Cora Ratto: in search of harmony

Alberto Mercado Saucedo

In addition to one of the first mathematicians trained in Argentina, he was also the protagonist of emblematic struggles, both for women's rights and in defense of democracy in the world. Her career as a mathematician was dramatically interrupted on several occasions by political ruptures in her country, which finally caused her to die in exile in 1981.

Corina Eloisa Ratto, who is often remembered as Cora Ratto de Sadosky, was born in 1912 In the Argentine capital, he entered the University of Buenos Aires to study mathematics in the 1930s, a time of explosive growth in the discipline, especially thanks to the impulse of Julio Rey Pastor, a Spaniard who arrived in the country in 1917 for a project to promote the development of mathematics. Cora had many other interests and during her university studies she participated in the leadership of the Argentine University Federation, the highest organization of university students in the country. He became increasingly involved in political and humanitarian causes in favor of victims of the racial discrimination of Nazism.

He married Manuel Sadosky, his partner in studies and political struggles, in 1937, while both were finishing their university careers. Manuel immediately completed a doctorate at the UBA, graduated in 1940 with a thesis on methods of approximate resolution of differential equations and was to become a renowned scientist; In particular, he is remembered for having managed the acquisition of Clementina the first computer in Argentina and for having created a career in computer science. In summary, he is considered the father of computing in the country. But this article is about Cora and not about Manuel, so we return to her: it is not difficult to imagine that she would also undertake a doctorate, taking into account the consolidation of research in mathematics that was achieved in Buenos Aires at the time. Rey Pastor's leadership bears fruit, and a good number of students receive PhDs, especially under his direction. In 1936, the UMA, the Argentine Mathematical Union, was founded, the first organization of its kind in Latin America. The work of Rey Pastor was joined by the arrival of Luis A. Santaló and Beppo Levi in ​​1939, and the Buenos Aires Mathematics Seminar reached important scientific activity. The growth of the discipline in the country is promising.

We cannot be sure if the idea of ​​continuing with her studies crossed the mind of Cora in those years, but the truth is that other responsibilities are yet to come. In 1940, the same year that Manuel received his doctorate, the couple's daughter was born. In addition, with the outbreak of the Second World War, Cora became the protagonist of a unique struggle for women's rights and for the defense of democratic values. She became Secretary General of the Junta de la Victoria, a political organization that brings together women from very different fields and whose main objective is to support the invaded countries in the global confrontation. Its main reference is the organized aid in favor of the Spanish republicans in the civil war, in which Cora was directly involved as a representative of student organizations of the UBA. The political experience of the Board is unprecedented in Latin America and in the world, and can be considered as a precedent for the approval of the right of women to vote in Argentina that occurred in 1947, a moment that represents a turning point in Cora's life.

That year, at the time that the activity of the Junta de la Victoria ends and the first government of Juan Domingo Perón begins in Argentina, Manuel obtains a grant to do research in France. All this means a milestone in the life of the family, which settled in Paris, where Cora began a doctorate directed by Maurice Frechet, a renowned mathematician who contributed to developing the foundations of functional analysis, and who by the way is the author of the well-known concept from metric space, generalization of the notion of distance used to study abstract sets. Cora interrupts her thesis due to another family move, this time to Italy, where Manuel is doing a postdoctoral research stay. The family returned to Argentina at the end of the 1940s, politically very complicated times, which in particular means that they cannot access any job at the university.

The conditions of the country changed in 1955, the University of Buenos Aires gained autonomy and both Cora and Manuel obtained jobs as academics at the School of Sciences. A decade of fruitful academic activity follows, the golden age of Argentine science, according to testimonies from scientists who witnessed it. Cora obtained her doctorate in 1959 with a thesis in harmonic analysis directed by Mischa Cotlar, who at a very young age had immigrated from her native Ukraine to Uruguay and then to Argentina, where she studied mathematics in a self-taught way and did research without any formal position until she obtained a doctorate from the University of Chicago in 1953, after which he returned to Argentina and had an important scientific career and trained a large number of students, including Cora.

During this time of great harmony, Cora Sadosky, the daughter of Cora and Manuel, entered the university to study mathematics, took classes at the UBA with Pedro Alberto Calderón and Antoni Zygmund, renowned researchers in harmonic analysis. He finished his bachelor's degree in 1960, a year after his mother graduated from her doctorate. He traveled to do postgraduate studies in Chicago, where he did a thesis, also in harmonic analysis, under the direction of Calderón. Cora Sadosky – who passed away in 2010 – would become a benchmark in the area and would also be remembered for her permanent fight for the visibility of women in mathematics.

Harmonic analysis, an area in which mother and daughter specialize, takes its name from the term harmony, introduced in classical Greece to refer to musical notes that when sounding together they sound in agreement, they sound nice when they overlap; harmonics are sounds you want . We can think that this is precisely what happens in a fundamental mathematical fact in the area: Joseph Fourier, a French mathematician born in 1768, showed that any periodic wave can be decomposed into simple superimposed waves, each one of frequency equal to a multiple of a frequency. fixed. They are basic waves that function as the harmonics of the decomposition of sounds, in whose superposition an infinite number of frequencies can intervene and that are known as Fourier series, typically formed by sinusoidal functions. Well, in harmonic analysis, the representation of functions is studied by means of these series, and their properties are generalized thanks to the relationships with various mathematical concepts such as Hilbert spaces and group theory, which provides a powerful abstract framework that allows to obtain deep and interesting results. The well-known wavelet theory is an interesting example: it is a refinement of the Fourier series whose development began in the 80's with the work of the French engineer Jean Morlet in seismic prospecting and which was mathematically systematized by his compatriot Yves Meyer. The applications of this theory range from the compression method of the well-known JPG-2000 format to the detection of gravitational waves carried out by the North American LIGO observatory, among many others.

We return to Buenos Aires and the golden decade, years of fervent work by Cora, during which she teaches courses, organizes advanced seminars and manages the publication of several research monographs. He wrote, in co-authorship with Misha Cotlar, the book Introduction to Algebra of unpublished rigor for texts in Spanish of the time. Without a doubt, Cora had a great influence on his academic environment, especially in the training of many students who would become researchers years later, especially in harmonic analysis. In 1958 CONICET was created, a key organization for the scientific development of Argentina, and the Editorial Universitaria de Buenos Aires was born, an emblematic project in the world of books in Spanish.

This fruitful period for Argentine science culminates in 1966 with a coup in the country, which has a pathetic representation in the infamous night of the long sticks : the university is brutally intervened by agents of the military dictatorship, many teachers are beaten and literally thrown into the streets; tripartite government ends in the institution. Argentine science suffers a great loss: hundreds of people who dedicate their lives to research are forced to leave the university or even to leave the country.

Cora and Manuel resist and stay in Buenos Aires, where Manuel dedicates himself to technology-related businesses. During the following years, Cora wrote and published various articles, mainly of political content, translated mathematics and philosophy texts from French and created the periodical Columna 10 with the aim of raising public awareness of the tragedy from the war in Vietnam. The political situation worsens and the family suffers direct threats from fascist groups such as the Alianza Anticomunista Argentina, known as AAA, for which Manuel and Cora are forced to leave the country in 1974. Back from a congress, they do not take the flight in connection that would return them to Buenos Aires, and they settle in Caracas, Venezuela. Some time later they moved to Barcelona, ​​where Cora finally died in 1981.

Since 1996, the Cora Ratto Prize was established in Vietnam, dedicated to women with good performance in the mathematics Olympics.

Cora lived in a world that demanded multiple efforts of different kinds from her and that faced her with various obstacles; Despite this, he maintained a passionate fight, both in academia and in the political organization, against the injustices he witnessed, for which he is remembered as a great inspiring example.

References:
Cotlar, Mischa; Ratto de Sadosky, Cora. Introduction to Algebra. Notions of linear algebra. Editorial Universitaria de Buenos Aires, Buenos Aires 1966.

Bettye Anne Case (Editor), Anne M. Leggett (Editor). Complexities: Women in Mathematics.

Sandra McGee Deutsch. Argentine Women Against Fascism: The Junta de la Victoria, 1941 – 1947. Politics, Religion & Ideology Vol. 13, No. 2, 221–236, June 2012.

Remembering Cora Sadosky, a tribute in the Newsletter of the Association for Women in Mathematics, Vol. 41, No. 2 (March-April 2011), 5-14.

From wavelets to gravitational waves: the mathematics behind the scientific events of 2017 . Alberto Mercado. El counter, December 30, 2017.

About the author: Alberto Mercado Saucedo is a professor of mathematics at the Technical University Federico Santa María (Valparaíso, Chile) [19659003] About the illustrator: Constanza Rojas Molina is a professor in the mathematics department of the CY Cergy Paris Université (Cergy-Pontoise, France)

The article Cora Ratto: in search of harmony has been written in Cuaderno de Cultura Científica .

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