Chronology for 1930 to 1940

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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.

1931
G D Birkhoff proves the general ergodic theorem. This will transform the Maxwell-Boltzmann kinetic theory of gases into a rigorous principle through the use of Lebesgue measure.

1931
Gödel publishes Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (On Formally Undecidable Propositions in Principia Mathematica and Related Systems). He proves fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved.

1931
Von Mises introduces the idea of a sample space into probability theory.

1931
Borsuk publishes his theory of retracts in metric differential geometry.

1932
Haar introduces the "Haar measure" on groups.

1932
Hall publishes A contribution to the theory of groups of prime power order.

1932
Magnus proves that the word problem is true for one relator groups.

1932
Von Neumann publishes Grundlagen der Quantenmechanik on quantum mechanics. (See this History Topic.)

1933
Kolmogorov publishes Foundations of the Theory of Probability which presents an axiomatic treatment of probability.

1934
Gelfond and Schneider solve "Hilbert's Seventh problem" independently. They proved that aq is transcendental when a is algebraic (≠ 0 or 1) and q is an irrational algebraic number.

1934
Leray shows the existence of weak solutions to the Navier-Stokes equations.

1934
Zorn establishes "Zorn's lemma" so named (probably) by Tukey. It is equivalent to the axiom of choice.

1935
Church invents "lambda calculus" which today is an invaluable tool for computer scientists.

1936
Turing publishes On Computable Numbers, with an application to the Entscheidungsproblem which describes a theoretical machine, now known as the "Turing machine". It becomes a major ingredient in the theory of computability.

1936
Church publishes An unsolvable problem in elementary number theory. "Church's Theorem", which shows there is no decision procedure for arithmetic, is contained in this work.

1937
Vinogradov publishes Some theorems concerning the theory of prime numbers in which he proves that every sufficiently large odd integer can be expressed as the sum of three primes. This is a major contribution to the solution of the Goldbach conjecture.

1938
Kolmogorov publishes Analytic Methods in Probability Theory which lays the foundations of the theory of Markov random processes.

1939
Douglas gives a complete solution to the Plateau problem, proving the existence of a surface of minimal area bounded by a contour.

1939
Abraham Albert publishes Structure of Algebras.

1940
Baer introduces the concept of an injective module, then begins studying group actions in geometry.

1940
Aleksandrov introduces exact sequences.


List of mathematicians alive in 1930.

List of mathematicians alive in 1940.



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JOC/EFR August 2001

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