Stefan Mazurkiewicz
Encyclopedia
Stefan Mazurkiewicz was a Polish
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...

 mathematician
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....

 who worked in mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

, and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning
Polish Academy of Learning
The Polish Academy of Arts and Sciences or Polish Academy of Learning , headquartered in Kraków, is one of two institutions in contemporary Poland having the nature of an academy of sciences....

 (PAU). His students included Karol Borsuk
Karol Borsuk
Karol 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...

, Bronisław Knaster, Kazimierz Kuratowski
Kazimierz Kuratowski
Kazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.-Biography and studies:...

, Stanisław Saks, and Antoni Zygmund
Antoni Zygmund
Antoni 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...

. For a time Mazurkiewicz was a professor ath the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...

, however he spent most of his career as a professor at the University of Warsaw
University of Warsaw
The University of Warsaw is the largest university in Poland and one of the most prestigious, ranked as best Polish university in 2010 and 2011...

.
The Hahn-Mazurkiewicz theorem, a basic result on curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

s prompted by the phenomenon of space-filling curve
Space-filling curve
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square...

s, is named for Mazurkiewicz and Hans Hahn
Hans Hahn
Hans Hahn was an Austrian mathematician who made contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory.-Biography:...

. His 1935 paper Sur l'existence des continus indécomposables is generally considered the most elegant piece of work in point-set topology.

During the Polish-Soviet War
Polish-Soviet War
The Polish–Soviet War was an armed conflict between Soviet Russia and Soviet Ukraine and the Second Polish Republic and the Ukrainian People's Republic—four states in post–World War I Europe...

 (1919-1921), Mazurkiewicz as early as 1919 broke the most common Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

n 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...

 for the Polish General Staff
General Staff
A military staff, often referred to as General Staff, Army Staff, Navy Staff or Air Staff within the individual services, is a group of officers and enlisted personnel that provides a bi-directional flow of information between a commanding officer and subordinate military units...

's cryptological agency
Biuro Szyfrów
The Biuro Szyfrów was the interwar Polish General Staff's agency charged with both cryptography and cryptology ....

. Thanks to this, orders issued by Soviet commander Mikhail Tukhachevsky
Mikhail Tukhachevsky
Mikhail Nikolayevich Tukhachevsky was a Marshal of the Soviet Union, commander in chief of the Red Army , and one of the most prominent victims of Joseph Stalin's Great Purge.-Early life:...

's staff were known to Polish Army leaders. This contributed substantially, perhaps decisively, to Polish victory at the critical Battle of Warsaw
Battle of Warsaw (1920)
The Battle of Warsaw sometimes referred to as the Miracle at the Vistula, was the decisive battle of the Polish–Soviet War. That war began soon after the end of World War I in 1918 and lasted until the Treaty of Riga resulted in the end of the hostilities between Poland and Russia in 1921.The...

and possibly to Poland's survival as an independent country.

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