Mathematician:Stefan Banach

Mathematician

Polish mathematician who founded the modern field of functional analysis.

Most famous for his collaborative paper with Alfred Tarski in 1924, in which the Banach-Tarski Paradox was raised.

This demonstrated that a contra-intuitive truth could be deduced from the ZFC axioms of set theory, specifically, by assuming the truth of the Axiom of Choice.

Impassioned controversy rages to this day.

Protegé of Hugo Steinhaus, who discovered him quite by accident.

Nationality

Polish

History

• Born: 30 March 1892, Ostrowsko, near Kraków, Austria-Hungary (now Poland)
• Died: 31 Aug 1945, Lvov, (now Ukraine)

Theorems and Definitions

• Banach's Contraction Principle
• Banach Fixed-Point Theorem
• Banach's Matchbox Problem
• Closed Range Theorem (proved by Banach in 1932: Théorie des opérations linéaires)

• Banach-Alaoglu Theorem (with Leonidas Alaoglu) (also known as Alaoglu's Theorem)
• Banach-Mazur Theorem (with Stanisław Meiczyslaw Mazur)
• Banach-Schauder Theorem (with Juliusz Paweł Schauder)
• Banach-Steinhaus Theorem (with Hugo Steinhaus)
• Banach-Stone Theorem (with Marshall Harvey Stone)
• Banach-Tarski Paradox (with Alfred Tarski)

• Hahn-Banach Theorem (independently of Hans Hahn)
• Hahn-Banach Separation Theorem (independently of Hans Hahn)

• Amenable Banach Algebra
• Banach Algebra
• Banach Bundle
• Banach Function Algebra
• Banach Integral
• Banach Limit
• Banach Manifold
• Banach Measure
• Banach Space

• Banach-Mazur Game (with Stanisław Meiczyslaw Mazur)
• Banach-Saks Space (with Stanisław Saks)

Results named for Stefan Banach can be found here.

Definitions of concepts named for Stefan Banach can be found here.

Publications

• 1922: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (Fund. Math. Vol. 3: pp. 133 – 181) (in which Banach Fixed-Point Theorem is presented)
• 1924: Sur la décomposition des ensembles de points en parties respectivement congruentes (Fund. Math. Vol. 6: pp. 244 – 277) (with Alfred Tarski) (in which Banach-Tarski Paradox is presented)
• 1929: Rachunek różniczkowy i całkowy, tom I (Differential and Integral Calculus, vol. 1)
• 1930: Rachunek różniczkowy i całkowy, tom II (Differential and Integral Calculus, vol. 2)
• 1931: Über die Baire'sche Kategorie gewisser Funktionenmengen (Studia Math. Vol. 3: pp. 174 – 179)
• 1930: Sur la convergence forte dans le champ $L^p$ (with Stanisław Saks)
• 1931: Teoria operacji. Tom I. Operacje liniowe (Theory of operations, vol. 1: Linear operations)
• 1932: Théorie des opérations linéaires (Theory of Linear Operations) (in which the concept now known as the Banach space was formulated)
• 1938: Mechanika w zakresie szkół akademickich, Monografie Matematyczne 8 (Mechanics for Academic Schools, Mathematical Monographs 8)

• 1929: Co-founder of Studia Mathematica with Hugo Steinhaus

Notable Quotes

Good mathematicians see analogies. Great mathematicians see analogies between analogies.

Critical View

Banach was my greatest scientific discovery.

-- Hugo Steinhaus

Sources

• John J. O'Connor and Edmund F. Robertson: "Stefan Banach": MacTutor History of Mathematics archive

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: Banach, Stefan (1892-1945)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: Banach, Stefan (1892-1945)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: Banach, Stefan (1892-1945)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Banach, Stefan (1892-1945)