The Polish School of Mathematics was the
mathematics community that flourished 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 ...
in the 20th century, particularly during the
Interbellum
In the history of the 20th century, the interwar period lasted from 11 November 1918 to 1 September 1939 (20 years, 9 months, 21 days), the end of the First World War to the beginning of the Second World War. The interwar period was relative ...
between
World Wars I and
II.
Overview
The Polish School of Mathematics subsumed:
*the
Lwów School of Mathematics
The Lwów school of mathematics ( pl, lwowska szkoła matematyczna) was a group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine). The mathematicians often met at the famous Scottish Café to ...
- mostly focused on
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...
;
*the
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 pu ...
- mostly focused 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 ...
,
mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
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 ...
; and
*the
Kraków School of Mathematics
The Kraków School of Mathematics ( pl, krakowska szkoła matematyczna) was a subgroup of the Polish School of Mathematics represented by mathematicians from the Kraków universities—Jagiellonian University, and the AGH University of Science and ...
- mostly focused on
differential equations,
analytic functions
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...
,
differential geometry.
Nomenclature
Poland's mathematicians provided a name to
Polish notation
Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast ...
and
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 be ...
.
Background
It has been debated what stimulated the exceptional efflorescence of mathematics in Poland after
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 ...
. Important preparatory work had been done by the
Polish "Positivists" following the disastrous
January 1863 Uprising. The Positivists extolled
science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earli ...
and
technology
Technology is the application of knowledge to reach practical goals in a specifiable and Reproducibility, reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in me ...
, 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
In the history of the 20th century, the interwar period lasted from 11 November 1918 to 1 September 1939 (20 years, 9 months, 21 days), the end of the First World War to the beginning of the Second World War. The interwar period was relative ...
period.
Historical Influences
Over the centuries, Polish mathematicians have influenced the course of history.
Copernicus
Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated ...
used mathematics to buttress his revolutionary
heliocentric theory
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth a ...
. Four hundred years later,
Marian Rejewski — subsequently assisted by fellow
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 ...
-
cryptologist
This is a list of cryptographers. Cryptography is the practice and study of techniques for secure communication in the presence of third parties called adversaries.
Pre twentieth century
* Al-Khalil ibn Ahmad al-Farahidi: wrote a (now lost) bo ...
s
Jerzy Różycki
Jerzy Witold Różycki (; Vilshana, Ukraine, 24 July 1909 – 9 January 1942, Mediterranean Sea, near the Balearic Islands) was a Polish mathematician and cryptologist who worked at breaking German Enigma-machine ciphers before and during World ...
and
Henryk Zygalski
Henryk Zygalski (; 15 July 1908 – 30 August 1978) was a Polish mathematician and cryptologist who worked at breaking German Enigma ciphers before and during World War II.
Life
Zygalski was born on 15 July 1908 in Posen, German Empire (now Pozn ...
— in December 1932 first broke the German
Enigma machine cipher, thus laying the foundations for
British
British may refer to:
Peoples, culture, and language
* British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies.
** Britishness, the British identity and common culture
* British English, ...
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...
reading of Enigma ciphers ("
Ultra
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 (GC&CS) at Bletchley Park. ' ...
"). After the war,
Stanisław Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ...
showed
Edward Teller
Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care for ...
how to construct a practicable
hydrogen bomb.
See also
*
Lwów-Warsaw School of Logic.
References
*
Kazimierz Kuratowski
Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.
Biography and studies
Kazimierz Kuratowski was born in Warsaw, (t ...
(1980) ''A Half Century of Polish Mathematics: Remembrances and Reflections'', Oxford,
Pergamon Press
Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier.
History
The ...
, .
* Roman Murawski (2014) ''The Philosophy and Mathematics of Logic in the 1920s and 1930s in Poland'', Maria Kantor translator,
Birkhäuser
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields:
* Springer continues to publish science (particu ...
{{ISBN, 978-3-0348-0830-9
History of mathematics
History of education in Poland
Polish mathematics