Hermann Klaus Hugo Weyl

Hermann Weyl had met Erwin Shcrodinger in 1921, who at that time was working as a professor in the University of Zurich. Though the two were close friends, Weyl had a love affair with Shcrodinger’s wife Annemarie Schrödinger for some time.

Weyl’s first wife was Friederike Bertha Helene Joseph, who was better known as Helene or Hella. She was the daughter of Dr. Bruno Jospeph, a physician. Helene herself was a philosopher, and a translator of Spanish literature into German and English. They got married in September 1913.

Hermann and Helene had two sons. The first one, Fritz Joachim Weyl was born in February 1915 and the second one, Michael Weyl, was born in September 1917.

Hermann Weyl was born on 9 November 1885 in a small town near Hamburg, Germany, named Elmshorn. However, not much is known about his parents or his childhood.

He studied Mathematics and Physics in both Gottingen and Munich from 1904 to 1908. He completed his Ph.D. in the University of Gottingen, under the supervision of David Hilbert, one of the most influential as well as universal mathematicians of the 19th and 20th centuries. Weyl was a big admirer of him.

After receiving his Ph. D. he held a teaching post in the same university, as a privatdozent, till the year 1913. Then he moved to Zürich Technische Hochschule where he occupied the chair of mathematics from 1913 to 1930.

It was in Zurich that he met Albert Einstein as a colleague, and worked together on various subjects of their interest. Other than Einstein, he was also influenced by Erwin Schrodinger, a Nobel-Prize winning theoretical physicist.

He was offered a faculty position in 1930, in the Institute for Advanced Study in Princeton, New Jersey, but he declined the offer as he didn’t wish to leave his homeland. But he had a Jewish wife, and when the political situation in Germany got worse, he changed his mind and accepted the position in the university and remained there till his retirement in 1951.

Hermann Weyl published ‘On the asymptotic distribution of eigenvalues’ in the year 1911, where he proved that it is according to the Weyl law, that the eigenvalues of the Laplacian in the compact domain are distributed. He also formulated his own Weyl conjecture.

By using matrix representation, he also evolved a general theory of continuous groups and found out that just by using group theory, we could find out most of the regularities of the quantum phenomena on the atomic level. His findings were published in ‘Group Theory and Quantum Mechanics’ in the year 1928, where he helped mold modern quantum theory.

He worked on and developed the theory of compact groups from 1923 to 1938, in terms of matrix representations. He also proved a fundamental character formula in the compact Lie group case.

In 1939, he wrote and published a mathematics book, ‘The Classical Groups: Their Invariants and Representation’. It not only described classical invariant theory, but is also considered hugely responsible for the revival of interest in it.

Hermann Weyl published ‘In the Continuum’ where the developed the logic of the predictive analysis using the lower levels of the ramified theory of types, which was initially formed by Bertrand Russell. Not only he developed most of classical calculus, but he did so without using the axiom of choice or the proof by contradiction.