Stanisław Mazur 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....

 and a member of the Polish Academy of Sciences

Polish Academy of Sciences

The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

.

Mazur made important contributions to geometrical methods in linear and nonlinear functional analysis

Nonlinear functional analysis

Nonlinear functional analysis is a branch of Mathematical Analysis. It deals with nonlinear mappings and its subject matter includes:* generalizations of calculus to Banach spaces* implicit function theorems...

 and to the study of Banach algebra

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 which at the same time is also a Banach space...

s. Mazur was also interested in summability theory, infinite games and computable function

Computable function

Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithm. They are used to discuss computability without referring to any concrete model of computation such as Turing machines or register...

s.

Lwòw and Warsaw

Mazur was a student of Stefan Banach

Stefan Banach

Stefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....

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

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

, where he participated in the mathematical activities at the Scottish Café

Scottish Café

The Scottish Café was the café in Lwów where, in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and topology....

. On 6 November 1936, Mazur posed the "basis problem" of determining whether every Banach space

Banach space

In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...

 has a Schauder basis

Schauder basis

In mathematics, a Schauder basis or countable basis is similar to the usual 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...

, with Mazur promising a "live goose" as a reward: Thirty-seven years later, a live goose was awarded by Mazur to Per Enflo

Per Enflo

Per H. Enflo is a mathematician who has solved fundamental problems in functional analysis. Three of these problems had been open for more than forty years:* The basis problem and the approximation problem and later...

 in a ceremony that was broadcast throughout Poland.

From 1948 Mazur worked 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...

.

More about Stanislaw Mazur at The MacTutor History of Mathematics archive

See also

• Approximation problem
• Approximation property
  Approximation property
  In mathematics, a Banach space is said to have the approximation property , if every compact operator is a limit of finite-rank operators. The converse is always true....
  
  
• Banach-Mazur theorem
  Banach-Mazur theorem
  In mathematics, the Banach–Mazur theorem is a theorem of functional analysis. Very roughly, it states that most well-behaved normed spaces are subspaces of the space of continuous paths...
  
  
• Banach-Mazur game
• Compact operator
  Compact operator
  In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y...
  
  
• Gel'fand-Mazur theorem
• Mazur–Ulam theorem
• Schauder basis
  Schauder basis
  In mathematics, a Schauder basis or countable basis is similar to the usual 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...
  
  
• Scottish Café
  Scottish Café
  The Scottish Café was the café in Lwów where, in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and topology....