Wac%C5%82aw Sierpi%C5%84ski
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Wac%C5%82aw Sierpi%C5%84ski

Wac?aw Franciszek Sierpi?ski (Polish: ['vat?swaf fra?'tik r'pij?sk?i] ; 14 March 1882 - 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions and topology. He published over 700 papers and 50 books.

Three well-known fractals are named after him (the Sierpi?ski triangle, the Sierpi?ski carpet and the Sierpi?ski curve), as are Sierpi?ski numbers and the associated Sierpi?ski problem.

Educational background

Sierpi?ski enrolled in the Department of Mathematics and Physics at the University of Warsaw in 1899 and graduated four years later. In 1903, while still at the University of Warsaw, the Department of Mathematics and Physics offered a prize for the best essay from a student on Voronoy's contribution to number theory. Sierpi?ski was awarded a gold medal for his essay, thus laying the foundation for his first major mathematical contribution. Unwilling for his work to be published in Russian, he withheld it until 1907, when it was published in Samuel Dickstein's mathematical magazine 'Prace Matematyczno-Fizyczne' (Polish: 'The Works of Mathematics and Physics').

After his graduation in 1904, Sierpi?ski worked as a school teacher of mathematics and physics in Warsaw. However, when the school closed because of a strike, Sierpi?ski decided to go to Kraków to pursue a doctorate. At the Jagiellonian University in Kraków he attended lectures by Stanis?aw Zaremba on mathematics. He also studied astronomy and philosophy. He received his doctorate and was appointed to the University of Lwów in 1908.

Life of Sierpi?ski

Sierpinski square, a fractal

In 1907 Sierpi?ski first became interested in set theory when he came across a theorem which stated that points in the plane could be specified with a single coordinate. He wrote to Tadeusz Banachiewicz (then at Göttingen), asking how such a result was possible. He received the one-word reply 'Cantor'. Sierpi?ski began to study set theory and, in 1909, he gave the first ever lecture course devoted entirely to the subject.

Sierpi?ski maintained an output of research papers and books. During the years 1908 to 1914, when he taught at the University of Lwów, he published three books in addition to many research papers. These books were The Theory of Irrational Numbers (1910), Outline of Set Theory (1912), and The Theory of Numbers (1912).

Grave of Wac?aw Sierpi?ski

When World War I began in 1914, Sierpi?ski and his family were in Russia. To avoid the persecution that was common for Polish foreigners, Sierpi?ski spent the rest of the war years in Moscow working with Nikolai Luzin. Together they began the study of analytic sets. In 1916, Sierpi?ski gave the first example of an absolutely normal number.

When World War I ended in 1918, Sierpi?ski returned to Lwów. However shortly after taking up his appointment again in Lwów he was offered a post at the University of Warsaw, which he accepted. In 1919 he was promoted to a professor. He spent the rest of his life in Warsaw.

During the Polish-Soviet War (1919-1921), Sierpi?ski helped break Soviet Russian ciphers for the Polish General Staff's cryptological agency.

In 1920, Sierpi?ski, together with Zygmunt Janiszewski and his former student Stefan Mazurkiewicz, founded the mathematical journal Fundamenta Mathematicae. Sierpi?ski edited the journal, which specialized in papers on set theory.

During this period, Sierpi?ski worked predominantly on set theory, but also on point set topology and functions of a real variable. In set theory he made contributions on the axiom of choice and on the continuum hypothesis. He proved that Zermelo-Fraenkel set theory together with the Generalized continuum hypothesis imply the Axiom of choice. He also worked on what is now known as the Sierpi?ski curve. Sierpi?ski continued to collaborate with Luzin on investigations of analytic and projective sets. His work on functions of a real variable includes results on functional series, differentiability of functions and Baire's classification.

Sierpi?ski retired in 1960 as professor at the University of Warsaw, but continued until 1967 to give a seminar on the Theory of Numbers at the Polish Academy of Sciences. He also continued editorial work as editor-in-chief of Acta Arithmetica, and as a member of the editorial board of Rendiconti del Circolo Matematico di Palermo, Composito Matematica, and Zentralblatt für Mathematik.

In 1964 he was one of the signatories of the so-called Letter of 34 to Prime Minister Józef Cyrankiewicz regarding freedom of culture.

Sierpi?ski is interred at the Pow?zki Cemetery in Warsaw, Poland.

Honors received

Honorary Degrees: Lwów (1929), St. Marks of Lima (1930), Amsterdam (1931), Tarta (1931), Sofia (1939), Prague (1947), Wroc?aw (1947), Lucknow (1949), and Moscow (1967).

For high involvement with the development of mathematics in Poland, Sierpi?ski was honored with election to the Polish Academy of Learning in 1921 and that same year was made dean of the faculty at the University of Warsaw. In 1928, he became vice-chairman of the Warsaw Scientific Society, and that same year was elected chairman of the Polish Mathematical Society.

He was elected to the Geographic Society of Lima (1931), the Royal Scientific Society of Liège (1934), the Bulgarian Academy of Sciences (1936), the National Academy of Lima (1939), the Royal Society of Sciences of Naples (1939), the Accademia dei Lincei of Rome (1947), the Germany Academy of Sciences (1950), the American Academy of Arts and Sciences (1959), the Paris Academy (1960), the Royal Dutch Academy (1961),[1] the Academy of Science of Brussels (1961), the London Mathematical Society (1964), the Romanian Academy (1965) and the Papal Academy of Sciences (1967).

In 1949 Sierpi?ski was awarded Poland's Scientific Prize, first degree.


Sierpi?ski authored 724 papers and 50 books, mostly in Polish. His book Cardinal and Ordinal Numbers was originally published in English in 1958. Two books, Introduction to General Topology (1934) and General Topology (1952) were translated into English by Canadian mathematician Cecilia Krieger. Another book, Pythagorean Triangles (1954), was translated into English by Indian mathematician Ambikeshwar Sharma, published in 1962, and republished by Dover Books in 2003; it also has a Russian translation.[2] Another work of his published in English is the Elementary Theory of Numbers (translated by A. Hulanicki in 1964), based on his Polish Teoria Liczb (1914 and 1959).).[3]

See also


  1. ^ "W. Sierpinski (1882 - 1969)". Royal Netherlands Academy of Arts and Sciences. Retrieved 2015.
  2. ^ Hopkins, Brian (January 2019), "review of Pythagorean Triangles", The College Mathematics Journal, 50 (1): 68-72, doi:10.1080/07468342.2019.1547955
  3. ^ W. Sierpinski (1 February 1988). Elementary Theory of Numbers: Second English Edition (edited by A. Schinzel). Elsevier. p. iv, 5-6. ISBN 978-0-08-096019-7.

External links

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