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, mathematical structure, structure, space, Mathematica ...

. He was known for contributions to

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), 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 mathema ...

(research on the axiom of choice and the continuum hypothesis),

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, theory of functions, and

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

. He published over 700 papers and 50 books. Three well-known

fractal In mathematics, a fractal is a Shape, 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 scale ...

s are named after him (the Sierpiński triangle, the Sierpiński carpet, and the Sierpiński curve), as are Sierpiński numbers and the associated Sierpiński problem.

Early life and education

Sierpiński was born in 1882 in Warsaw, Congress Poland, to a doctor father Konstanty and mother Ludwika (''née'' Łapińska). His abilities in mathematics were evident from childhood. He enrolled in the Department of Mathematics and Physics at the University of Warsaw in 1899 and graduated five 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, 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 , officially the Royal Capital City of Kraków, is the List of cities and towns in Poland, second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city has a population of 804,237 ...

to pursue a

doctorate A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

. At the Jagiellonian University in Kraków, he attended lectures by Stanisław Zaremba on

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. He also studied

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

and

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

. In 1906, he received his doctorate and in 1908 was appointed to the University of Lwów. In 1910, he became head of the Faculty of Mathematics at the university.

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 (then at

Göttingen Göttingen (, ; ; ) 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. According to the 2022 German census, t ...

), asking how such a result was possible. He received the one-word reply ' Cantor'. 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, 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 or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

began in 1914, Sierpiński and his family were in

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

. To avoid the persecution that was common for Polish foreigners, Sierpiński spent the rest of the war years in

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

working with Nikolai Luzin. Together they began the study of analytic sets. In 1916, Sierpiński gave the first example of an absolutely normal number. When

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, 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 tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

. He spent the rest of his life in

Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...

. During the Polish–Soviet War (1919–1921), Sierpiński helped break Soviet Russian

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

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 rank, enlisted, and civilian staff who serve the commanding officer, commander of a ...

's cryptologic agency. In 1920, Sierpiński, together with Zygmunt Janiszewski and his former student Stefan Mazurkiewicz, founded the mathematical journal '' Fundamenta Mathematicae''. Sierpiński edited the journal, which specialized in papers on

. During this period, Sierpiński worked predominantly on

, but also on point set topology and functions of a real variable. In

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 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 Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...

, differentiability of functions and Baire's classification. Sierpiński worked at the State Institute of Mathematics, which was incorporated into the

Polish Academy of Sciences The Polish Academy of Sciences (, 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 distinguished scholars a ...

in 1952. He retired in 1960 as

at the University of Warsaw, but continued until 1967 to give a seminar on the Theory of Numbers at the

. 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'', ''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. Sierpiński is interred at the Powązki Cemetery in

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...

Honors received

Honorary Degrees: Lwów (1929), St. Marks of Lima (1930),

Tartu Tartu is the second largest city in Estonia after Tallinn. Tartu has a population of 97,759 (as of 2024). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the ...

(1932),

Amsterdam Amsterdam ( , ; ; ) is the capital of the Netherlands, capital and Municipalities of the Netherlands, largest city of the Kingdom of the Netherlands. It has a population of 933,680 in June 2024 within the city proper, 1,457,018 in the City Re ...

(1932),

Sofia Sofia is the Capital city, capital and List of cities and towns in Bulgaria, largest city of Bulgaria. It is situated in the Sofia Valley at the foot of the Vitosha mountain, in the western part of the country. The city is built west of the Is ...

(1939),

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

(1939),

Bordeaux Bordeaux ( ; ; Gascon language, Gascon ; ) is a city on the river Garonne in the Gironde Departments of France, department, southwestern France. A port city, it is the capital of the Nouvelle-Aquitaine region, as well as the Prefectures in F ...

(1947),

Prague Prague ( ; ) is the capital and List of cities and towns in the Czech Republic, largest city of the Czech Republic and the historical capital of Bohemia. Prague, located on the Vltava River, has a population of about 1.4 million, while its P ...

(1948),

Wrocław Wrocław is a city in southwestern Poland, and the capital of the Lower Silesian Voivodeship. It is the largest city and historical capital of the region of Silesia. It lies on the banks of the Oder River in the Silesian Lowlands of Central Eu ...

(1948),

Lucknow Lucknow () is the List of state and union territory capitals in India, capital and the largest city of the List of state and union territory capitals in India, Indian state of Uttar Pradesh and it is the administrative headquarters of the epon ...

(1949), and

(1967). For high involvement with the development of

, Sierpiński 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 The chair, also chairman, chairwoman, or chairperson, 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 gro ...

of the

Scientific Society, and that same year was elected chairman of the Polish Mathematical Society. He was elected to the Geographic Society of

Lima Lima ( ; ), founded in 1535 as the Ciudad de los Reyes (, Spanish for "City of Biblical Magi, Kings"), is the capital and largest city of Peru. It is located in the valleys of the Chillón River, Chillón, Rímac River, Rímac and Lurín Rive ...

(1931), Royal Scientific Society of

Liège Liège ( ; ; ; ; ) is a City status in Belgium, city and Municipalities in Belgium, municipality of Wallonia, and the capital of the Liège Province, province of Liège, Belgium. The city is situated in the valley of the Meuse, in the east o ...

(1934), Bulgarian Academy of Sciences (1936), National Academy of

(1939), Royal Society of Sciences of

Naples Naples ( ; ; ) is the Regions of Italy, regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 908,082 within the city's administrative limits as of 2025, while its Metropolitan City of N ...

(1939), Accademia dei Lincei of

Rome Rome (Italian language, Italian and , ) is the capital city and most populated (municipality) of Italy. It is also the administrative centre of the Lazio Regions of Italy, region and of the Metropolitan City of Rome. A special named with 2, ...

(1947), Germany Academy of Sciences (1950),

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) 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 other ...

(1959), Paris Academy (1960), Royal Dutch Academy (1961), Academy of Science of Brussels (1961),

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

(1964), Romanian Academy (1965) and Papal Academy of Sciences (1967). In 1946, he received the Stefan Banach Prize of the Polish Mathematical Society. In 1949, Sierpiński was awarded Poland's Scientific Prize, first degree. In 2014, a sculpture in the form of a tree inspired by a fractal created by Sierpiński was unveiled at the Wallenberg Square in

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

as part of an exhibition organized by the Polish Ministry of Foreign Affairs on the 10th anniversary of Poland joining the

European Union The European Union (EU) is a supranational union, supranational political union, political and economic union of Member state of the European Union, member states that are Geography of the European Union, located primarily in Europe. The u ...

and 15th anniversary of Poland joining

NATO The North Atlantic Treaty Organization (NATO ; , OTAN), also called the North Atlantic Alliance, is an intergovernmental organization, intergovernmental Transnationalism, transnational military alliance of 32 Member states of NATO, member s ...

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'' (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