ArticleslgStudy

mathematics

Stanisław Mazur

Stanisław Mazur is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Stanisław Mazur rather than just read about it. In short: Stanisław Mieczysław Mazur (Polish: [ˈmazur]; 1 January 1905 – 5 November 1981) was a Polish mathematician, a member of the Polish Academy of Sciences and one of the leading representatives of the Lwów School of Mathematics Mazur made important contributions to geometrical methods in linear and nonlinear functional analysis and to the study of Banach algebras. He was also interested in summability theory, infinite g…

Stanisław Mazur — main illustration
Stanisław Mazur — illustration

Key takeaways

  • Stanisław Mazur belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Stanisław Mazur to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Stanisław Mazur from memory before moving on to harder problems.

Reference excerpt

Stanisław Mieczysław Mazur (Polish: [ˈmazur]; 1 January 1905 – 5 November 1981) was a Polish mathematician, a member of the Polish Academy of Sciences and one of the leading representatives of the Lwów School of Mathematics Mazur made important contributions to geometrical methods in linear and nonlinear functional analysis and to the study of Banach algebras. He was also interested in summability theory, infinite games and computable functions.

Life and career

Mazur was born on 1 January 1905 in Lwów, then part of the Kingdom of Galicia and Lodomeria within Austria-Hungary, to Tomasz Mazur and Aniela (née Zawrotniak). In 1923, he graduated from a gymnasium in Lwów. Between 1923–1926, Mazur studied at the Jan Kazimierz University (now the University of Lviv). In 1925, he completed an internship at the Sorbonne in Paris. Mazur was a student of Stefan Banach at Jan Kazimierz University. His doctorate entitled O szeregach warunkowo sumowalnych (On Conditionally Summable Series), under Banach's supervision, was awarded in 1932. Mazur, with Juliusz Schauder, was an Invited Speaker at the International Congress of Mathematicians in 1936 in Oslo. In 1936, he earned his habilitation and in 1947, he became a professor at the University of Łódź and the following year at the University of Warsaw. Mazur was a close collaborator with Banach at Lwów and was a member of the Lwów School of Mathematics, where he participated in the mathematical activities at the Scottish Café. He was the author or co-author of 47 problems included in the Scottish Book. On 6 November 1936, he posed the "basis problem" of determining whether every Banach space has a Schauder basis, 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 for constructing a counter-example. In 1939, he became a deputy to the People’s Assembly of Western Ukraine; from 1940 he served as a councillor on the Lviv City Council, and after the Soviets returned in 1944 he joined the Main Board of the Union of Polish Patriots. In 1946, Mazur was awarded the Officer's Cross of the Order of Polonia Restituta. From 1948 Mazur worked at the University of Warsaw. He also worked at the State Institute of Mathematics, which was incorporated into the Polish Academy of Sciences in 1952. He was a foreign member of the Hungarian Academy of Sciences. In 1949, he received the Stefan Banach Prize conferred by the Polish Mathematical Society. In 1978, he was awarded an honorary life membership in the Polish Mathematical Society and in 1980, an honorary doctorate at the University of Warsaw. His notable doctoral students included Aleksander Pełczyński and Wiesław Żelazko.

See also List of Polish mathematicians Approximation problem Compact operator Schauder basis

References

External links O'Connor, John J.; Robertson, Edmund F., "Stanisław Mazur", MacTutor History of Mathematics Archive, University of St Andrews Stanisław Mazur at the Mathematics Genealogy Project

Illustrations

Stanisław Mazur illustration
Stanisław Mazur: Mazur awards a live goose to Per Enflo, who solved Mazur's 1936 problem in the Scottish book. The photograph comes from the book Pół wieku matematyki polskiej 1920-1970 ("Half a Century of Polish Mathematics 1920-1970").
Mazur awards a live goose to Per Enflo, who solved Mazur's 1936 problem in the Scottish book. The photograph comes from the book Pół wieku matematyki polskiej 1920-1970 ("Half a Century of Polish Mathematics 1920-1970").

Worked examples

Example 1 — a first encounter with Stanisław Mazur

Start with the simplest possible case. Write down what Stanisław Mazur claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Stanisław Mazur before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Stanisław Mazur ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Stanisław Mazur

In research
Stanisław Mazur appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Stanisław Mazur in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Stanisław Mazur is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 1981 deaths, 20th-century Polish mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Stanisław Mazur outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Stanisław Mazur” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Stanisław Mazur in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Stanisław Mazur means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Stanisław Mazur out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Stanisław Mazur in simple terms?

Stanisław Mieczysław Mazur (Polish: [ˈmazur]; 1 January 1905 – 5 November 1981) was a Polish mathematician, a member of the Polish Academy of Sciences and one of the leading representatives of the Lwów School of Mathematics Mazur made important contributions to geometrical methods in linear and non…

Why does Stanisław Mazur matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Stanisław Mazur?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Stanisław Mazur.

Tags

  • 1905 births
  • 1981 deaths
  • 20th-century Polish mathematicians
  • Academic staff of the University of Lviv
  • Academic staff of the University of Warsaw
  • Functional analysts
  • Lwów School of Mathematics
  • Measure theorists
  • Members of the Central Committee of the Polish United Workers' Party
  • Members of the Polish Academy of Sciences
  • Members of the Polish Sejm 1947–1952
  • Members of the Polish Sejm 1952–1956

Keep exploring