Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a
Polish 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, structure, space, models, and change.
History
On ...
.
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 conce ...
(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 to ...
),
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, "Mat ...
, theory of
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
s, 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 ...
. He published over 700 papers and 50 books.
Three well-known
fractals are named after him (the
Sierpiński triangle, 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 o ...
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 1596 ...
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 ''li ...
. 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 celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
and
philosophy. He received his doctorate and was appointed to the
University of Lwów
The University of Lviv ( uk, Львівський університет, Lvivskyi universytet; pl, Uniwersytet Lwowski; german: Universität Lemberg, briefly known as the ''Theresianum'' in the early 19th century), presently the Ivan Franko Na ...
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 conce ...
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
Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911.
General information
The ori ...
), 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 conce ...
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, 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 one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
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-eig ...
. To avoid the persecution that was common for
Polish 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 millio ...
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/Ru ...
. 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 one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
ended in 1918, Sierpiński returned to
Lwów. However shortly after taking up his appointment again in
Lwów 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 o ...
, 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". Professors ...
. 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 officia ...
.
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
ciphers for the
Polish General Staff's
cryptologic agency.
In 1920, Sierpiński, together with
Zygmunt Janiszewski
Zygmunt Janiszewski (12 July 1888 – 3 January 1920) was a Polish mathematician.
Early life and education
He was born to mother Julia Szulc-Chojnicka and father, Czeslaw Janiszewski who was a graduate of the University of Warsaw and served as t ...
and his former student
Stefan Mazurkiewicz, 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 conce ...
.
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 conce ...
, but also on
point set topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geomet ...
and
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
s 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 conce ...
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 to ...
. 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 to ...
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
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
s 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". Professors ...
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 o ...
, but continued until 1967 to give a seminar on the
Theory of Numbers
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, "Mathe ...
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 o ...
. 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. It was established in 1935 by Salomon Lubelski and Arnold Walfisz. The journal is published by the Institute of Mathematics of the Polish Academy of Sc ...
'', and as a member of the editorial board of ''
'', ''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 numb ...
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 officia ...
,
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
.
Honors received
Honorary Degrees:
Lwów (1929),
St. Marks of Lima (1930), Tarta (1931),
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the capital and most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 in the urban ar ...
(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 millio ...
(1967).
For high involvement with the development of
mathematics in
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
, 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 scie ...
in 1921 and that same year was made
dean
Dean may refer to:
People
* Dean (given name)
* Dean (surname), a surname of Anglo-Saxon English origin
* Dean (South Korean singer), a stage name for singer Kwon Hyuk
* Dean Delannoit, a Belgian singer most known by the mononym Dean
Titles
* ...
of the
faculty 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 o ...
. 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 officia ...
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 ...
(1931), the Royal Scientific Society of
Liège (1934), the
Bulgarian Academy of Sciences (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 ...
(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 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, a ...
(1959), the
Paris Academy
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...
(1960), the
Royal Dutch Academy (1961), the
Academy of Science of Brussels (1961), the
London Mathematical Society (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 byl ...
(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
''Cardinal and Ordinal Numbers'' is a book on transfinite numbers, by Polish mathematician Wacław Sierpiński. It was published in 1958 by Państwowe Wydawnictwo Naukowe, as volume 34 of the series Monografie Matematyczne of the Institute of Mathe ...
'' 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.
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 Charpa ...
*
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 Si ...
*
Seventeen or Bust
*
Sierpiński carpet
*
Sierpiński's constant
*
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 name ...
*
Sierpiński triangle
*
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)