Hermann Klaus Hugo Weyl

Hermann Weyl was a German mathematician, physicist, and philosopher who made significant contributions to various fields of mathematics and physics in the 20th century. He was also known for his philosophical writings on the foundations of mathematics, logic, and the nature of reality. Weyl studied mathematics and physics at the University of Munich and the University of Göttingen, where he was influenced by David Hilbert, his doctoral advisor. He obtained his doctorate in 1908 and his habilitation in 1910. He became a privatdozent at Göttingen until 1913, when he moved to Zürich as a professor of mathematics at ETH Zürich. There he worked on topics such as Riemann surfaces, Lie groups, differential geometry, and the theory of relativity. In 1923, he published his famous book Raum-Zeit-Materie (Space-Time-Matter), which presented a unified theory of gravity and electromagnetism based on a generalization of Riemannian geometry. He also introduced the concept of gauge invariance, which later became fundamental in quantum field theory. In 1928, he became Hilbert's successor at Göttingen, where he continued his research on quantum mechanics, group theory, and number theory. He also collaborated with Emmy Noether and John von Neumann on the foundations of mathematics and logic. In 1933, after the rise of Nazism in Germany, Weyl left Göttingen and returned to Zürich. He became a Swiss citizen in 1939. In 1935, he published another influential book Symmetrie (Symmetry), which explored the role of symmetry in mathematics, physics, art, and nature. He also developed the concept of continuous groups using matrix representations, which led to the classification of simple Lie algebras. In 1939, he accepted an invitation to join the Institute for Advanced Study in Princeton, New Jersey, where he worked until his retirement in 1951. There he interacted with Albert Einstein, Kurt Gödel, Oswald Veblen, and other eminent scholars. He also wrote several books on philosophy and history of mathematics, such as Philosophy of Mathematics and Natural Science (1949) and The Classical Groups: Their Invariants and Representations (1939). Weyl died of a heart attack in Zürich in 1955 at the age of 70. He was cremated and his ashes were scattered over Lake Zürich. He was survived by his second wife Ellen Bär and his two sons from his first marriage. He was widely regarded as one of the greatest mathematicians of the 20th century and a pioneer of modern mathematical physics.