Stefan Mazurkiewicz (born September 25, 1888 in Warsaw, Poland - died June 19, 1945, Grodzisk Mazowiecki) 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 (PAU). His students included Karol Borsuk, Bronisław Knaster, Kazimierz Kuratowski, Stanisław Saks and Antoni Zygmund. The Biuro Szyfrów ( (?), Polish for Cipher Bureau) was the Polish agency concerned with cryptology between World Wars I and II. The Bureau enjoyed notable successes against Soviet cryptography during the Polish-Soviet War, helping to preserve Polands independence. ... Polish copy of Enigma. ... The grill (Polish: ruszt), in cryptology, was a method used, chiefly early on, by the mathematician-cryptologists of the Polish Cipher Bureau in decrypting German Enigma machine ciphers. ... The clock, in cryptology, was a method devised by Polish mathematician-cryptologist Jerzy Różycki, at the Polish General Staffs Cipher Bureau, to facilitate decrypting German Enigma messages. ... Diagram of cyclometer, from Marian Rejewski’s papers The cyclometer was a cryptologic device designed by the Polish Cipher Bureau (BS-4) to help decrypt the German Enigma machine during the 1930s. ... The card catalog, or catalog of characteristics, in cryptology, was a system designed, and first completed about 1935, by Polish Cipher Bureau mathematician-cryptologist Marian Rejewski to facilitate decrypting German Enigma messages. ... The bomba (plural bomby) was a special-purpose codebreaking machine designed by Polish cryptanalysts and used to crack the German Enigma machine prior to World War II. A bomba was designed to exploit an obscure but fatal weakness in the Enigma cipher. ... The method of perforated sheets was a codebreaking technique used against the Enigma machine (see Cryptanalysis of the Enigma). ... The Lacida (or LCD) was a rotor cipher machine designed before World War II by the Polish Cipher Bureau for wartime use by Polish higher commands. ... Rendering of the Saxon Palace, as it is to be rebuilt. ... Kabaty is the southernmost neighborhood of the city of Warsaw, located in its Ursynów district. ... PC Bruno was the code name for the intelligence station operated at a farmhouse in the west of France to which French cryptanalysts retired after Paris was captured by the Germans in 1940. ... Polish-French Cadix radio-intelligence team, southern France, 1940-1942. ... Maksymilian Ciężki (1899–November 9, 1951) was the head of the German section of the Polish Cipher Bureau during the 1930s, during which time the organisation was able to decrypt German Enigma messages. ... From left: Jan GraliÅ„ski, Jerzy Różycki and Piotr SmoleÅ„ski at Cadix in southern France. ... Lt. ... Gwido Langer (died March 30, 1948) was chief of the Polish General Staffs Cipher Bureau from at least mid-1931. ... Stanislaw Lesniewski (March 30, 1886–May 13, 1939) was a Polish mathematician, philosopher and logician. ... Wiktor MichaÅ‚owski (died 1973) was a Polish Army officer who worked at the interbellum Polish Cipher Bureaus German section, . Reportedly he participated, as a lieutenant, in the initial, unsuccessful Polish attempts to break the German Enigma cipher, along with then-Lt. ... Former civilian cryptanalyst with the General Staff Biuro Szyfrów (Cipher Bureau) German Section (BS4). ... Major Franciszek Pokorny was a Polish Army officer who headed the Polish General Staffs Cipher Bureau before Major (eventually, Lt. ... Marian Rejewski (probably 1932, the year he first solved the Enigma machine). ... Jerzy Różycki, about 1928. ... WacÅ‚aw Franciszek SierpiÅ„ski (March 14, 1882 — October 21, 1969), a Polish mathematician, was born and died in Warsaw. ... From left: Jan GraliÅ„ski, Jerzy Różycki and Piotr SmoleÅ„ski at Cadix in southern France. ... Henryk Zygalski, about 1930. ... September 25 is the 268th day of the year (269th in leap years) in the Gregorian calendar. ... 1888 (MDCCCLXXXVIII) is a leap year starting on Sunday (click on link for calendar) of the Gregorian calendar or a leap year starting on Tuesday of the Julian calendar. ... Warsaw (Polish: , (?), in full The Capital City of Warsaw, Polish: Miasto StoÅ‚eczne Warszawa) is the capital of Poland and its largest city. ... June 19 is the 170th day of the year (171st in leap years) in the Gregorian Calendar, with 195 days remaining. ... 1945 (MCMVL) was a common year starting on Monday (the link is to a full 1945 calendar). ... Grodzisk Mazowiecki is a town in central Poland with 24,900 inhabitants in 1995. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Analysis is the generic name given to any branch of mathematics that depends upon the concepts of limits and convergence. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Informally, probable is one of several words applied to uncertain events or knowledge, being closely related in meaning to likely, risky, hazardous, and doubtful. ... WacÅ‚aw Franciszek SierpiÅ„ski (March 14, 1882 — October 21, 1969), a Polish mathematician, was born and died in Warsaw. ... The Polish Academy of Skills (Polish: Polska Akademia Umiejętności, PAU), till 1919 just The Academy of Skills (Akademia Umiejętności, AU) founded in 1872 in Kraków as continuation of the Kraków Scientific Society (Towarzystwo Naukowe Krakowskie, est. ... Karol Borsuk (May 8, 1905 - January 24, 1982) was a Polish mathematician born in Warsaw. ... BronisÅ‚aw Knaster (1893–1990) was a Polish mathematician; from 1939 university professor at Lwów, from 1945 at WrocÅ‚aw. ... Kazimierz Kuratowski (born February 2, 1896, Warsaw, died June 18, 1980, Warsaw) was a Polish mathematician. ... StanisÅ‚aw Saks (30 December 1897 – 23 November 1942) was a Polish mathematician. ... Antoni Zygmund (25 December 1900 _ 30 May 1992) was a Polish mathematician. ...

The Hahn-Mazurkiewicz theorem, a basic result on curves prompted by the phenomenon of space-filling curves, is named for Mazurkiewicz and Hans Hahn. His 1935 paper Sur l'existence des continus indécomposables is generally considered the most elegant piece of work in point-set topology. Space-filling curves or Peano curves are curves, first described by Giuseppe Peano, whose ranges contain the entire 2-dimensional unit square (or the 3-dimensional unit cube). ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... Space-filling curves or Peano curves are curves, first described by Giuseppe Peano, whose ranges contain the entire 2-dimensional unit square (or the 3-dimensional unit cube). ... Hans Hahn (1879 - 1934) was an Austrian mathematician who made many contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory. ... In mathematics, general topology or point set topology is that branch of topology which studies elementary properties of topological spaces and structures defined on them. ...

During the Polish-Soviet War (1919-1921), Mazurkiewicz as early as 1919 broke the commonest Russian cipher for the Polish General Staff's cryptological agency. Thanks to this, orders issued by Soviet commander Mikhail Tukhachevsky's staff were known to Polish Army leaders. This contributed substantially, perhaps decisively, to Polish victory at the critical Battle of Warsaw and possibly to Poland's survival as an independent country. Combatants Russian Soviet Federated Socialist Republic Second Polish Republic Commanders Mikhail Tukhachevsky Semyon Budyonny Joseph Stalin Józef PiÅ‚sudski Edward Rydz-ÅšmigÅ‚y Strength 950,000 including reserves 5 million 360,000 including reserves 738,000 Casualties Unknown, dead estimated at 100,000 - 150,000 Unknown, dead estimated at... This article is about algorithms for encryption and decryption. ... A General Staff is a group of professional military officers who act in a staff or administrative role under the command of a general officer. ... The Biuro Szyfrów ( (?), Polish for Cipher Bureau) was the Polish agency concerned with cryptology between World Wars I and II. The Bureau enjoyed notable successes against Soviet cryptography during the Polish-Soviet War, helping to preserve Polands independence. ... Marshal of the Soviet Union Mikhail Tukhachevsky Mikhail Nikolayevich Tukhachevsky (also spelled Tukhachevski, Tukhachevskii, Russian: Михаил Николаевич Тухачевский) (February 16, 1893 - June 12, 1937), Soviet military... The Battle of Warsaw (sometimes referred to as the Miracle at the Vistula, Polish Cud nad WisÅ‚Ä…) was the decisive battle of the Polish-Soviet War, the war that began soon after the end of World War I in 1918 and lasted until the Treaty of Riga in 1921. ...

See also

• Biuro Szyfrów

The Biuro Szyfrów ( (?), Polish for Cipher Bureau) was the Polish agency concerned with cryptology between World Wars I and II. The Bureau enjoyed notable successes against Soviet cryptography during the Polish-Soviet War, helping to preserve Polands independence. ...

External links

• Stefan Mazurkiewicz at the Mathematics Genealogy Project
• O'Connor, John J., and Edmund F. Robertson. "Stefan Mazurkiewicz". MacTutor History of Mathematics archive.