# Zofia Szmydt

### Quick Info

Warsaw, Poland

Warsaw, Poland

**Zofia Szmydt**was a Polish mathematician who became the first woman to win the prestigious Stefan Banach Prize from the Polish Mathematical Society in 1956. She applied topological methods to the study of nonlinear ordinary differential equations and also studied Mellin Transformations.

### Biography

**Zofia Szmydt**was the daughter of Józef Konstanty Szmydt (1885-1960) and Zofia Wanda Gąsiorowska (1893-1977). Józef was a farmer with a higher education, working on the Komarów estate in the Vilnius region. He married Zofia Gąsiorowska, who had been born in Saint Petersburg, Russia on 21 April 1893, in October 1919 in the Church of the Holy Cross in Warsaw. This required special permission since they were related. In 1912 Zofia Gąsiorowska had begun studying philology and history at the Faculty of Philosophy of the Jagiellonian University. She had taught in Warsaw during World War I but in 1917 she returned to the Jagiellonian University where she obtained a doctorate in philosophy in June 1917. She had returned to school teaching and publishing papers before marrying Józef Szmydt. Józef Szmydt and Zofia Szmydtowa had two children, Maria Danuta Szmydt (2 December 1920 - 17 May 2011) and Zofia Szmydt (29 July 1923 - 6 November 2010), the subject of this biography. Zofia Szmydtowa, the mother of the mathematician, worked at the Department of the History of Polish Literature at the Faculty of Polish Studies at the University of Warsaw from 1926, becoming a professor in 1933. From 1929 the family lived in Warsaw in an apartment previously owned by Władysław Stanisław Reymont, a Polish novelist who had been awarded the Nobel Prize in Literature in 1924. Let us quote the beginning of the article [13] about Zofia Szmydtowa:-

Zofia Szmydtowa's work is a phenomenon that cannot be presented in a concise description. It is not only about the breadth of her interests, encompassing both ancient, Greek and Roman literature, as well as Western European literature, mainly French, Italian and Spanish, but also about her specific method of researching literary phenomena, combining philological precision with the features of contemporary comparative studies and with Zofia Szmydtowa's characteristic critical intuition, inventiveness in formulating hypotheses and aesthetic sensitivity.Zofia Szmydt began her schooling in Warsaw in 1929. After her primary education, she attended a junior high school before completing her schooling at the Cecylia Plater-Zyberkówna School in Warsaw. Cecylia Plater-Zyberk had entered a convent in Warsaw in 1880, then three years later founded a craft school for girls. In 1886 she founded a girls' secondary school which was given full recognition by the Education Authority in 1917; it was this school that Zofia Szmydt was attending when Germany invaded Poland in September 1939 and World War I began. The occupying German forces quickly moved to limit education of Poles. Heinrich Himmler, second in command to Hitler, produced a document on 5 May 1940 which required all education in Poland to be in German and [2]:-

... for the non-German population of the East there can be no type of school above the four-grade rudimentary school. The job of these schools should be confined to the teaching of counting (no higher than up to 500), the writing of one's name, and the teaching that God's commandment means obedience to the Germans, honesty, industry and politeness. Reading I do not consider essential.Polish teachers and lecturers, at great risk to their lives, organised secret underground courses taught in private houses. Even a clandestine examination system was set up and Zofia was able to pass the matriculation examination in mathematics and physics in 1940. The occupying German forces had closed the University of Warsaw and turned its buildings into a military barracks, but lecturers continued to teach classes in secret using private houses and religious buildings. Zofia was able to obtain a university education with this clandestine university system. She lived throughout the war with her parents in their Warsaw home and was able to earn money by giving private lessons. Her mother was one of the brave university professors who participated in the secret teaching of the underground University of Warsaw.

Although Germany and the Soviet Union had made a treaty before the invasion of Poland, in June 1941 Germany attacked the Soviets. At first they made deep advances into the Soviet Union but as the war progressed the Red Army drove them back. In the summer of 1944 the Red Army was advancing towards Warsaw and German troops began to leave the city. The Polish Resistance saw an opportunity to retake control of Warsaw and on 1 August 1944 the Warsaw Uprising began. The Red Army halted their advance allowing the German troops to regroup and defeat the Uprising. In the 2-month battle that followed most of the city was destroyed and it is estimated that the German forces killed around 40000 civilians. Much of Zofia Szmydtowa's research was destroyed with the family's property and, after the Poles surrendered, the Germans sent the Szmydt family along with many other surviving Polish families to Kraków. Zofia Szmydt was forced to leave Warsaw with her parents and to live in to Kraków. There she supported herself giving private tuition.

German occupiers evacuated Kraków on 17 January 1945 and, two days later, Soviet forces entered Krakow. The Jagiellonian University reopened on 19 March 1945 but it was a difficult time with 25% of the staff having been killed. Chairs had to be developed and staff appointed. Soon after the University opened, in March 1945, Szmydt enrolled for a mathematics degree in the Faculty of Philosophy. She already had a good mathematics education from the underground University of Warsaw so she was soon in a position to take examinations in Kraków [4]:-

During her studies, she passed with very good results exams in differential and integral calculus with an introduction to analysis, analytic geometry, principles of higher algebra with elements of number theory, theoretical mechanics, experimental physics, main principles of philosophical sciences, theory of analytic functions, differential equations, integral equations and hydrodynamics. She passed her final exam in December 1945 with a good result. Her master's thesis 'On the characteristic roots of matrices' received a very good grade. She received her Master of Philosophy diploma in mathematics on 20 March 1946.These were hard times for the whole Jagiellonian University and mathematics was no exception to these difficulties. It was led by Tadeusz Ważewski and other members of staff included Franciszek Leja, Stanisław Gołąb and Bronisław Knaster. Andrzej Turowicz, who had left mathematics in 1945 to join the Benedictine Abbey in Tyniec, was brought back to help with lecturing in 1946. Szmydt certainly flourished with these fine mathematicians as her teachers. Also in the Department of Mathematics at that time was Zofia Krygowska who was studying for her doctorate. Even before the award of her Master's Degree, Szmydt was appointed as a senior assistant in the Faculty of Mathematics and Natural Sciences of the Jagiellonian University on 1 January 1946.

The Institute of Mathematics of the Polish Academy of Sciences was named the State Mathematical Institute when it was established by the Polish government on 20 November 1948; it was headed by Wacław Sierpiński. Branches were established in major Polish cities including Kraków. In March 1949, in addition to her position at the Jagiellonian University, Szmydt was appointed as a senior assistant in the Department of Differential Equations of the Department of Differential Equations of the State Institute of Mathematics.

While undertaking duties at the University and at the Institute, Szmydt studied for her doctorate advised by Tadeusz Ważewski. He proposed that she work on a problem he suggested on the existence of nontrivial first integrals of the equation $y' = f(x, y)$ in simply connected domains. She solved the problem and submitted the 14-page thesis

*On the first integrals of the differential equation*$y' = f(x, y)$ for her doctorate. She was examined for the doctorate offering mathematics as her main subject and logic as her minor subject. She was examined by a committee chaired by Bogdan Kamieński with members Franciszek Leja, Tadeusz Ważewski and Stanisław Gołąb. Bogdan Kamieński (1897-1973) was a leading physical chemist who, at the time of Szmydt's examination on 18 February 1949, was dean of the Faculty of Mathematics and Natural Sciences at the Jagiellonian University. She was awarded her doctorate on 5 December 1949.

Szmydt's first paper,

*Sur les racines caractéristiques et sur les directions caractéristiques de certaines matrices*, was related to her Master's thesis and was published in 1949. This paper [10], published under the name Zofia Szmydtówna, was reviewed by Olga Taussky-Todd [12]:-

Several theorems due to Frobenius concerning matrices with positive or nonnegative elements are generalised to the cases of matrices whose off-diagonal elements are positive ($a^{+}$-matrices) or nonnegative (a-matrices). The author observes that the original proofs of some of these theorems made no use of the signs of the main diagonal elements. For other theorems the proof can be reduced to the Frobenius case. It is shown that the characteristic root with largest real part of an a-matrix is real [see also Rohrbach (1931)]; for an $a^{+}$-matrix this root is simple. The components $x_{i}$ of the corresponding characteristic vectors are such that $x_{i}x_{j} ≥ 0$ for an a-matrix and $x_{i}x_{j} > 0$ for an $a^{+}$-matrix. The components of a vector which corresponds to a smaller real characteristic root cannot all be positive. Finally, a theorem concerning the vectors which correspond to complex roots is proved; this result has no analogue among the Frobenius theorems.Szmydt's second paper

*Sur les intégrales premières de l'équation*$y' = f(x, y)$ was basically her doctoral thesis translated into French and published in 1950. C Miranda writes in the review [15]:-

The author shows that for every integer n one can construct an open and simply connected set $\Omega _{n}$ and a function $f_{n}(x, y)$ endowed with derivatives of any high order, such that every first integral of the equation $y' = f_{n}(x, y)$ that is continuous in $\Omega _{n}$ with all derivatives up to and including those of order n is necessarily constant in $\Omega _{n}$.Szmydt had been promoted to assistant professor at the Jagiellonian University on 1 March 1951 and continued in this position until 31 August 1952. In 1952 the State Mathematical Institute became part of the Polish Academy of Sciences and was given its current name. Sierpiński became the first President of the Scientific Council of the Institute of Mathematics. Szmydt was promoted to assistant professor at the Institute of Mathematics, a role she held between 31 July 1953 and 31 July 1954 when she became an independent researcher. Later in 1954 she was given the title of associate professor. In parallel with her work at the Institute of Mathematics of the Polish Academy of Sciences she was employed as an independent researcher in the Department of Mathematics at the Faculty of Chemistry of the Warsaw University of Technology from 1 September 1953 to 31 August 1954.

We note that on the 1955 paper

*Sur l'allure asymptotique des intégrales de certains systèmes d'équations différentielles non linéares*, the sixth of her published papers, she gives her address (in both Polish and French) as Institute of Mathematics of the Polish Academy of Sciences Kraków. Up to 1955 all her papers are written in French but her first paper in English was

*On the degree of regularity of surfaces formed by the asymptotic integrals of differential equations*(1955). This paper contains results which she had communicated to the 8th Congress of Polish Mathematicians held in Warsaw 6-12 September 1953. Among other papers delivered to this Congress were:

*The present state of investigations on the foundations of mathematics*, by Andrzej Mostowski;

*The influence of new mathematical methods on the development of classical mathematical disciplines,*by Tadeusz Ważewski;

*Theory of probability as a tool for investigations in science and the field of production*, by Hugo Steinhaus; and

*The organisation, the present state, and the problems of mathematics in Poland*, by Kazimierz Kuratowski.

In 1956, Szmydt was awarded the Stefan Banach Prize by the Polish Mathematical Society. This prestigious prize had been first awarded in 1946 to Hugo Steinhaus and other winners of the prize before Szmydt had been Władysław Orlicz (1948), Stanisław Mazur (1949), and Jan Mikusiński (1950). She was the first woman to receive this prize, the next being Danuta Przeworska-Rolewicz in 1969.

In 1957 Szmydt submitted the thesis

*Limit problems of a new type for hyperbolic partial differential equations*for her habilitation. This thesis consisted of six previously published papers:

*Sur un nouveau type de problèmes pour un système d'équations différentielles hyperboliques du second ordre à deux variables indépendantes*(1956);

*Sur une généralisation des problèmes classiques concernant un système d'équations différentielles hyperboliques du second ordre à deux variables indépendantes*(1956);

*Sur le problème de Goursat concernant les équations différentielles hyperboliques du second ordre*(1957);

*Sur un problème concernant un système d'équations différentielles hyperboliques d'ordre arbitraire à deux variables indépendantes*(1957);

*Sur l'existence de solutions de certains nouveaux problèmes pour un système d'équations différentielles hyperboliques du second ordre à deux variables indépendantes*(1957); and

*Sur l'existence d'une solution unique de certains problèmes pour un système d'équations différentielles hyperboliques du second ordre à deux variables indépendantes*(1957).

The reviewers of her thesis were Adam Bielecki (1910-2003), who was a professor at the Institute of Mathematics of the Polish Academy of Sciences, and Tadeusz Ważewski. She defended her thesis before the Scientific Council of the Institute of Mathematics on 22 February 1958 and she was awarded her habilitation.

After the award of her habilitation, Szmydt was awarded a scholarship to make a research visit to Italy for six months in 1958-59. This was very successful and led to the award of two Italian scholarships which allowed her to spend time in Italy, first from November 1959 to April 1960, and then from February to July of 1962. She continue to be based at the Institute of Mathematics of the Polish Academy of Sciences in Kraków until 1971 but also gave lectures at the Jagiellonian University in 1952-1953, 1966-1967 and 1969-1970. Zofia Szmydt's parents had returned to Warsaw from Kraków in February 1945 where her father had died in 1960. Her mother, who had been appointed as a full professor at the University of Warsaw on 1 March 1959 continued to live in Warsaw after the death of her husband and retired in 1965. By 1971 her health had become poor and Zofia Szmydt made a request to the Institute of Mathematics of the Polish Academy of Sciences to let her move from the Kraków branch to the Warsaw branch so that she could support her mother. Her mother died on 3 March 1977 and Zofia Szmydt continued to live in Warsaw.

In 1972 Szmydt published the book [7]

*Transformacja Fouriera i równania różniczkowe liniowe*. Grzegorz Łysik explains that it was written [4]:-

... to present the foundations of the theory of linear partial differential equations with particular emphasis on distributional limit problems for the basic equations of mathematical physics (heat, Schrödinger, wave, Laplace and Poisson equations). This monograph contains the first extensive study in Polish literature of the foundations of the theory of distribution and Fourier transforms in the distributional approach. ... In the world literature, it was a unique publication in which the author included her own research achievements together with a precise and professional discussion of the tools and methods used. Moreover, it is the only book in which the concept of determining variables in the distribution was discussed in detail and applied to differential equations. Additionally, it contains the first publication by Bogdan Ziemian and the first version of his joint work with Szmydt, in which, using the invariance of the wave operator with respect to the Lorentz transformation group, formulas for its fundamental solution were derived.The original Polish version of the book was translated into English and published as

*Fourier transformation and linear differential equations*(1977). This book is [8] in our list of references and it was reviewed by Z Zielezny [13] who writes:-

The English edition is a revised and enlarged version of the original Polish edition. Its main purpose is to give a modern exposition of the fundamental theory of linear partial differential equations of mathematical physics. It is a monograph designed for graduate students in mathematics, physics and engineering, as well as for researchers.On 24 September 1973, Szmydt was awarded the Commander's Cross of the Order of Polonia Restituta, in recognition of her services in educating students and for publishing the textbook

The solutions of the differential equations are sought in the space of distributions and the main tool is the Fourier transformation. A special feature is the application of an operation called "fixation of variables in a distribution" which was introduced by S Łojasiewicz in 1958.

The book is self-contained and does not require any knowledge of the classical theory of partial differential equations. A number of theorems from functional analysis which are applied in the text are formulated in the introduction.

The first two chapters contain the basic facts of the theory of distributions and Fourier transforms. In Chapter III, the author presents the general definitions and theorems on partial differential equations. The subsequent three chapters are devoted to the principal differential operators of mathematical physics: the wave operator, the operator of heat conduction, and the Laplace and Helmholtz operators. Numerous exercises are designed to illustrate or complement the text. The book concludes with an appendix on fundamental solutions of the wave operator.

*Fourier Transformation and Linear Differential Equations.*

One of Szmydt's three students whom she advised for a doctorate was Bogdan Ziemian (1953-1997) who was awarded his doctorate in 1981. From October 1991 she collaborated with Ziemian on writing the book

*The Mellin transformation and Fuchsian type partial differential equations*which was published in 1992. She retired on 1 October 1993 but continued to undertake research in collaboration with Bogdan Ziemian. They published a total of 18 research papers, three of which were written after Szmydt retired. In total she published 58 papers, the final two being obituaries of Bogdan Ziemian. Her last paper, written with two co-authors, ends with the sentence:-

On 13 March 1997, Bogdan and his wife were involved in a tragic accident. Bogdan Ziemian did not survive; his final act was to save the life of his wife.Let us end with a quotation from Emelie Agnes Kenney's paper [3]:-

Szmydt was known as a sophisticated instructor who gave smooth presentations; as a person, she was thought of as very generous, but somewhat averse to attending social functions. Roman Sznajder, who took six courses with her, recalls attending the International Congress of Mathematicians in 1978 in Helsinki with Szmydt. She gave Sznajder her invitation to attend a reception at the home of the Mayor of Helsinki, since he did not have one. She also kept on hand a supply of restaurant coupons so that her students could eat for free.

Written by J J O'Connor and E F Robertson

Last Update November 2024

Last Update November 2024