on topology. He told Gitler that topology was the topic for him and gave the boy a topology book to study; Gitler loved it. The Escuela Nacional Preparatoria not only set him up to be a topologist, but it was also where he met fellow student Raquel Goldwain whom he later married. Raquel had been born in Mexico City on 19 March 1935.

Gitler graduated from the Escuela Nacional Preparatoria in 1952 and later that year began his studies of engineering at the National School of Engineering (ENI), part of the National Autonomous University of Mexico. In his first year of the engineering course he was taught calculus by Emilio Lluis Riera (1925-2020). Riera had a bachelor's and master's degree from the UNAM and when he taught Gitler he was near to completing his doctorate in mathematics at the new Ciudad Universitaria. Riera quickly spotted Gitler's potential as a mathematician and advised him to enrol in the B.Sc. mathematics course. He did this but did not give up his engineering degree so at this stage he was studying for two degrees simultaneously. In addition, he was also teaching mathematics at the ENI. When he began to undertake this heavy load, at least engineering and mathematics were taught in the same building but after a year mathematics moved to the new Ciudad Universitaria on the opposite side of Mexico City [14]:-

... every day he crisscrossed the city starting early in the morning the engineering courses; then teaching mathematics at ENI, and then until 10 pm studying mathematics; not only that: he decided to finish engineering in only 4 years so he had an accelerated pace.He wrote an engineering thesis advised by Heberto Castillo Martínez (1928-1997) who later had a political career as an activist for workers' rights.

Gitler had been lucky that his Jewish parents had fled from Poland before World War II. He also benefitted in perhaps a very surprising way. Solomon Lefschetz had a great love for travel and during the 1920s and 1930s had made many trips to European countries. The outbreak of World War II in 1939 meant that Europe was no longer possible for travel so Lefschetz looked for other places to visit. Mexico seemed like a good choice and in 1944 he spent the summer in Mexico City at the National Autonomous University of Mexico. It was the first of many visits and he eventually fell into the habit of spending the summer months there every year. He continued this until 1966. Lefschetz had arranged for the outstanding young mathematician José Adem to go to Princeton for his Ph.D. studies in 1949 and then five or six years later he met up with Gitler in the Ciudad Universitaria and realised that here was another outstanding young mathematician. By this time José Adem was a researcher in the Ciudad Universitaria and had got to know Gitler. Lefschetz talked with José Adem and both felt sure that Gitler should go to Princeton to undertake research for a Ph.D.

Before travelling to Princeton, Gitler married Raquel Goldwain in September 1956. The newly married couple then flew with Air France from Mexico City to Idlewild Airport, New York, arriving there on 11 September 1956. At Princeton, Norman Steenrod was Gitler's thesis advisor. Gitler graduated with a Ph.D. in 1960 having submitted his 95-page thesis

*Cohomology Operations with Bundles of Coefficients*. In 1963 he published the paper

*Cohomology Operations with Local Coefficients*in which he gives the following note [13]:-

This paper contains the main results of a Doctoral Thesis developed by the author under the guidance of Prof N E Steenrod and submitted to Princeton University in 1960.Samuel and Raquel Gitler had three children, Isidoro Gitler (born 2 August 1957 in Princeton), Miriam Gitler (born 28 December 1958) and Susanna Gitler. The family lived at 228-B Halsey Street in Princeton and made several trips back to Mexico City during their time there. For example Samuel, Raquel and Isidoro returned to Princeton from a visit to Mexico City on 15 July 1958. Also Samuel, Raquel, Isidoro and Miriam Gitler flew back to Princeton from their 1959 summer visit to Mexico City on 19 October. Samuel's father, Moszesz Gitler Hammer, had flown from Mexico City to New York on 2 August 1959 giving 228-B Halsey Street, Princeton as his United States address.

After graduating, Gitler spent a short spell at Brandeis University in Waltham, Massachusetts. On 9 August 1960 he flew into New York giving his address in Waltham as 32 Concord Road. He returned to Mexico City in 1961 and, together with José Adem, founded the Mathematics Department of the Centre for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav). This Centre was founded on 17 April 1961 and was initially planned as a postgraduate department of the National Polytechnic Institute. Gitler worked at this Mathematics Department from 1961 to 1987, becoming a full professor in 1964. He also collaborated in 1961 in the foundation of the Higher School of Physics and Mathematics of the National Polytechnic Institute.

The authors of [14] write:-

The work of Sam Gitler is one of the more remarkable oeuvres in Mexican science in the XX century. Sam Gitler together with José Adem founded the modern Mexican mathematical school in algebraic topology, and maintained the highest standards in mathematical research in Mexico during decades in which, with no internet and repeated severe economical crisis, the isolation was considerable. Both were the founding fathers of the Department of Mathematics at the Centre of Research and Advanced Studies (Centro de Investigación y de Estudios Avanzados del IPN-Cinvestav), one of the most important mathematics departments in Latin America. While he published in many international journals of the highest regard, it is notable that most of his papers appeared in the Boletín de la Sociedad Matemática Mexicana solidifying its prestige as a venue for topology, for this was the intellectual love of Gitler's life: algebraic topology.The work that Gitler undertook in algebraic topology is rather too technical to describe here in detail. Let us give at least a flavour with some quotes from [16]:-

One of the problems that Gitler attacked with lucidly (together with José Adem and other collaborators) was the celebrated immersion problem. This problem asks whether projective geometries with points at infinity in any dimension (Brunelleschi (1404-1472), Kepler, Desargues (1591-1661), Monge, Chasles, Poncelet, etc.) can be immersed in ordinary Euclidean geometries. David Hilbert asked his student Werner Boy to show that it was impossible to find an immersion of the real projective space of dimension two $\mathbb{R}P^{2}$ into the classical Euclidean space $\mathbb{R}^{3}$ in 1901; Hilbert was very surprised as Boy found such an immersion. Another important result was Whitney's embedding theorem which states that every n-manifold admits an embedding into $\mathbb{R}^{2n-1}$, together with Boy's result, at the beginning of Gitler's career, no additional explicit immersions were known. ... Gitler published one paper per year devoted to the problem from 1963 to 1969.Gitler made many research visits throughout his career. He was invited to the Institute for Advanced Studies in Princeton, United States on several occasions. He was there from August 1964 to April 1965, again from September 1985 to June 1986 and from September 2010 to May 2011. He was invited to spend several months at All Souls College, Oxford, England, beginning in September 1976. As with many of his visits, his family were with him. Elias Micha, also a Mexican, was undertaking graduate studies at Oxford at this time and writes in [17]:-

...

The opus magnum of Gitler was undoubtedly 'A Spectrum whose Cohomology is a certain Cyclic Module over the Steenrod Algebra' (Topology, 1972), in collaboration with Ed Brown; one of the most relevant works in algebraic topology of the twentieth century. It became a fundamental building block of modern homotopy theory going well beyond its original motivation.

It was in Oxford where I had the opportunity to meet the Gitler family and where I became another member of it, inasmuch as my friendship with Sam was extended from the beginning to Rachel and to his children Isidoro, Miriam, and Susy. With incredulity, I became aware that the doors of Sam's home were always open, and that it was a meeting place for several mathematicians and friends. The hospitality and cordiality with which me and my family were greeted by Rachel, her disposition to lodge us for several days and feed us splendidly, made me feel from the start as another member of that wonderful family, which I consider a fundamental part of my life.For more of Elias Micha's appreciation of Sam Gitler, see THIS LINK.

...

A distinctive quality of Sam's personality that I cannot omit is his exaggerated humility. Just as much in the clothes that he wears everyday, as in his personal manner, Sam does not carry on his shoulders the weight of the postures of the famous and conceited intellectual, or of the inaccessible man of success. On the contrary, he seems to pass, anxious not to be noticed. I recall the occasion in Oxford when, at tea time, Sam was taking about mathematics (for a change) to a group of students, myself included, when he hastily told us that he was going to travel to Mexico for about four days to receive a small recognition, and rapidly returned to the subject of mathematics. Several months later we learned that in that trip to Mexico, Sam received from the President of the country, The National Prize for the Sciences, which is the highest award possible for a Mexican Scientist.

In 1987 Gitler accepted an invitation to become the Chairman of the Mathematics Department at the University of Rochester in Rochester, Monroe County, New York in the United States. While there, he lived at 459 French Road in Rochester. At this time Mexico was going through an economic crisis and this was a factor in his decision to go to the United States. The

*New York Times*of 16 December 1987 reported [20]:-

The Mexican Government is struggling to regain control of an economic crisis that has unleashed a new round of record inflation, caused Mexicans to shun the peso and send their savings abroad, and stirred up labour discontent. Tonight, the Government announced an ''economic solidarity pact'' that includes sweeping tax increases and budget cuts designed to reduce the deficit.The authors of [14] write:-

In Rochester, he helped to build one of the most important groups in topology in the world.In 2001 Gitler returned to his former position at the Mathematics Department of the Centre for Research and Advanced Studies of the National Polytechnic Institute in Mexico City.

Many honours and awards were given to Gitler. We have already mentioned the National Prize of Science in 1976, but he was also president of the Mexican Mathematical Society from 1967 to 1969, chair at Cinvestav from 1973 to 1981, a member of El Colegio the Nacional from 1986, the highest recognition for his achievements given to members of the Mexican scientific and artistic community, and elected an inaugural fellow of the American Mathematical Society in 2012.

A conference

*Homotopy Theory and Its Applications*in honour of Samuel Gitler's sixtieth birthday was held at Cocoyoc, Mexico 9-13 August 1993. The editors write in the Preface [1]:-

In August 1993 a meeting was held in Cocoyoc, Mexico on the subject of Homotopy Theory and its Applications. There were many foreign participants in addition to a number of Mexican topologists. The main focus of the meeting was to highlight the current development of methods in homotopy theory, and how they can be applied to interesting problems involving classifying spaces, moduli spaces, representation theory, etc. The 16 papers in this volume testify to the diversity and activity in this area of mathematics.In 2002 an English translation of a Spanish text written by Gitler in collaboration with Marcelo Alberto Aguilar and Carlos Prieto de Castro with title

This conference was partly held to celebrate Samuel Gitter's sixtieth birthday. ... Sam Gitler has contributed significantly to the development of mathematics in Mexico. He served as editor of the Boletín de la Sociedad Matemática Mexicana and ran many seminars which helped to educate young topologists in Mexico.

*Algebraic topology from a homotopical viewpoint*was published. The publisher writes:-

The purpose of this book is to introduce algebraic topology using the novel approach of homotopy theory, an approach with clear applications in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. The basic concepts of homotopy theory, such as fibrations and cofibrations, are used to construct singular homology and cohomology, as well as K-theory. Throughout the text many other fundamental concepts are introduced, including the construction of the characteristic classes of vector bundles. Although functors appear constantly throughout the text, no knowledge about category theory is expected from the reader. This book is intended for advanced undergraduates and graduate students with a basic knowledge of point set topology as well as group theory and can be used in a two semester course.It was reviewed by Donald Davis who wrote [6]:-

This carefully written text presents a new approach to a first course in algebraic topology. The main novelty is defining the homology groups of a (pointed path-connected) CW complex as the homotopy groups of its infinite symmetric product. Cohomology groups are defined as homotopy classes of maps into Eilenberg-Mac Lane spaces, which are defined as infinite symmetric products of Moore spaces. This differs dramatically from most standard texts by making no mention of singular or simplicial homology. ... The novel approach to homology used in this book can be disconcerting to one who is used to the standard treatment. ...A conference

...

In conclusion, this text has developed a truly new approach to introductory algebraic topology.

*Recent Developments in Algebraic Topology*in honour of Samuel Gitler's seventieth birthday was held at San Miguel de Allende, Mexico 3-6 December 2003. The editors write in the Preface [2]:-

A conference on homotopy theory was held at San Miguel de Allende, México, on 3-6 December 2003. The conference covered several areas of current interest in the field ... The meeting was organised by the Department of Mathematics of the Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV) to celebrate Sam Gitler's seventieth birthday. It was extraordinary to see that the meeting was attended by many of his collaborators, colleagues, students, and friends. ...Pablo Cabanas Diaz writes in [5] about Gitler's remarkable work:-

In spite of the different important positions he has held, he has always been an enthusiastic topologist in his more than forty years of professional activity. Sam has written over forty papers as well as several books. All of them show a deep knowledge of topology and an acute point of view. Sam has been an active teacher. Several generations of mathematicians have benefitted from his expertise as well as from his immense generosity.

His mathematical work is one of the most notable within 20th century Mexican science. He was the founder of the modern Mexican mathematical school. He was able to sustain very high standards in mathematical research in Mexico for decades; if we consider that he achieved it at a time when there was no internet and during serious and repeated economic crises. His achievements are impressive given that Mexico's isolation in the field of mathematics was enormous. His contributions to mathematical knowledge materialised in nine collaborations in books, journals and conference proceedings, and in sixty-four articles published in specialised journals of the highest level, either individually or in collaboration with some of his colleagues.Gitler died on Wednesday 10 September 2014 and a Jewish funeral was held on the following day. His wife Raquel died at the age of 87 on Sunday, 24 July 2022.

### References (show)

- A Adem, R J Milgram and D C Ravenel (eds.),
*Homotopy Theory and Its Applications: A Conference on Algebraic Topology in Honor of Samuel Gitler, August 9-13, 1993, Cocoyoc, Mexico*(American Mathematical Society, 1995). - A Adem, J González and G Pastor (eds), Recent Developments in Algebraic Topology: Conference to Celebrate Sam Gitler's 70th Birthday December 3-6, 2003, San Miguel de Allende, México (American Mathematical Society, 2006).
- Agencias, Dr Samuel Gitler Z"L, Multigalardonado matemático miembro del Colegio Nacional,
*diariojudio.com*(10 September 2014).

https://diariojudio.com/comunidad-judia-mexico/dr-samuel-gitler-multigalardonado-matematico-miembro-del-colegio-nacional/13053/ - Agencias, La ciencia mexicana se duele por Samuel Gitler, EL Financiero (10 September 2014).

https://www.elfinanciero.com.mx/after-office/la-ciencia-mexicana-se-duele-por-samuel-gitler/ - P Cabanas Diaz, OTRAS INQUISICIONES: Grandes maestros: Samuel Gitler Hammer, Al Momento (21 July 2021).

https://almomento.mx/otras-inquisiciones-grandes-maestros-samuel-gitler-hammer/ - D M Davis, The mathematical work of Sam Gitler, 1960-2003, in
*A Adem, J González and G Pastor (eds), Recent Developments in Algebraic Topology: Conference to Celebrate Sam Gitler's 70th Birthday December 3-6, 2003, San Miguel de Allende, México*(American Mathematical Society - D M Davis, Review: Algebraic topology from a homotopical viewpoint, by Marcelo Aguilar, Samuel Gitler and Carlos Prieto,
*Mathematical Reviews*MR1908260**(2003c:55001)**. - S L de Medrano, Santiago López Samuel Gitler and the topology of intersections of quadrics,
*Bol. Soc. Mat. Mex.*(3)**23**(1) (2017), 5-21. - Fallece reconocido matemático mexicano Samuel Gitler Hammer, spanish.people.com.cn (11 September 2014).

http://spanish.people.com.cn/n/2014/0911/c92121-8781274.html - V Gugenheim, Review: Cohomology Operations with Local Coefficients, by Samuel Gitler,
*Mathematical Reviews*MR0158398**(28 #1621)**. - Prof Dr Samuel Gitler Hammer,
*Departamento de Matemáticas, Gobierno de México*.

https://www.math.cinvestav.mx/~sgitler/html/biografia.html

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Written by J J O'Connor and E F Robertson

Last Update June 2023

Last Update June 2023