Mathematician:Stefan Banach

Mathematician
Polish mathematician who founded the modern field of functional analysis.

Most famous for his collaborative paper with 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, 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 ) (also known as Alaoglu's Theorem)
 * Banach-Mazur Theorem (with )
 * Banach-Schauder Theorem (with )
 * Banach-Steinhaus Theorem (with )
 * Banach-Stone Theorem (with )
 * Banach-Tarski Paradox (with )


 * Hahn-Banach Theorem (independently of )
 * Hahn-Banach Separation Theorem (independently of )


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


 * Banach-Mazur Game (with )
 * Banach-Saks Space (with )

Publications

 * 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)
 * 1930: Sur la convergence forte dans le champ $L^p$ (with )
 * 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)
 * 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)

Notable Quotes

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

Critical View

 * Banach was my greatest scientific discovery.