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1920

Takagi publishes his fundamental paper on class field theory.

1920

Hasse discovers the "local-global" principle.

1920

Siegel's dissertation is important in the theory of Diophantine approximations.

1920

*Fundamenta Mathematica* is founded by Sierpinski and Mazurkiewicz.

1921

Keynes publishes his *Treatise on Probability* in which he argues that probability is a logical relation and so it is objective. A statement involving probability relations has a truth-value independent of people's opinions. This is to have a profound effect on statistics as well as economics.

1921

Fisher introduces the concept of likelihood into statistics.

1921

Borel publishes the first in a series of papers on game theory and becomes the first to define games of strategy.

1921

Emmy Noether publishes *Idealtheorie in Ringbereichen* which is of fundamental importance in the development of modern abstract algebra.

1922

Richardson publishes *Weather Prediction by Numerical Process*. He is the first to apply mathematics, in particular the method of finite differences, to predicting the weather. The calculations are prohibitive by hand calculation and only the development of computers will make his idea a reality.

1922

Banach is awarded his habilitation for a thesis on measure theory. He begins his work on a development of normed vector spaces.

1922

Fraenkel attempts to put set theory into an axiomatic setting.

1922

Chebotaryov proves the density theorem on primes in an arithmetical progression.

1922

Fejér and Riesz publish an important work on conformal mappings.

1922

Kolmogorov constructs a summable function which diverges almost everywhere.

1923

Study publishes important work on real and complex algebras of low dimension.

1924

Alexander introduces the now famous "Alexander horned sphere".

1925

Fisher publishes *Statistical Methods for Research Workers*. He gives experimental and statistical methods which can be used in biology.

1925

Whitehead publishes *Science and the Modern World*. It results from a series of lectures given in the United States and serves as an introduction to his later metaphysics. He considers the growth, success, and impact of "scientific materialism" which is the notion that nature is merely matter and energy.

1925

Besicovitch solves "Kakeya's problem" on minimising areas.

1925

Krull proves the "Krull-Schmidt theorem" for decomposing abelian groups of operators.

1926

Reidemeister publishes an important book on knot theory: *Knoten und gruppen*.

1926

Artin and Schreier publish a paper on ordering formally real fields and real closed fields.

1926

Banach and Tarski publish the "Banach-Tarski paradox" in a joint paper in *Fundamenta Mathematicae*: *Sur la decomposition des ensembles de points en parties respectivement congruentes*.

1927

Emmy Noether, Helmut Hasse and Richard Brauer work on non-commutative algebras.

1927

Artin publishes his reciprocity law in *Beweis des allgemeinen Reziprozitätsgesetzes*.

1928

Von Mises publishes *Probability, Statistics and Truth*.

1928

Von Neumann proves the minimax theorem in game theory.

1928

Hopf introduces homology groups.

1929

Gelfond makes his Conjecture about the linear independence of algebraic numbers over the rational numbers.

1930

Van der Waerden's famous work *Modern Algebra* is published. This two volume work presents the algebra developed by Emmy Noether, Hilbert, Dedekind and Artin.

1930

Hurewicz proves his embedding theorem for separable metric spaces into compact spaces.

1930

Kuratowski proves his theorem on planar graphs.

List of mathematicians alive in 1920.

List of mathematicians alive in 1930.

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