# Kazimierz Żorawski

### Quick Info

Szczuczyn, Poland (now Shchuchyn, Belarus)

Narutowicz, Poland

**Kazimierz Żorawski**was a Polish mathematician who worked on invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics.

### Biography

**Kazimierz Żorawski**'s parents were Juliusz Bronislaw Wiktor Żorawski (1833-1905) and Kazimiera Kamienska. Juliusz had not had much of an education due to the political and economic problems in Poland during the time he was growing up. However, he did very well for himself becoming a farmer, then going on to run an experimental agricultural station. He also was a shareholder in the Krasiniec sugar refinery. Kazimiera, Kazimierz's mother, was a strong supporter of Poland which at this time was partitioned between Russia, Prussia, and Austria. There were a number of groups in Poland who conspired against this foreign rule. One of these groups was the Reds who organised demonstrations in Warsaw in 1861. These were harshly suppressed by Russian troops leading to several deaths. Russia decided to break up the Reds by drafting large numbers of them into the Russian army. In January 1863 the Reds reacted against this by calling for an uprising against the Russians. Kazimiera, and her father, took part in this uprising and they were captured by the Russians. Both were imprisoned and although Kazimiera was released, her father died in prison in Warsaw.

Kazimierz was one of his parents' six children. He had three brothers Władysław, Juliusz, and Stanisław, and two sisters Bronislawa and Anna. It was at a Gymnasium in Warsaw that he completed his secondary education in 1884 and then entered the University of Warsaw to study mathematics. A major event in his life occurred in the following year when a young eighteen year old girl, Maria Sklodowska, was employed as a governess to the Żorawski family.

For readers of this archive who do not recognise the name Maria Sklodowska, let us suggest that you will recognise her by her married name of Marie Curie, the famous physicist who was twice a winner of the Nobel Prize for her work on radioactivity. Maria's father was a teacher of mathematics and physics who had lost his savings through bad investments. In an attempt to help with the family's education, Maria took on the position of governess. From her earnings as the Żorawski family governess she aimed to finance her sister Bronia's medical studies in Paris, on the understanding that Bronia would in turn later help her to get an education. Kazimierz and Maria fell in love and wanted to marry. However Żorawski's parents refused to consent to the marriage since Maria's family were too poor. For several years Kazimierz and Maria hoped that Kazimierz's parents would relent and approve the marriage, but this never happened.

In 1888, after four years at the University of Warsaw, Żorawski graduated with a first degree in mathematics. His work was of such high quality that he was given the opportunity to continue his mathematical studies abroad. He spent time in Leipzig where he studied continuous groups of transformations now called Lie groups, and Göttingen where he studied differential equations. He was awarded his doctorate in 1891 from the University of Leipzig for his thesis on the applications of Lie groups to differential geometry. Lie had been appointed to Leipzig in 1886 to succeed Klein. Engel was also at Leipzig and at the time when Żorawski studied their they were working on their major work

*Theorie der Transformationsgruppen*Ⓣ which was published in three volumes between 1888 and 1893. Lie later said:-

Among the work done in Leipzig, let us remember in particular the superb work of Żorawski on integral invariants. With much ability, Żorawski worked to resolve difficult and complicated calculations which were necessary to solve the problems ...It was in 1891 that Maria Sklodowska went to Paris to begin her education supported by her sister, and Kazimierz and Maria's hopes of being able to marry finally came to an end. Żorawski was appointed as a lecturer at the Lwów Polytechnic (now in Lviv in Ukraine) in 1892 and was promoted to professor in the Mechanical Engineering Department in the following year. He habilitated at the Jagiellonian University in Kraków in 1893, then went to Berlin in 1895 to study geodesy. After returning to the Jagiellonian University of Kraków he was named extraordinary professor on 1 May 1895, being promoted to ordinary professor of mathematics in 1898. In 1900 Stanisław Zaremba was also appointed as professor at the Jagiellonian University and together Żorawski and Zaremba built a major school of mathematics. After Żorawski's death, Slebodzinski wrote:-

One can say that, thanks to these two scientists, Polish mathematics ceased being a mere consumer of foreign thinking and analysis. Both played pivotal roles in the development of this science. Under the political conditions of the time, Stanisław Zaremba and Kazimierz Żorawski were, for fifteen years, the only representatives of cutting-edge Polish mathematics ... judging these facts by contrasting them with the current state of affairs, shows their immense progress and accomplishments ... in spite of the catastrophic effects on Polish mathematics caused by the Nazi occupation.A government grant allowed Żorawski to visit both Leipzig and Paris during the winter semester 1901-02 to further his studies. After returning to Kraków, Żorawski continued to teach courses on analytical and synthetic geometry, differential geometry, the formal theory of the differential equations, the theory of the forms, and the theory of the Lie groups. The main topics of his research were invariants of differential forms, integral invariants of Lie groups, differential geometry, and fluid mechanics. Let us quote the titles of two of Żorawski's papers which were written in German and published during his time in Kraków:

*Über infinitesimale Transformationen der Ebene, welche gewissen geometrischen Bedingungen genügen*Ⓣ (1901) and

*Über Eigenschaften eines vielfachen Integrals, welche Verallgemeinerungen zweier Sätze der Theorie der Wirbelbewegung sind*Ⓣ (1913). He remained in Kraków during the years of World War I. After the war ended with the surrender of the Central Powers, Poland proclaimed itself independent on 11 November 1918.

We related above the story of how Żorawski and Maria Sklodowska wished to marry but were unable to do so because of Żorawski's parents. Of course, as is well known, Maria Sklodowska married Pierre Curie in Paris in 1895. Żorawski married Leokadia Jewniewicz, the daughter of Maria Moszczynska and Hipolit Jewniewicz. Hipolit was a professor of applied mathematics at St Petersburg and had a major text

*The Theory of Elasticity*published posthumously in Warsaw in 1910. Leokadia was a talented pianist. Kazimierz and Leokadia Żorawski had three children, Juliusz, Leokadia and Maria.

An informal Mathematical Society was established in Kraków in 1917, and Żorawski was one of several mathematicians directly involved with setting up this new society. It was officially constituted after the end of World War I. At 5 p.m. on 2 April 1919 a meeting was held in the Philosophy Seminar at 12 St Anne Street, Kraków, at which the Mathematical Society was constituted. Among the sixteen mathematicians present were Stefan Banach, Otto Nikodym, Stanisław Zaremba, and Kazimierz Żorawski. The session was introduced by Żorawski who said that an all-Polish Mathematical Society was being set up in Warsaw, and he proposed a motion to initiate a 'Mathematical Society in Kraków' which might later become associated with the new Warsaw Society. The motion was passed unanimously and Stanisław Zaremba was elected to preside over the Constituting Session. Soon after this, later in the year 1919, Żorawski moved to Warsaw where he accepted a professorship at the Technical University. He also taught at the University of Warsaw. When the various Polish mathematical societies combined in 1920 into the Polish Mathematical Society, Żorawski became a founder member of the new Society. Also in 1920 he was elected to the Warsaw Scientific Society and served as president of this society from 1926 to 1931. His great contributions to the Warsaw Scientific Society were marked by the Society with the creation of the Commemorative Żorawski Medal in 1931.

In 1926 Żorawski became a professor at the University of Warsaw and continued in this role until he retired in 1935. Retirement meant that his formal responsibilities at the university had ended but this meant that he had more time to now undertake the writing of a major mathematical work on analytical geometry. He was progressing with this major project when World War II broke out. Żorawski remained in Warsaw and continued to make progress on his many volume treatise. As July 1944 was drawing to a close the Russian army was advancing into Poland. The Russians encouraged the Poles in Warsaw to stage an uprising against the occupying German forces, promising help. The Poles did exactly that and soon took control of the city. However when German reinforcements were sent in and the Russians, despite having their army close by, refused to help the uprising and, even more serious for the Poles, refused to allow the Allies to use their air bases to supply the Poles fighting in the city, the uprising was crushed after over two months. The Germans then systematically deported the city's population and destroyed the city itself. Żorawski, along with many thousands of the inhabitants of Warsaw, was taken by the Germans to Pruszków. His house and the three-quarters finished multi-volume work he had been writing on analytical geometry were destroyed.

After some time Żorawski was released from Pruszków and he went with a number of other scientists to Nieborów. After the war ended and Russian troops had completely occupied Poland, Żorawski returned to Warsaw where his daughter Leokadia Paprocka was living. After living with his daughter of a while the Ministry for Education gave him a small bedroom with a kitchen in a students' dormitory in Narutowicz. Remarkably, Żorawski then set about rewriting his book which had been destroyed following the Warsaw Uprising. He rewrote about two-thirds of the book, amounting to 2650 pages.

Żorawski was elected a full member of the Polish Academy of Sciences in 1952. He also was honoured with the Commander's Cross of the Order of Polonia Restituta and the Gold Cross of Merit. After he died in early 1953 his family received a telegram from Bronislaw Knaster, Edward Marczewski, Hugo Steinhaus, and Władysław Slebodzinski which read:-

... we wish to express to the family of Professor Kazimierz Żorawski our deep compassion. He was the first of the scientists of his generation to bring the name of Poland to the forefront of world mathematics.

### References (show)

- W Slebodzinski, Scientific work of K Zorawski (Polish),
*Prace Mat.***2**(1956), 79-93. - W Slebodzinski, L'oeuvre scientifique de Kazimierz Zorawski,
*Colloq. Math.***4**(1956), 74-88.

### Additional Resources (show)

Other websites about Kazimierz Żorawski:

Written by J J O'Connor and E F Robertson

Last Update July 2007

Last Update July 2007