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Weyl, Hermann

theory geometry mechanics hilbert

[viyl] (1885–1955) German mathematician: contributed to symmetry theory, topological spaces and Riemannian geometry.

Weyl was a student under at Göttingen and, on becoming a Privatdozent there, also worked with him. In 1913 he declined a professorship at Göttingen and moved to Zürich, where he worked with . He returned to take up the professorship when Hilbert retired in 1930, but increasing Nazi power led him to move to Princeton with and Einstein, retiring in 1951. As well as his outstanding mathematical work, Weyl published on philosophy, logic and the history of mathematics.

Weyl acquired from Hilbert research interests in group theory and Hilbert space and operators. Once developed, these techniques proved central to the rapidly evolving theory of quantum mechanics and the unification of matrix mechanics and wave mechanics. Weyl showed how symmetry relates to group theory and continuous groups, and how this can be a powerful tool in solving quantum mechanical problems.

When Weyl moved to Zürich, Einstein interested him in the mathematics of relativity and Riemannian geometry. In seeking to generalize this, Weyl developed the geometry of affinely connected spaces and differential geometry. Weyl anticipated the non-conservation of parity in particles, a feature that has since been observed by particle physicists working with leptons.

Weyl produced a small number of highly influential papers on number theory, proving results on the equidistribution of sequences of real numbers modulo 1. This was taken up in later work by and J E Littlewood (1885–1977).

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