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, 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 collectio ...

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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

, 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 language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

. 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 illu ...

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 curve, fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursion, recu ...

, the

Sierpiński carpet The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions; another is Cantor dust. The technique of subdividing a shape into smaller copies of ...

, and the

Sierpiński curve Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit n \to \infty completely fill the unit square: thus their limit curve, also called the Sierpiń ...

), 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 Samuel Dickstein (February 5, 1885 – April 22, 1954) was a Democratic Congressional Representative from New York (22-year tenure), a New York State Supreme Court Justice, and a Soviet spy. He played a key role in establishing the committee th ...

'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 ''l ...

. At the

Jagiellonian University The Jagiellonian University (Polish: ''Uniwersytet Jagielloński'', UJ) is a public research university in Kraków, Poland. Founded in 1364 by King Casimir III the Great, it is the oldest university in Poland and the 13th oldest university in ...

in Kraków, he attended lectures by Stanisław Zaremba on

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

. 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

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

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 Ukraine ...

, 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). Wacław Siepiński grave

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 List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

. To avoid the persecution that was common for

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/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 d ...

s. In 1916, Sierpiński gave the first example of an absolutely normal number. When

ended in 1918, Sierpiński returned to

. However shortly after taking up his appointment again in

he was offered a post at the

, which he accepted. In 1919 he was promoted to a

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

. 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 ...

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

General Staff A military staff or general staff (also referred to as army staff, navy staff, or air staff within the individual services) is a group of officers, enlisted and civilian staff who serve the commander of a division or other large military un ...

'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 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 syst ...

. Sierpiński edited the journal, which specialized in papers on

. During this period, Sierpiński worked predominantly on

, 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

s of a real variable. In

he made contributions on the

and on the

. 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 as ...

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 collectio ...

. He also worked on what is now known as the

. Sierpiński continued to collaborate with Luzin on investigations of analytic and projective sets. His work on

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 its ...

of functions and Baire's classification. Sierpiński retired in 1960 as

at the

, 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 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. 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 ''

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 zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur ...

''. 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 ...

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 populous ...

Honors received

Honorary Degrees:

(1929), St. Marks of Lima (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

(1967). For high involvement with the development of

, 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 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

. In 1928, he became vice-

chairman The chairperson, also chairman, chairwoman or chair, is the presiding officer of an organized group such as a board, committee, or deliberative assembly. The person holding the office, who is typically elected or appointed by members of the grou ...

of the

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 River, Chillón, Rímac River, Rímac and Lurín Rivers, in the desert zone of t ...

(1931), the Royal Scientific Society of

Liège Liège ( , , ; wa, Lîdje ; nl, Luik ; german: Lüttich ) is a major city and municipality of Wallonia and the capital of the Belgian province of Liège. The city is situated in the valley of the Meuse, in the east of Belgium, not far from b ...

(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

(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 on the Via della Lungara in Rom ...

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, and ...

(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 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 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 Cypra Cecilia Krieger-Dunaij (9 April 1894 – 17 August 1974) was an Austro-Hungarian (more specifically, Galician)-born mathematician of Jewish ancestry who lived and worked in Canada. Krieger was the third person (and first woman) to earn a P ...

. 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 in 1 ...

'' (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).

References

External links