Wacław Sierpiński
   HOME

TheInfoList



OR:

Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a
Polish Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. He was known for contributions to
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...
(research on the
axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collection ...
and the
continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent ...
),
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
, theory of functions, and
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
. He published over 700 papers and 50 books. Three well-known
fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as il ...
s are named after him (the
Sierpiński triangle The Sierpiński triangle (sometimes spelled ''Sierpinski''), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equi ...
, the Sierpiński carpet, and the Sierpiński curve), as are Sierpiński numbers and the associated Sierpiński problem.


Educational background

Sierpiński enrolled in the Department of Mathematics and Physics at the
University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...
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. Sierpiński 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 Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...
, 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, Sierpiński worked as a school teacher of mathematics and physics in Warsaw. However, when the school closed because of a strike, Sierpiński decided to go to
Kraków Kraków (), or Cracow, is the second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city dates back to the seventh century. Kraków was the official capital of Poland until 159 ...
to pursue a
doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' ...
. At the Jagiellonian University in Kraków, he attended lectures by Stanisław Zaremba on mathematics. He also studied
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
and philosophy. He received his doctorate and was appointed to the University of Lwów in 1908.


Career

In 1907 Sierpiński first became interested in
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...
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 Tadeusz Julian Banachiewicz (13 February 1882, Warsaw – 17 November 1954, Kraków) was a Polish astronomer, mathematician and geodesist. Scientific career He was educated at University of Warsaw and his thesis was on "reduction constan ...
(then at
Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
), asking how such a result was possible. He received the one-word reply '
Cantor A cantor or chanter is a person who leads people in singing or sometimes in prayer. In formal Jewish worship, a cantor is a person who sings solo verses or passages to which the choir or congregation responds. In Judaism, a cantor sings and lead ...
'. Sierpiński began to study
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...
and, in 1909, he gave the first ever lecture course devoted entirely to the subject. Sierpiński maintained an output of research papers and books. During the years 1908 to 1914, when he taught at the University of
Lwów Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukrain ...
, 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). When
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...
began in 1914, Sierpiński and his family were in
Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eigh ...
. To avoid the persecution that was common for
Polish Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
foreigners, Sierpiński spent the rest of the war years in
Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...
working with
Nikolai Luzin Nikolai Nikolaevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlaɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 January 1950) was a Soviet/R ...
. Together they began the study of
analytic set In the mathematical field of descriptive set theory, a subset of a Polish space X is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student . Definition There are several equivalent ...
s. In 1916, Sierpiński gave the first example of an absolutely normal number. When
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...
ended in 1918, Sierpiński returned to
Lwów Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukrain ...
. However shortly after taking up his appointment again in
Lwów Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukrain ...
he was offered a post at the
University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...
, which he accepted. In 1919 he was promoted to a
professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professor ...
. He spent the rest of his life in
Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is official ...
. During the
Polish–Soviet War The Polish–Soviet War (Polish–Bolshevik War, Polish–Soviet War, Polish–Russian War 1919–1921) * russian: Советско-польская война (''Sovetsko-polskaya voyna'', Soviet-Polish War), Польский фронт (' ...
(1919–1921), Sierpiński helped break
Soviet Russia The Russian Soviet Federative Socialist Republic, Russian SFSR or RSFSR ( rus, Российская Советская Федеративная Социалистическая Республика, Rossíyskaya Sovétskaya Federatívnaya Soci ...
n
cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s for the
Polish Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
General Staff's cryptologic agency. In 1920, Sierpiński, together with Zygmunt Janiszewski and his former student
Stefan Mazurkiewicz Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (''PAU'') ...
, founded the mathematical journal
Fundamenta Mathematicae ''Fundamenta Mathematicae'' is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical sys ...
. Sierpiński edited the journal, which specialized in papers on
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...
. During this period, Sierpiński worked predominantly on
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...
, but also on point set topology and functions of a real variable. In
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...
he made contributions on the
axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collection ...
and on the
continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent ...
. He proved that
Zermelo–Fraenkel set theory In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such ...
together with the
Generalized continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent t ...
imply the
Axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collection ...
. He also worked on what is now known as the Sierpiński curve. Sierpiński 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 In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in ...
of functions and Baire's classification. Sierpiński retired in 1960 as
professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professor ...
at the
University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...
, but continued until 1967 to give a seminar on the Theory of Numbers at the
Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of ...
. He also continued editorial work as editor-in-chief of ''
Acta Arithmetica ''Acta Arithmetica'' is a scientific journal of mathematics publishing papers on number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers a ...
'', and as a member of the editorial board of ''
Rendiconti del Circolo Matematico di Palermo The Circolo Matematico di Palermo (Mathematical Circle of Palermo) is an Italian mathematical society, founded in Palermo by Sicilian geometer Giovanni B. Guccia in 1884.
'', ''Composito Matematica'', and '' Zentralblatt für Mathematik''. In 1964 he was one of the signatories of the so-called
Letter of 34 ''Letter of 34'' – two-sentence protest letter of Polish intellectuals against censorship in Communist Poland, addressed to the Prime Minister Józef Cyrankiewicz, delivered on 14 March 1964 to by Antoni Słonimski. The name refers to the num ...
to Prime Minister
Józef Cyrankiewicz Józef Adam Zygmunt Cyrankiewicz (; 23 April 1911 – 20 January 1989) was a Polish Socialist (PPS) and after 1948 Communist politician. He served as premier of the Polish People's Republic between 1947 and 1952, and again for 16 years between ...
regarding freedom of culture. Sierpiński is interred at the
Powązki Cemetery Powązki Cemetery (; pl, Cmentarz Powązkowski), also known as Stare Powązki ( en, Old Powązki), is a historic necropolis located in Wola district, in the western part of Warsaw, Poland. It is the most famous cemetery in the city and one of t ...
in
Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is official ...
,
Poland Poland, officially the Republic of Poland, , is a country in Central Europe. Poland is divided into Voivodeships of Poland, sixteen voivodeships and is the fifth most populous member state of the European Union (EU), with over 38 mill ...
.


Honors received

Honorary Degrees:
Lwów Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukrain ...
(1929),
St. Marks of Lima The National University of San Marcos ( es, Universidad Nacional Mayor de San Marcos, link=no, UNMSM) is a public research university located in Lima, the capital of Peru. It is considered the most important, recognized and representative educ ...
(1930), Tarta (1931),
Amsterdam Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...
(1932), Sofia (1939), Prague (1947), Wrocław (1947), Lucknow (1949), and
Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...
(1967). For high involvement with the development of mathematics in
Poland Poland, officially the Republic of Poland, , is a country in Central Europe. Poland is divided into Voivodeships of Poland, sixteen voivodeships and is the fifth most populous member state of the European Union (EU), with over 38 mill ...
, Sierpiński was honored with election to the
Polish Academy of Learning The Polish Academy of Arts and Sciences or Polish Academy of Learning ( pl, Polska Akademia Umiejętności), headquartered in Kraków and founded in 1872, is one of two institutions in contemporary Poland having the nature of an academy of scien ...
in 1921 and that same year was made dean of the
faculty Faculty may refer to: * Faculty (academic staff), the academic staff of a university (North American usage) * Faculty (division), a division within a university (usage outside of the United States) * Faculty (instrument) A faculty is a legal in ...
at the
University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...
. In 1928, he became vice- chairman of the
Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is official ...
Scientific Society, and that same year was elected chairman of the
Polish Mathematical Society The Polish Mathematical Society ( pl, Polskie Towarzystwo Matematyczne) is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Un ...
. He was elected to the Geographic Society of
Lima Lima ( ; ), originally founded as Ciudad de Los Reyes (City of The Kings) is the capital and the largest city of Peru. It is located in the valleys of the Chillón, Rímac and Lurín Rivers, in the desert zone of the central coastal part of t ...
(1931), the Royal Scientific Society of Liège (1934), the
Bulgarian Academy of Sciences The Bulgarian Academy of Sciences (abbreviated BAS; bg, Българска академия на науките, ''Balgarska akademiya na naukite'', abbreviated ''БАН'') is the National Academy of Bulgaria, established in 1869. The Academy ...
(1936), the National Academy of
Lima Lima ( ; ), originally founded as Ciudad de Los Reyes (City of The Kings) is the capital and the largest city of Peru. It is located in the valleys of the Chillón, Rímac and Lurín Rivers, in the desert zone of the central coastal part of t ...
(1939), the Royal Society of Sciences of
Naples Naples (; it, Napoli ; nap, Napule ), from grc, Νεάπολις, Neápolis, lit=new city. is the regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 909,048 within the city's adminis ...
(1939), the
Accademia dei Lincei The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini, Rome, Palazzo Corsini on the Vi ...
of
Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus ( legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...
(1947), the Germany Academy of Sciences (1950), the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...
(1959), the Paris Academy (1960), the Royal Dutch Academy (1961), the Academy of Science of Brussels (1961), the
London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...
(1964), the
Romanian Academy The Romanian Academy ( ro, Academia Română ) is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 active members who are elected for life. According to its by ...
(1965) and the Papal Academy of Sciences (1967). In 1949 Sierpiński was awarded Poland's Scientific Prize, first degree.


Publications

Sierpiński authored 724 papers and 50 books, almost all 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 ''Pythagorean Triangles'' is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński (titled ''Trójkąty pitagorejskie''), and published in Warsaw i ...
'' (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. 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). Another book, named "250 Problems in Elementary Number Theory" was translated into English (1970) and Russian (1968).


See also

* Arity theorem *
List of Poles This is a partial list of notable Polish or Polish-speaking or -writing people. People of partial Polish heritage have their respective ancestries credited. Science Physics * Czesław Białobrzeski * Andrzej Buras * Georges Charp ...
*
Menger sponge In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional S ...
* Seventeen or Bust * Sierpiński carpet *
Sierpiński's constant Sierpiński's constant is a mathematical constant usually denoted as ''K''. One way of defining it is as the following limit: :K=\lim_\left sum_^ - \pi\ln n\right/math> where ''r''2(''k'') is a number of representations of ''k'' as a sum of the ...
* Sierpiński curve * Sierpiński game * Sierpiński number * Sierpiński set *
Sierpiński space In mathematics, the Sierpiński space (or the connected two-point set) is a finite topological space with two points, only one of which is closed. It is the smallest example of a topological space which is neither trivial nor discrete. It is na ...
*
Sierpiński triangle The Sierpiński triangle (sometimes spelled ''Sierpinski''), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equi ...
* The Sierpiński moon crater


References


External links

* * * * *
Several of Sierpiński's books
Biblioteka Wirtualna Nauki.
Sierpiński: Fractals, Code Breaking, and a Crater on the Moon
{{DEFAULTSORT:Sierpinski, Waclaw 1882 births 1969 deaths Warsaw School of Mathematics People from Warsaw Governorate Number theorists Topologists Members of the Polish Academy of Learning Burials at Powązki Cemetery Cipher Bureau (Poland) Jagiellonian University alumni University of Warsaw alumni University of Warsaw faculty Members of the Polish Academy of Sciences Members of the Bulgarian Academy of Sciences Members of the French Academy of Sciences Members of the Royal Netherlands Academy of Arts and Sciences Members of the German Academy of Sciences at Berlin Recipients of the State Award Badge (Poland)