Hermann Klaus Hugo Weyl ( ; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski.
His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years.
Weyl contributed to an exceptionally wide range of fields, including works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism.
Freeman Dyson wrote that Weyl alone bore comparison with the "last great universal mathematicians of the nineteenth century", Henri Poincaré and David Hilbert. Michael Atiyah commented that whenever he examined a mathematical topic, he found that Weyl had preceded him.
Biography Hermann Weyl was born in Elmshorn, a small town near Hamburg, in Germany, and attended the Gymnasium Christianeum in Altona. His father, Ludwig Weyl, was a banker; whereas his mother, Anna Weyl (née Dieck), came from a wealthy family.
From 1904 to 1908, he studied mathematics and physics at both the University of Göttingen and the Ludwig-Maximilians-Universität München. His doctorate was awarded at the University of Göttingen under the supervision of David Hilbert, whom he greatly admired.
In September 1913, in Göttingen, Weyl married Friederike Bertha Helene Joseph (30 March 1893Universität Zũrich Matrikeledition – 5 September 1948 Hermann Weyl Collection (AR 3344) (Sys #000195637), Leo Baeck Institute, Center for Jewish History, 15 West 16th Street, New York, NY 10011. The collection includes a typewritten document titled "Hellas letzte Krankheit" ("Hella's Last Illness"); the last sentence on page 2 of the document states: "Hella starb am 5. September , mittags 12 Uhr." ("Hella died at 12:00 Noon on September 5 "). Helene's funeral arrangements were handled by the M. A. Mather Funeral Home (now named the Mather-Hodge Funeral Home), located at 40 Vandeventer Avenue, Princeton, New Jersey. Helene Weyl was cremated on 6 September 1948, at the Ewing Cemetery & Crematory, 78 Scotch Road, Trenton (Mercer County), New Jersey.), who went by the name Helene (nickname "Hella"). Helene was a daughter of Dr. Bruno Joseph (13 December 1861 – 10 June 1934), a physician who held the position of Sanitätsrat in Ribnitz-Damgarten, Germany. Helene was a philosopher (she was a disciple of phenomenologist Edmund Husserl) and a translator of Spanish literature into German and English (especially the works of Spanish philosopher José Ortega y Gasset).For additional information on Helene Weyl, including a bibliography of her translations, published works, and manuscripts, see the following link: "In Memoriam Helene Weyl" by Hermann Weyl. This document, which is one of the items in the Hermann Weyl Collection at the Leo Baeck Institute in New York City, was written by Hermann Weyl at the end of June 1948, about nine weeks before Helene died on 5 September 1948, in Princeton, New Jersey. The first sentence in this document reads as follows: "Eine Skizze, nicht so sehr von Hellas, als von unserem gemeinsamen Leben, niedergeschrieben Ende Juni 1948." ("A sketch, not so much of Hella's life as of our common life, written at the end of June 1948.") It was through Helene's close connection with Husserl that Hermann became familiar with (and greatly influenced by) Husserl's thought. Hermann and Helene had two sons, Fritz Joachim Weyl (19 February 1915 – 20 July 1977) and Michael Weyl (15 September 1917 – 19 March 2011),WashingtonPost.com both of whom were born in Zürich, Switzerland. Helene died in Princeton, New Jersey, on 5 September 1948. A memorial service in her honor was held in Princeton on 9 September 1948. Speakers at her memorial service included her son Fritz Joachim Weyl and mathematicians Oswald Veblen and Richard Courant.In Memoriam Helene Weyl (1948) by Fritz Joachim Weyl. See: (i) http://www.worldcat.org/oclc/724142550 and (ii) http://d-nb.info/993224164 In 1950. Hermann married sculptor Ellen Bär (née Lohnstein) (17 April 1902 – 14 July 1988),artist-finder.com who was the widow of professor Richard Josef Bär (11 September 1892 – 15 December 1940) of Zürich.
After taking a teaching post for a few years, Weyl left Göttingen in 1913 for Zurich to take the chair of mathematicsWeyl went to ETH Zürich in 1913 to fill the professorial chair vacated by the retirement of Carl Friedrich Geiser. at ETH Zurich, where he was a colleague of Albert Einstein, who was working out the details of the theory of general relativity. Einstein had a lasting influence on Weyl, who became fascinated by mathematical physics. In 1921, Weyl met Erwin Schrödinger, a theoretical physicist who at the time was a professor at the University of Zurich. They were to become close friends over time. Weyl had some sort of childless love affair with Schrödinger's wife Annemarie (Anny) Schrödinger (née Bertel), who at the same time was helping raise an illegitimate daughter of Erwin's named Ruth Georgie Erica March, who was born in 1934 in Oxford, England. Ruth Georgie Erica March was born on 30 May 1934 in Oxford, England, but—according to the records presented here—it appears that her birth wasn't "registered" with the British authorities until the 3rd registration quarter (the July–August–September quarter) of the year 1934. Ruth's actual, biological father was Erwin Schrödinger (1887–1961), and her mother was Hildegunde March (née Holzhammer) (born 1900), wife of Austrian physicist Arthur March (23 February 1891 – 17 April 1957). Hildegunde's friends often called her "Hilde" or "Hilda" rather than Hildegunde. Arthur March was Erwin Schrödinger's assistant at the time of Ruth's birth. The reason Ruth's surname is March (instead of Schrödinger) is because Arthur had agreed to be named as Ruth's father on her birth certificate, even though he wasn't her biological father. Ruth married the engineer Arnulf Braunizer in May 1956, and they have lived in Alpbach, Austria for many years. Ruth has been very active as the sole administrator of the intellectual (and other) property of her father Erwin's estate, which she manages from Alpbach.
Weyl was a Plenary Speaker of the International Congress of Mathematicians (ICM) in 1928 at Bologna and an Invited Speaker of the ICM in 1936 at Oslo. He was elected a fellow of the American Physical Society in 1928, a member of the American Academy of Arts and Sciences in 1929, a member of the American Philosophical Society in 1935, and a member of the National Academy of Sciences in 1940. For the academic year 1928–1929, he was a visiting professor at Princeton University, where he wrote a paper, "On a problem in the theory of groups arising in the foundations of infinitesimal geometry," with Howard P. Robertson.
Weyl left the University of Zurich in 1930 to become Hilbert's successor at the University of Göttingen, leaving when the Nazis assumed power in 1933, particularly as his wife was Jewish. He had been offered one of the first faculty positions at the new Institute for Advanced Study in Princeton, New Jersey, but had declined because he did not desire to leave his homeland. As the political situation in Germany grew worse, he changed his mind and accepted when offered the position again. He remained there until his retirement in 1951. Together with his second wife Ellen, he spent his time in Princeton and Zürich, and died from a heart attack on 8 December 1955, while living in Zürich.
Weyl was cremated in Zurich on 12 December 1955.137: Jung, Pauli, and the Pursuit of a Scientific Obsession (New York and London: W. W. Norton & Company, 2009), by Arthur I. Miller (p. 228). His ashes remained in private hands until 1999, at which time they were interred in an outdoor columbarium vault in the Princeton Cemetery.Hermann Weyl's cremains (ashes) are interred in an outdoor columbarium vault in the Princeton Cemetery at this location: Section 3, Block 04, Lot C1, Grave B15. The remains of Hermann's son Michael Weyl (1917–2011) are interred right next to Hermann's ashes in the same columbarium vault.
Weyl was a pantheist.
Contributions
Distribution of eigenvalues
In 1911 Weyl published Über die asymptotische Verteilung der Eigenwerte (On the asymptotic distribution of eigenvalues) in which he proved that the eigenvalues of the Laplacian in a compact domain are distributed according to the so-called Weyl law. In 1912 he suggested a new proof, based on variational principles. Weyl returned to this topic several times, considered elasticity system and formulated the Weyl conjecture. These works started an important domain—asymptotic distribution of eigenvalues—of modern analysis.
Geometric foundations of manifolds and physics
In 1913, Weyl published Die Idee der Riemannschen Fläche (The Concept of a Riemann Surface), which gave a unified treatment of Riemann surfaces. In it Weyl utilized point set topology, in order to make Riemann surface theory more rigorous, a model followed in later work on manifolds. He absorbed L. E. J. Brouwer's early work in topology for this purpose.
Weyl, as a major figure in the Göttingen school, was fully apprised of Einstein's work from its early days. He tracked the development of relativity physics in his Raum, Zeit, Materie (Space, Time, Matter) from 1918, which reached its 4th edition in 1922. In 1918, he introduced the notion of gauge, and gave the first example of what is now known as a gauge theory. Weyl's gauge theory was an unsuccessful attempt to model the electromagnetic field and the gravitational field as geometrical properties of spacetime. The Weyl tensor in Riemannian geometry is of major importance in understanding the nature of conformal geometry.
His overall approach in physics was based on the phenomenological philosophy of Edmund Husserl, specifically Husserl's 1913 Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch: Allgemeine Einführung in die reine Phänomenologie (Ideas of a Pure Phenomenology and Phenomenological Philosophy. First Book: General Introduction). Husserl had reacted strongly to Gottlob Frege's criticism of his first work on the philosophy of arithmetic and was investigating the sense of mathematical and other structures, which Frege had distinguished from empirical reference.
Topological groups, Lie groups and representation theory
From 1923 to 1938, Weyl developed the theory of compact groups, in terms of matrix representations. In the compact Lie group case he proved a fundamental character formula.
These results are foundational in understanding the symmetry structure of quantum mechanics, which he put on a group-theoretic basis. This included spinors. Together with the mathematical formulation of quantum mechanics, in large measure due to John von Neumann, this gave the treatment familiar since about 1930. Non-compact groups and their representations, particularly the Heisenberg group, were also streamlined in that specific context, in his 1927 Weyl quantization, the best extant bridge between classical and quantum physics to date. From this time, and certainly much helped by Weyl's expositions, Lie groups and Lie algebras became a mainstream part both of pure mathematics and theoretical physics.
His book The Classical Groups reconsidered invariant theory. It covered symmetric groups, general linear groups, orthogonal groups, and symplectic groups and results on their invariants and representations.
Harmonic analysis and analytic number theory