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1950

Carnap publishes

1950

Hamming publishes a fundamental paper on error-detecting and error-correcting codes.

1950

Hodge puts forward the "Hodge Conjecture" on projective algebraic varieties.

1951

Serre uses spectral sequences to the study of the relations between the homology groups of fibre, total space and base space in a fibration. This enables him to discover fundamental connections between the homology groups and homotopy groups of a space and to prove important results on the homotopy groups of spheres.

1952

Hörmander begins working on the theory of partial differential equations. Ten years later he will receive a Fields Medal for this work.

1954

Serre is awarded a Fields Medal for his work on spectral sequences and his work developing complex variable theory in terms of sheaves.

1954

Kolmogorov publishes his second paper on the theory of dynamical systems. This marks the beginning of KAM-theory, which is named after Kolmogorov, Arnold and Moser.

1955

Cartan and Eilenberg develop homological algebra which allows powerful algebraic methods and topological methods to be related.

1955

Novikov proves the insolubility of the word problem for groups.

1955

Taniyama poses his conjecture on elliptic curves which will play a major role in the proof of Fermat's Last Theorem.

1956

Milnor publishes *On manifolds homeomorphic to the 7-sphere* which opens up the new field of differential topology.

1957

Kolmogorov solves "Hilbert's Thirteenth Problem" on continuous functions of three variables which cannot be represented by continuous functions of two variables.

1958

Thom is awarded a Fields Medal for his work on topology, in particular on characteristic classes, cobordism theory and the "Thom transversality theorem".

1959

Boone proves that many decision problems for groups are insoluble.

1959

Marshall Hall publishes his famous text *Theory of Groups*.

1960

M Suzuki discovers new infinite families of finite simple groups.

List of mathematicians alive in 1950.

List of mathematicians alive in 1960.

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