Chronology

1950 - 1960

1950

• Carnap publishes Logical Foundations of Probability.
• Hamming publishes a fundamental paper on error-detecting and error-correcting codes.
• 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.
• 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.
• Novikov proves the insolubility of the word problem for groups.
• 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.
• Marshall Hall publishes his famous text Theory of Groups.