Wacław Sierpiński

Wacław Sierpiński

Wacław Franciszek Sierpiński [ ˈvatswaf fraɲˈtɕiʃɛk ɕɛrˈpiɲski ] (born March 14, 1882 in Warsaw ; † October 21, 1969 ibid) was a Polish mathematician . He is known for his outstanding contributions to set theory (studies on the axiom of choice and the (generalized) continuum hypothesis ), number theory , function theory and topology .

Three well-known fractals , the Sierpinski triangle , the Sierpinski carpet and the Sierpiński curve , are named after him, as well as the Sierpinski problem , the Sierpiński number and the Sierpiński constant in number theory.

Life

education

Wacław Franciszek Sierpiński was born on March 14, 1882 in Warsaw. His father Konstanty was a doctor, his mother's name was Ludwika, née Łapińska. Sierpiński's extraordinary talent for mathematics was discovered in elementary school. However, education was difficult during the Russian rule over Poland .

Despite this, Sierpiński finished the fifth grammar school in Warsaw at the age of eighteen in 1900 - Warsaw had belonged to Russia since the Third Partition of Poland in 1795 - and studied mathematics and physics at the Tsarist University of Warsaw from 1899 . The lectures were all given in Russian. In 1903 there was a competition in the mathematics department of the University of Voronoi on number theory . Sierpiński wrote his first scientific paper on it and won the gold medal.

Warsaw University's Izvestia magazine wanted to publish this work, but Sierpiński declined to publish it in Russian. It was not until four years later, in 1907, that the work was published in a Polish-language mathematical journal. All students were required to attend Russian classes and take an exam while studying. It was considered a matter of honor among Polish patriots to make this test as bad as possible. Sierpiński did not answer a single question in the test and received a grade of poor. He turned down the offer of a repeat. Fortunately, a professor had sympathy with him and gave him a "good" in Russian. So Sierpiński could finish his studies in 1904 at the age of 22.

In the autumn of the same year he taught mathematics and physics at a girls' high school. Because of a strike against the Russification this school was closed and Sierpiński moved to Krakow , which belongs to Austria-Hungary , to study philosophy and astronomy in addition to mathematics. In 1906 he was awarded a doctorate in philosophy. In 1907 he spent a few months in Göttingen to work with the Polish mathematician Tadeusz Banachiewicz .

In July 1908, at the age of 26, he completed his habilitation at the University of Lemberg and taught there until 1914. In the period from 1910 to 1914, his first books, Theory of Irrational Numbers , Outline of Set Theory and Theory of Numbers, were published .

Time in russia

When the First World War broke out in 1914, he and his family fled to Belarus on the estate of his in-laws. As a supposed Austrian, he was interned in Vyatka (renamed Kirow from 1934 ). Moscow mathematicians friends managed to bring him to the Russian capital in 1915, where he stayed until the end of the war.

During this time he worked with the Russian mathematician Nikolai Nikolajewitsch Lusin . In 1918 he returned to Poland via Finland and Sweden, where he taught first in Lviv and then at the University of Warsaw and stayed until the end of his life. He founded the important journal Fundamenta Mathematicae together with other representatives of the so-called Warsaw School of Mathematicians , Stefan Mazurkiewicz and Zygmunt Janiszewski , one of his former students. During the Polish-Soviet War in 1920 he worked in the Biuro Szyfrów , the “cipher office” of the General Staff, on the deciphering of Soviet secret codes .

In the interwar period he led a lively scientific life and worked a lot on set theory. He published eight new books, two brochures and seven school books. Sierpiński was a member of many scholarly associations in and outside Poland. He represented his country at mathematical congresses. In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich ( Sur les ensembles de points qu'on sait définir effectivement ).

During the Second World War

During the Second World War he stayed in Warsaw, where he formally worked for the Warsaw city administration during the time of the German occupation , but actually taught at the Polish underground university. Sierpiński managed to smuggle his work to Italy, where it was published. Under each of his papers it said: The evidence for these theories will be published in the publications of the Fundamenta Mathematicae . Everyone understood that it should really mean that Poland will survive. After the Warsaw Uprising was put down in October 1944, German troops systematically destroyed the city. The Sierpińskis' apartment also went up in flames and the precious library was lost; Likewise, the university library burned down, the private libraries of three other Warsaw mathematics professors were destroyed, and with them almost all of the 32 volumes of the Fundamenta Mathematicae . More than half of all lecturers in the university's mathematics department died. These losses spurred Sierpiński to write new writings and books. He was very productive throughout his life and wrote an astonishing total of 724 articles and 50 books.

Chair in Krakow

Sierpiński's grave

He got to Krakow in February 1945 via the camp in Pruszków outside Warsaw. After a semester at the Jagiellonian University , he returned to his chair in the fall and again published the journal Fundamenta Mathematicae . In 1946 he was awarded the Stefan Banach Prize . From 1948 he worked at the State Mathematical Institute, and after it became part of the Polish Academy of Sciences, he was head of the Scientific Council from 1953 to 1967. From 1956 to 1969 he was editor of Acta Arithmetica magazine , which had been published before the war. In 1948 he became a corresponding member of the Académie des sciences , in 1960 he became an external member ( associé étranger ).

In 1960 he retired, but held a number theory seminar at the Polish Academy of Sciences until 1967. In 1962 he gave a lecture at the International Congress of Mathematicians (ICM) in Stockholm ( Sur les nombres de la forme ${\displaystyle a^{2^{n}}+1}$ ). He was invited speaker at the ICM in Toronto in 1924, in Bologna in 1928, in Zurich in 1932 and in Oslo in 1936. Sierpiński died on October 21, 1969 at the age of 87 in Warsaw.

Other about the work

Sierpinski proved the equivalence of the continuum hypothesis to different theorems of Euclidean elementary geometry and showed that the axiom of choice follows from the generalized continuum hypothesis.

Fonts

• Hypothése du continu, Warsaw, Lwoff 1934, 2nd edition Chelsea 1956 (German: The Continuum Hypothesis )
• Introduction to general topology, University of Toronto Press 1934
  • as General Topology , Dover 2000
• Les ensembles projectifs et analytiques, Gauthier-Villars 1950 (German: The projective and analytical sets)
• Leçons sur les nombres transfinis, Gauthier-Villars 1928, 1950 (German: lectures on transfinite numbers)
• Algébre des ensembles, Warsaw 1951 (German: Quantity Algebra)
• Cardinal and Ordinal Numbers, Warsaw, PWN 1965 (German: cardinal and ordinal numbers )
• Elementary theory of numbers, Warsaw 1964, 2nd edition North Holland 1988 (editor Andrzej Schinzel )
• 250 problems in elementary number theory, Elsevier 1970
• A selection of problems in the theory of numbers, Macmillan 1964
• Oeuvres choisis, 3 volumes, Warsaw, PWN 1974 to 1976 (selected works, eds. Stanisław Hartman , Kazimierz Kuratowski , Edward Marczewski and others)
• Congruence of sets, and other monographs, Chelsea Publ. 1967
• Pythagorean triangles, Dover 2003

Trivia

In addition to the mathematical objects mentioned in the introduction, a crater on the back of the moon with a diameter of 69 km has been named Sierpinski in his honor since 1970.

Web links

• John J. O'Connor, Edmund F. Robertson :  Waclaw Sierpinski. In: MacTutor History of Mathematics archive .
• Mathematics Genealogy Project: Wacław Sierpiński
• Polish Virtual Science Library with publications by Polish mathematicians

Individual evidence

1. ^ List of the membres depuis la création de l'Académie des sciences. Les membres du passé dont le nom commence par S. Académie des sciences, accessed on March 2, 2020 (French, list of members since 1666: letter S).