Hermann Weyl invented gauge theory while trying to geometrise electromagnetism
In 1918 Hermann Weyl tried to describe gravity and electromagnetism as features of spacetime geometry. The attempt failed, but along the way he introduced the idea of a gauge, the seed of the gauge theories that underpin modern particle physics. Michael Atiyah joked that wherever he went in mathematics, Weyl had been there first.
Weyl was born on 9 November 1885 in Elmshorn, near Hamburg, the son of a banker. He studied at Göttingen and Munich from 1904 to 1908 and earned his doctorate under David Hilbert, whom he revered. He belongs to the Göttingen tradition of Gauss, Hilbert and Minkowski, though he spent most of his career in Zürich and Princeton. Freeman Dyson said only Weyl compared with Poincaré and Hilbert, the last great universal mathematicians.
His early work set lasting agendas. In 1911 he proved what is now called Weyl's law on how the eigenvalues of the Laplacian are distributed, launching a whole field of analysis. His 1913 book on Riemann surfaces used point-set topology to give the subject a rigorous footing, a model for later work on manifolds. That year he took the mathematics chair at ETH Zurich, becoming a colleague of Albert Einstein just as general relativity was taking shape, and Einstein's influence drew him into mathematical physics.
His 1918 book Space, Time, Matter tracked relativity through four editions by 1922, and the Weyl tensor remains central to conformal geometry. From 1923 to 1938 he built the theory of compact groups through matrix representations, proving a fundamental character formula. These results put the symmetry of quantum mechanics on a group-theoretic basis, including spinors. His philosophy of physics drew on Edmund Husserl's phenomenology, which he met through his wife Helene, a Husserl disciple and translator of Ortega y Gasset. In Zurich he became close friends with Erwin Schrödinger.
In 1930 Weyl succeeded Hilbert at Göttingen, but when the Nazis took power in 1933 he left, partly because Helene was Jewish. Having once declined a post at the new Institute for Advanced Study in Princeton, he now accepted and stayed until retiring in 1951. He died on 8 December 1955; his ashes, privately held for decades, were placed in Princeton Cemetery in 1999.
Source: Hermann Weyl
