Mischa Cotlar

Quick Info

1 August 1913
Sarny, Ukraine
16 January 2007
Buenos Aires, Argentina

Mischa Cotlar was a Uruguayan mathematician who worked in the fields of harmonic analysis, ergodic theory and spectral theory.


Mischa Cotlar's parents were Ovsey Cotlar (1879-1952) and Sara Medved (-1965). Ovsey Cotlar ran a flour mill, but was more famous as an outstanding chess player. He died in 1952 and an obituary in the September-October 1952 issue of the Chess magazine Caissa stated:-
Recently passed away in the capital (Buenos Aires), the Russian teacher Ovsey Cotlar, widely known for his research on the Lasker defence of the Queen's gambit and the Rubinstein system of the Ruy Lopez, work that adorned the pages of 'Caissa' at the time. Despite his advanced age of 73 years, he could still expect other contributions to the theory which is why his death is more regrettable.
Chess was not Ovsey Cotlar's only passion, however, for he was also deeply interested in mathematics and music. Mischa had an older brother Sasha Cotlar, born 7 April 1910, died 1991. In 1928 the Cotlar family, who were Jewish, emigrated from the Ukraine, forced out by the Bolshevik revolution, and arrived in Montevideo. Mischa was only 15 at this time and had only had one year of formal education. He had been taught both mathematics and music by his father and was an excellent pianist.

The Cotlar family were poor, living in a single room in Montevideo, and they all had to work to earn a living. Ovsey became a newspaper salesman, selling newspapers in front of a hotel on the Avenida 18 de Julio, the main street in Montevideo. Sasha worked on the tramway while Mischa played the piano from 4 p.m. to 4 a.m. in a harbour bar. The first possession that Ovsey bought was a piano for Mischa. It was paid for in instalments and only fitted into their one room accommodation with great difficulty.

That this was no ordinary poor family became apparent once Ovsey Cotlar began playing competitive chess. The Uruguayan Chess Society held an annual competition which Ovsey won. This gained him immediate fame with reporters interviewing the newspaper seller who had beaten all the Uruguayan chess players. Ovsey told the reporters that he had a son who was mathematically gifted and this was reported in the papers. This immediately made the Uruguayan mathematician Rafael Laguardia take notice since he was himself an avid chess player. Laguardia was an excellent mathematician who had studied with Émile Picard at the Sorbonne in France. He invited Cotlar to join a mathematical group that met in his home. José Luis Massera writes [13]:-
It was immediately evident that he not only was very talented but showed a great originality.
Joining Laguardia's small group gave him access to several mathematicians but, perhaps even more significant, it meant that he gained access to Laguardia's excellent mathematical library. Before leaving the Ukraine, Cotlar had studied Dmitry Grave's number theory book and solved some of the open problems in the book. He showed Laguardia his solutions and Laguardia was totally amazed that a boy with only one year of formal schooling could produce mathematics which was not only correct but was rigorously written with ingenious arguments. Although Cotlar had solved some open problems, other mathematicians had solved them too and published the results but, of course, Cotlar had no way of knowing this. After being a member of Laguardia's group for two years, in 1930 Laguardia asked him to teach a course on number theory at the Engineering School of the Universidad de la República. At this time he was still earning money by playing the piano in the harbour bar but, in 1931, Laguardia arranged for him to play in a trio to entertain the customers at the up-market British Hotel in the seaside resort on Punta del Este.

Julio Rey Pastor began to visit Laguardia's group in Montevideo. José Luis Massera writes that [13]:-
... every weekend "Don" Julio Rey Pastor came to visit us from Buenos Aires and taught us on some of the new developments of mathematics - of which we knew nothing. Our mathematical relation with Rey Pastor was very fruitful, since we were able to discuss our mathematical problems freely in a one-to-one basis. In this way, our horizons were open to the then new mathematics: general topology, algebra, modern analysis. Don Julio had a very complex personality, and occasionally he was very difficult to deal with; but the overall balance of our relationship with him is, undoubtedly, enormously positive for the development of mathematics in Uruguay.
Rey Pastor encouraged Cotler to move to Argentina and, in 1935, he moved to Buenos Aires. With a letter of introduction addressed to Juan Carlos Vignaux, he arrived at the School of Sciences. With no formal qualifications he could not register as a student but he was allowed to attend classes. He met Manuel Sadosky who wrote [17]:-
Cora Ratto - then my classmate and later my wife - and I immediately took a liking to the "Russian peasant," who was withdrawn and extremely humble. After a short while, Mischa told Cora that he missed playing the piano very much. Music allowed him to take refuge from the often dismal surrounding reality to enter a world of peace and harmony. Cora immediately invited him to play at her home and, after a long argument, convinced Mischa to accept the offer. Cora's mother delighted in Mischa's playing and always considered it a great personal vindication to have met a talented young man willing to use an instrument she had not succeeded in making important to her own children. Mischa, in his desire not to intrude, sat on the very edge of the piano stool, and we were always worried about the stability of the system and imagined the pianist rolling on the floor! Little by little, Mischa carved his place in Buenos Aires. He earned his living tutoring students and even got a more stable situation teaching in a private academy that prepared candidates to enter the Naval School.
In 1937 Cotlar met Yanny Frenkel, a Ph.D. student of Rey Pastor, who was born in Melitopol, Russia on 21 May 1909. We note here a slight discrepancy since although Yanny gives this date of birth on one of her trips into the United States, on two other trips she gives her age which would correspond to a 1910 date of birth. They were married in 1938.

Cotlar, with no formal qualifications, could not obtain an official teaching position. However he did make contacts with some people who would be significant collaborators. Beppo Levi was Jewish and dismissed from his position in Bologna, Italy, after Mussolini brought in the Manifesto of Race in July 1938. He was a friend of Rey Pastor and in October 1939 he emigrated to Argentina to be the director of the recently founded mathematical institute at the Universidad del Litoral in Rosario. Although he was 64 years old at this time, he was able to continue research and administration for a further 20 years and became one of Cotlar's friends and collaborators. They produced three joint papers, the first being published in 1943. Equally important was the fact that Cotlar published nine papers in Mathematicae Notae, a journal founded by Beppo Levi. The other significant person that Cotlar met was Rodolfo A Ricabarra (1925-1984); they became firm friends and published seven joint papers, the first being published in 1949.

For a list of Mischa Cotlar's publications, see THIS LINK.

For a list of Yanny Frenkel's publications (note she published under the name Yanny Frenkel rather than Yanny Cotlar), see THIS LINK.

In 1945 Cotlar was appointed as a research instructor at the Universidad National de La Plata when the engineer A Martínez Civelli was rector, but six months later a new rector was appointed and Cotlar was quickly dismissed.

Several mathematicians who were based in the United States made visits to Argentina. George D Birkhoff visited Buenos Aires in 1942 and immediately saw what a talented mathematician Cotlar was and said he would recommend him for a Guggenheim Fellowship. Sadly George Birkhoff died in 1944 before this was completed. Antoni Zygmund, who was based at the University of Chicago, made his first visit to Argentina in 1949 on a Fulbright scholarship. He discovered two exceptional students, Mischa Cotlar and Alberto Calderón, and arranged for Calderón to study at Chicago for a Ph.D. advised by him. Garrett Birkhoff, George Birkhoff's son, came across paper work in his father's papers concerning Cotlar and the Guggenheim Fellowship and he took the application forward. Cotlar was recommended for a Guggenheim Fellowship by Garrett Birkhoff, which he won in 1950. On 24 January 1951 Mischa and Yanny Cotlar flew from Buenos Aires to New York. They spent six months at Yale University, where Mischa studied ergodic theory with Shizuo Kakutani. Marshall Stone had agreed that, despite Cotlar having no formal qualifications, the University of Chicago would accept him onto a Ph.D. course. He went there and was advised by Antoni Zygmund. Cotlar said [2]:-
In 1951 I did not have any degree but they got me a scholarship to go to Chicago. I wanted to go to classes, especially Zygmund's classes, but he said to me: "What are you doing here? Go and do your own things."
Cotlar may not have had any qualifications, but by 1950 he had already 27 publications. He was awarded a doctorate by the University of Chicago in 1953 for his thesis On the theory of Hilbert transforms. Following this, he and his wife returned to Argentina sailing from New York to Buenos Aires on the ship the Rio Araza, departing on 28 March 1953. To obtain a position at the University of Buenos Aires he would have been required to sign allegiance to Juan Perón, then President of Argentina, and this he would not do having strong moral principles. There was another possibility [17]:-
By 1953, thanks to the "diplomatic" efforts of that great man, Antonio Monteiro, a Departamento de Investigaciones Científicas (DIC), was created at the Universidad Nacional de Cuyo. And the only requirements to join the DIC were professional! The appointment of Mischa as Director of DIC was a "bomb" in our small circle, The job of director or chairman entails bureaucratic chores; it is necessary to deal with files and budgets; but, worst of all, it requires wearing a tie for official ceremonies! Who could imagine Mischa in such a garb? A group of intelligent. enthusiastic, and heterodox people gathered at DIC. They published a journal, the 'Revista Matemática Cuyana', to record the research produced there. Its contents received very favorable comments in the mathematical reviews. The results of the work at DIC fructified Argentine mathematics for years to come, since after it was closed in 1956, again for political reasons, its researchers went on to teach students who are now well-known mathematicians themselves. In fact, when the university situation changed dramatically in 1956, Mischa and his collaborators were asked to join university faculties all over the country.
While at DIC, Cotlar published four important papers in the Revista Matemática Cuyana, These are [35]-[38] in the list of his publications we give at THIS LINK.

After DIC was closed, Cotlar was appointed Professor of Mathematics at the School of Sciences of the Universidad de Buenos Aires in 1957. He spent nine years in this position during which time he wrote three monographs ([42], [47] and [52] in the list of his publications). He also wrote two textbooks, namely Introducción al Algebra with Cora Ratto de Sadosky, and Nociones de Espacios Normados with Roberto Cignoli.

Arturo Illia had become President of Argentina following elections in June 1963. He tried to split the Perónists, who controlled the unions, from their exiled leader Perón. The Perónists reacted by supporting a coup against President Arturo Illia in June 1966 and General Juan Carlos Onganía, the commander in chief of the army, took control of the country. Following the military takeover, the University of Buenos Aires was attacked by police in August 1966. Cotlar resigned, along with 400 other academics, and after a short stay in Montevideo, was appointed to Rutgers University in the United States in 1967. He spent the year 1969-70 at the University of Nice in France at the invitation of Jean Dieudonné. In 1971 he taught at the Universidad Central de Venezuela while still holding a tenured professorship at Rutgers. In the following year Cotlar and his wife Yanny both returned to Argentina. Cotlar was appointed as professor at the Universidad de la Plata, where his friend and colleague Rodolfo Ricabarra also joined the faculty. After a couple of years, the political situation once again made life impossible.

Argentina was ruled by the military until elections were held in March 1973. Héctor J Cámpora became president and began to work towards having the exiled Juan Perón return. He did so in June 1973 which caused violent fighting but he became president in October 1973. Opposition increased and the police, paramilitaries and intelligence branches of the administration, began to crack down on political, student, and union leaders. Human rights activists were particularly targeted. Cotlar left and was appointed to the Central University of Venezuela in Caracas. Stefania Marcantognini writes in [12] about Cotlar's seminar at the Central University of Venezuela in Caracas:-
The Seminar which has been held until today for almost twenty years, has hosted what we can today call the group of Harmonic Analysis and Theory of Operators of Venezuela, a group of young Venezuelan mathematicians who in various universities of the country seek to develop research activities in those areas. The influence of Mischa is reflected in the attitude and work capacity of this group, which is beginning to be recognized beyond our borders. The Seminar has remained open to mathematicians from other areas who find a platform to discuss their ideas and find in Mischa a mathematician of extraordinary qualities and a man of friendly character. Mischa is, undoubtedly, the mathematician with the longest and most prestigious career among those who have worked permanently in Venezuela, and those of us who have the privilege of knowing him, we also know that he adds to his quality as a scientist a deeply modest and sincere personality.
Cora Sadosky writes [20]:-
In Caracas, Mischa and I began to collaborate in earnest and together we established an ambitious research program. Mathematically, our Caracas exile was extraordinarily productive. Although Mischa was part of the Zygmund school, he had an astonishing intellectual affinity with the Ukrainian school of Mathematics lead by Professors Krein and Gohberg, the leaders of the extraordinarily original and fertile school of operator theory. In spite of my analytic upbringing, I could not resist Mischa's daring approaches to operator theory. In 1980 Daniel, Cora Sol and I moved to the U.S., and Mischa remained in Venezuela. He loved Caracas - the climate, the mountains, the flowers, and the Venezuelans. Mischa and Yanny came to visit us every year, in Washington, DC, Princeton, and Berkeley - and for many years I spent several weeks in Caracas. Thus our mathematical collaboration was not interrupted. When Mischa and Yanny decided to return to Buenos Aires, Mischa still kept sending me scores of hand-written manuscripts with new ideas that we needed to develop.
Cotlar was elected to the National Academy of Exact Sciences of Argentina in 1988. Alberto Calderón gave a speech introducing Cotlar to the Academy. You can read the speech at THIS LINK.

We would like to quote here Calderón's description to Cotlar's mathematical contributions [5]:-
Cotlar's mathematical work has very singular characteristics. One is its insights, bringing to light the deep roots and motivations of theories and theorems. The other is the vision that uncovers links and unsuspected relations between subjects that apparently have no connection at all. It is for these characteristics, I believe, that his works have a very definite taste of philosophical essays. Examples of this are the four consecutive papers that appeared in the 'Revista Matemática Cuyana, volume 1 (1955), Fasciculo 2'. In one of them, the result now known as Cotlar's Lemma shows the reason why, independently from Fourier Theory, the Hilbert Transform is bounded in L2L^{2}. In another of those papers, he gives the unified treatment of the Hilbert Transform and the Ergodic Theorem, which is known as the Principle of Transference in modern ergodic theory. Finally, I want to call attention to the fact that some of Cotlar's results, published in journals of little accessibility and slow distribution, have been named after other mathematicians who discovered them independently but years after him. One such example is the theorem of representation of s-Boolean algebras as a s-algebra of sets modulo an ideal of "null" sets, which today is known as the Loomis-Sikorski theorem.
We have mentioned Cotlar's modest personality several times but let us here quote the authors of [10] who write:-
Mischa is extremely modest and very dear to all those who are lucky enough to know him. As can be seen in the list of his publications, many of them are in collaboration with other mathematicians, one more indication of his friendly nature and his spirit of collaboration and also of the purely scientific interest that motivates him in his work.
Throughout his life Cotlar argued passionately for peace in the world and tried to encourage other scientists to join in his mission for peace. Towards the end of his life the cold war had essentially ended but this did not bring about the changes he wished in the world. He said [2]:-
There are still scientists working for destruction, to increase the killing power of the powerful. If the scientists and technicians refused to develop the weapons that are more deadly and precise every day, the world would be very different and we would not have what we see today, where so many innocents die who have nothing to do with the conflict while those responsible are safe.
For more on this the reader can see an English translation of Mischa Cotlar's 2006 Master Class on this topic at THIS LINK.

We also present an English translation of Carlos Borches' 2001 interview with Cotlar at THIS LINK.

An English translation of Mischa Cotlar's 'La Nación' obituary is available at THIS LINK.

Let us end with this quote from Cora Sadosky [20]:-
Mischa was never trapped into the brainless anti-Americanism of the times, and was never a "travel companion" of the Communists. He was deeply committed to a just peace in Israel/Palestine, and always defended Israel's right to exist. He also rejected the anti-Semitism barely hidden in many of the contemporary "progressive" agendas. However, along with many other pacifists, Mischa could not find a practical way to reconcile his absolute philosophical conviction about the wrongness of killing with the realities of war and peace. Mischa settled in Buenos Aires when Yanny's mental health deteriorated. He himself was also gravely sick, but he took loving care of Yanny until his death. In spite of his growing physical weakness, Mischa still tried to mobilize the international mathematical community for the creation of a new movement for the ethical responsibility of scientists. Unfortunately, this last appeal did not elicit a meaningful response. Mischa was an extraordinary person. He was endowed with many talents and the people around him were changed by his touch. All of the many friends that he met in his different endeavours will remember him with love and respect.

References (show)

  1. C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990).
  2. P Alegría, Mischa Cotlar, Department of Mathematics, Basque Country University. http://www.ehu.eus/~mtpalezp/mischa.html
  3. L Alvarez Alonso, Mischa Cotlar, in memoriam (1913-2007) (Spanish), Rev. Un. Mat. Argentina 49 (1) (2008), i-xi.
  4. L R Berrone, The correspondence of Beppo Levi and Misha Cotlar. Cotlar's first publications (Spanish), Bol. Asoc. Mat. Venez. 16 (2) (2009), 115-131.
  5. A P Calderón, Introduction of Professor Mischa Cotlar to the National Academy of Exact Sciences of Argentina, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), xix-xx.
  6. J Horváth, Encounters with Mischa Cotlar, Notices Amer. Math. Soc. 56 (5) (2009), 616-620.
  7. J Horváth, My meetings with Mischa Cotlar (Spanish), Bol. Soc. Mat. Mexicana (3) 15 (1) (2009), 1-9.
  8. J Horváth, The early papers of Mischa Cotlar (1936-1955), in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), 689-714.
  9. R José R León, Mischa: Veinte Años de Actividad en Venezuela, Asociación Matemática Venezolana, Boletín I (1) (1994), 47-50.
  10. E Lima de Sá and L Recht, Mischa Cotlar: Notas Biográficas y Bibliografía, Asociación Matemática Venezolana, Boletín I (1) (1994), 75-83.
  11. Mischa Cotlar: Obituary, La Nación (17 January, 2007).
  12. S Marcantognini, Mischa, mi maestro, Asociación Matemática Venezolana, Boletín I (1) (1994), 43-46.
  13. J L Massera, Mischa in Montevideo, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), xxi-xxiv.
  14. Mathematical publications of Mischa Cotlar, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), 681-687.
  15. Publications of Professor Mischa Cotlar. Conference in Honor of Mischa Cotlar (Buenos Aires, 1988), Rev. Un. Mat. Argentina 34 (1988), 10-15.
  16. A Quirós Gracián, Mischa Cotlar, in memoriam (Spanish), Gac. R. Soc. Mat. Esp. 10 (2) (2007), 398-401.
  17. M Sadosky, My friend Mischa Cotlar, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), xxv-xxvii.
  18. C Sadosky, Preface, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), v-vi.
  19. C Sadosky, Mischa Cotlar: A biography, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), xv-xiix.
  20. C Sadosky, On the life and work of Mischa Cotlar, Rev. Unión Mat. Argent. 49 (2) (2008), i-iv.
  21. C Sadosky, The mathematical contributions of Mischa Cotlar since 1955, in C Sadosky (ed.), Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar (Marcel Decker, Inc., New York and Basel, 1990), 715-742.

Additional Resources (show)

Written by J J O'Connor and E F Robertson
Last Update May 2018