Warsaw School of Mathematics
Encyclopedia
"Warsaw School of Mathematics" is the name given to a group of mathematician
s who worked at Warsaw
, Poland
, in the two decades between the World Wars, especially in the fields of logic
, set theory
, point-set topology and real analysis
. They published in the journal Fundamenta Mathematicae
, founded in 1920 — one of the world's first specialist pure-mathematics journals. It was in this journal, in 1933, that Alfred Tarski
— whose illustrious career would a few years later take him to the University of California, Berkeley
— published his celebrated theorem on the undefinability of the notion of truth.
Notable members of the Warsaw School of Mathematics have included:
Additionally, notable logicians of the Lwów-Warsaw School of Logic, working at Warsaw
, have included:
Fourier analysis has been advanced at Warsaw
by:
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s who worked at Warsaw
Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...
, Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
, in the two decades between the World Wars, especially in the fields of logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, point-set topology and real analysis
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
. They published in the journal Fundamenta Mathematicae
Fundamenta Mathematicae
Fundamenta Mathematicae is a scientific journal of mathematics with a special focus on the foundations of mathematics. At present, it concentrates on papers devoted to set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems...
, founded in 1920 — one of the world's first specialist pure-mathematics journals. It was in this journal, in 1933, that Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
— whose illustrious career would a few years later take him to the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
— published his celebrated theorem on the undefinability of the notion of truth.
Notable members of the Warsaw School of Mathematics have included:
- Wacław Sierpiński
- Kazimierz KuratowskiKazimierz KuratowskiKazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.-Biography and studies:...
- Edward MarczewskiEdward MarczewskiEdward Marczewski was a Polish mathematician. His surname until 1940 was Szpilrajn.Marczewski was a member of the Warsaw School of Mathematics...
- Bronisław Knaster
- Zygmunt JaniszewskiZygmunt JaniszewskiZygmunt Janiszewski was a Polish mathematician.-Life:His mother was Julia Szulc-Chojnicka. His father, Czeslaw Janiszewski, was a graduate of the University of Warsaw and was an important person in finance, being the director of the Société du Crédit Municipal in Warsaw.Janiszewski taught at the...
- Stefan MazurkiewiczStefan MazurkiewiczStefan Mazurkiewicz 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...
- Stanisław Saks
- Karol BorsukKarol BorsukKarol Borsuk was a Polish mathematician.His main interest was topology.Borsuk introduced the theory of absolute retracts and absolute neighborhood retracts , and the cohomotopy groups, later called Borsuk-Spanier cohomotopy groups. He also founded the so called Shape theory...
- Roman SikorskiRoman SikorskiRoman Sikorski was a Polish mathematician.Sikorski was from 1952 until 1982 professor at the Warsaw University...
- Nachman Aronszajn
- Samuel EilenbergSamuel EilenbergSamuel Eilenberg was a Polish and American mathematician of Jewish descent. He was born in Warsaw, Russian Empire and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor...
Additionally, notable logicians of the Lwów-Warsaw School of Logic, working at Warsaw
Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...
, have included:
- Stanisław Leśniewski
- Adolf LindenbaumAdolf LindenbaumAdolf Lindenbaum , was a Polish logician and mathematician.He was a student of Wacław Sierpiński, became a distinguished author of works on set theory and had served as an Assistant Professor at Warsaw University...
- Alfred TarskiAlfred TarskiAlfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
- Jan Łukasiewicz
- Andrzej MostowskiAndrzej MostowskiAndrzej Mostowski was a Polish mathematician. He is perhaps best remembered for the Mostowski collapse lemma....
Fourier analysis has been advanced at Warsaw
Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...
by:
- Aleksander Rajchman
- Antoni ZygmundAntoni ZygmundAntoni Zygmund was a Polish-born American mathematician.-Life:Born in Warsaw, Zygmund obtained his PhD from Warsaw University and became a professor at Stefan Batory University at Wilno...
- Józef MarcinkiewiczJózef MarcinkiewiczJózef Marcinkiewicz – died in 1940 in Kharkiv, Ukraine) was a Polish mathematician.He was a student of Antoni Zygmund; and later worked with Juliusz Schauder, and Stefan Kaczmarz. He was a professor of the Stefan Batory University in Wilno....
- Otton M. NikodymOtton M. NikodymOtto Marcin Nikodým was a Polish mathematician. He was educated at the Universities of Lwow and Warsaw, and the Sorbonne. Nikodym taught at the Universities of Kraków and Warsaw and at the High Polytechnical School in Kraków. He came to the United States in 1948 to join the faculty of Kenyon...
- Jerzy Spława-Neyman
See also
- Polish School of MathematicsPolish School of MathematicsThe Polish School of Mathematics refers to the mathematics community that flourished in Poland in the 20th century, particularly during the Interbellum between World Wars I and II.- Overview :The Polish School of Mathematics subsumed:...
- Kraków School of MathematicsKraków School of MathematicsKraków School of Mathematics was a sub-group of Polish School of Mathematics represented by mathematicians from the Kraków universities—Jagiellonian University and the AGH University of Science and Technology, active during the interwar period...
- Lwów School of MathematicsLwów School of MathematicsThe Lwów School of Mathematics was a group of mathematicians who worked between the two World Wars in Lviv, then known as Lwów and located in Poland, but now located in western Ukraine. The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the...