Stanisław Mieczysław Mazur (1 January 1905,

Lwów Lviv ( uk, Львів) is the largest city in Western Ukraine, western Ukraine, and the List of cities in Ukraine, seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is o ...

– 5 November 1981,

Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officiall ...

) was a Polish

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 ...

and a member of the

Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society o ...

. Mazur made important contributions to geometrical methods in linear and

nonlinear functional analysis Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings. Topics Its subject matter includes: * generalizations of calculus to Banach spaces * implicit function theorems * fixed-point theorems (B ...

and to the study of

Banach algebra In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach ...

s. He was also interested in summability theory, infinite games and

computable function Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do ...

Lwów and Warsaw

Mazur was a student of

Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an origina ...

at University of Lwów. His doctorate, under Banach's supervision, was awarded in 1935. Mazur, with

Juliusz Schauder Juliusz Paweł Schauder (; 21 September 1899, Lwów, Austria-Hungary – September 1943, Lwów, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equations and m ...

, was an Invited Speaker of the ICM in 1936 in

Oslo Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of ...

. Mazur was a close collaborator with Banach at Lwów and was a member of 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 ...

, where he participated in the mathematical activities at the

Scottish Café The Scottish Café ( pl, Kawiarnia Szkocka) was a café in Lwów, Poland (now Lviv, Ukraine) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in fun ...

. On 6 November 1936, he posed the " basis problem" of determining whether every

Banach space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...

has a

Schauder basis In mathematics, a Schauder basis or countable basis is similar to the usual ( Hamel) basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This ...

, with Mazur promising a "live goose" as a reward: 37 years later and in a ceremony that was broadcast throughout Poland, Mazur awarded a live goose to

Per Enflo Per H. Enflo (; born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved mathematical problems, problems that had been considered fundamental. Three of these problems had been open problem, ...

for constructing a counter-example. From 1948 Mazur worked at the

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...

References

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* * 1905 births 1981 deaths Lwów School of Mathematics People from the Kingdom of Galicia and Lodomeria Ukrainian Jews Polish Workers' Party politicians Members of the Central Committee of the Polish United Workers' Party Members of the Polish Sejm 1947–1952 Members of the Polish Sejm 1952–1956 Functional analysts Measure theorists Academic staff of the University of Lviv Members of the Polish Academy of Sciences Recipients of the Order of the Banner of Work Officers of the Order of Polonia Restituta Academic staff of the University of Warsaw Recipients of the State Award Badge (Poland) {{Poland-mathematician-stub

Lwów and Warsaw

See also

References

External links