Hermann Weyl

Hermann Weyl (1885–1955) was a German mathematician and theoretical physicist whose work connected symmetry, geometry, and physics, shaping modern mathematics and theoretical physics.

Lie group: A group that is also a smooth manifold, with multiplication and inversion compatible with its smooth structure. Lie groups gave Weyl a language for continuous symmetries in geometry and physics.
Gauge theory: A class of physical theories whose descriptions remain unchanged under local transformations of internal fields. Weyl’s 1918 attempt to unify gravity and electromagnetism introduced an early gauge idea.
David Hilbert: A German mathematician whose work shaped number theory, geometry, logic, and mathematical physics. Hilbert supervised Weyl’s doctoral work at the University of Göttingen.
University of Göttingen: A German university that became a major center of mathematics and theoretical physics in the nineteenth and twentieth centuries. Weyl studied and taught there during the institution’s mathematical heyday.
Weyl group: A finite group generated by reflections associated with the root system of a Lie algebra or Lie group. Weyl’s work established this symmetry structure as a central tool in Lie theory.
Representation theory: The study of mathematical structures through their actions as linear transformations on vector spaces. Weyl used representations to classify symmetries and organize quantum states.
General relativity: Einstein’s theory of gravity, in which gravitation is represented by spacetime curvature. Weyl extended geometric methods inspired by relativity and sought to unify its gravitational field with electromagnetism.
Albert Einstein: A theoretical physicist who developed special and general relativity and transformed modern physics. Weyl’s theories of gravitation and geometry responded directly to Einstein’s relativity.
The Continuum: Weyl’s 1918 book examining the foundations of real numbers and the continuum. It presents his constructive approach to mathematical foundations.
Weyl character formula: A formula computing the characters of finite-dimensional irreducible representations of semisimple Lie groups. It is one of Weyl’s lasting results in representation theory.

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