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Hamming publishes a fundamental paper on error-detecting and error-correcting codes.
Hodge puts forward the "Hodge Conjecture" on projective algebraic varieties.
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.
Hörmander begins working on the theory of partial differential equations. Ten years later he will receive a Fields Medal for this work.
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.
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.
Milnor publishes On manifolds homeomorphic to the 7-sphere which opens up the new field of differential topology.
Kolmogorov solves "Hilbert's Thirteenth Problem" on continuous functions of three variables which cannot be represented by continuous functions of two variables.
Thom is awarded a Fields Medal for his work on topology, in particular on characteristic classes, cobordism theory and the "Thom transversality theorem".
Boone proves that many decision problems for groups are insoluble.
Marshall Hall publishes his famous text Theory of Groups.
M Suzuki discovers new infinite families of finite simple groups.
List of mathematicians alive in 1960.
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JOC/EFR August 2001
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