The Polish School of Mathematics refers to the mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 community that flourished in 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 20th century, particularly during the Interbellum between World Wars I

World War I

World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...

 and II

World War II

World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

.

Overview

The Polish School of Mathematics subsumed:

• the Kraków School of Mathematics
  Kraków School of Mathematics
  Kraków 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...
  
  ;
• the Lwów School of Mathematics
  Lwów School of Mathematics
  The 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...
  
  ; and
• the Warsaw School of Mathematics
  Warsaw School of Mathematics
  "Warsaw School of Mathematics" is the name given to a group of mathematicians 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...
  
  .

Nomenclature

Poland's mathematicians provided a name to Polish notation

Polish notation

Polish notation, also known as prefix notation, is a form of notation for logic, arithmetic, and algebra. Its distinguishing feature is that it places operators to the left of their operands. If the arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that...

 and Polish space

Polish space

In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish...

.

Background

It has been debated what stimulated the exceptional efflorescence of mathematics in Poland after World War I

World War I

World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...

. Important preparatory work had been done by the Polish "Positivists"

Positivism in Poland

Positivism in Poland was a socio-cultural movement that defined progressive thought in literature and social sciences of Partitioned Poland following the suppression of the 1863 January Uprising against the occupying army of Imperial Russia...

 following the disastrous January 1863 Uprising

January Uprising

The January Uprising was an uprising in the former Polish-Lithuanian Commonwealth against the Russian Empire...

. The Positivists extolled science

Science

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

 and technology

Technology

Technology is the making, usage, and knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function. It can also refer to the collection of such tools, machinery, and procedures. The word technology comes ;...

, and popularized slogans of "organic work" and "building from the foundations." In the 20th century, mathematics was a field of endeavor that could be successfully pursued even with the limited resources that Poland commanded in the interbellum period.

Historical Influences

Over the centuries, Polish mathematicians have influenced the course of history. Copernicus used mathematics to buttress his revolutionary heliocentric theory. Four hundred years later, Marian Rejewski

Marian Rejewski

Marian Adam Rejewski was a Polish mathematician and cryptologist who in 1932 solved the plugboard-equipped Enigma machine, the main cipher device used by Germany...

 — subsequently assisted by fellow mathematician

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

-cryptologists Jerzy Różycki

Jerzy Rózycki

Jerzy Witold Różycki was a Polish mathematician and cryptologist who worked at breaking German Enigma-machine ciphers.-Life:Różycki was born in what is now Ukraine, the fourth and youngest child of Zygmunt Różycki, a pharmacist and graduate of Saint Petersburg University, and Wanda, née Benita. ...

 and Henryk Zygalski

Henryk Zygalski

Henryk Zygalski was a Polish mathematician and cryptologist who worked at breaking German Enigma ciphers before and during World War II.-Life:...

 — in December 1932 first broke the German Enigma machine

Enigma machine

An Enigma machine is any of a family of related electro-mechanical rotor cipher machines used for the encryption and decryption of secret messages. Enigma was invented by German engineer Arthur Scherbius at the end of World War I...

 cipher

Cipher

In cryptography, a cipher 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. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...

, thus laying the foundations for British

Great Britain

Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...

 World War II

World War II

World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

 reading of Enigma ciphers ("Ultra

Ultra

Ultra was the designation adopted by British military intelligence in June 1941 for wartime signals intelligence obtained by "breaking" high-level encrypted enemy radio and teleprinter communications at the Government Code and Cypher School at Bletchley Park. "Ultra" eventually became the standard...

"). After the war, Stanisław Ulam showed Edward Teller

Edward Teller

Edward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he did not care for the title. Teller made numerous contributions to nuclear and molecular physics, spectroscopy , and surface physics...

 how to construct a practicable hydrogen bomb.