Mathematician:Stefan Banach

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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.




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

Theorems and Definitions

Results named for Stefan Banach can be found here.

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


  • 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)

Notable Quotes

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

Critical View

Banach was my greatest scientific discovery.
-- Hugo Steinhaus