Hermann Weyl

Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician and physicist, one of the first people to combine general relativity with the laws of electromagnetism. From 1913 to 1930 he held the chair of mathematics at the Technische Hochschule of Zurich.

Weyl published works on space, time, matter, philosophy, logic, and the history of mathematics. Weyl researched mainly topological space and geometry (of the Bernhard Riemann derivation). Weyl also researched quantum mechanics and number theory. Weyl research is the framework for nonconservation of parity. This is a characteristic of weak interactions between subatomic lepton particles.

Table of contents

1 Biography

6 External links and references

Biography

Weyl was born in Elmshorn (a town near Hamburg), Germany.

From 1904 to 1908 he studied in Göttingen and Munich, mainly mathematics and physics. His doctorate was presented to him at Göttingen under the direction of Hilbert and Minkowski. In 1910, he obtained a teaching post of private lecturer at Göttingen. Weyl gains a professorship at the Technische Hochschule in Zürich, Switzerland in the year of 1913.

In 1913, Weyl published Die Idee der Riemannschen Fläche (The Concept of a Riemann Surface), which gave a unified treatment of Riemann surfaces. 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 electromagnetic field and the gravitational field as geometrical properties of spacetime.

George Polya and Weyl, during a mathematicians' gathering in Zürich (February 9, 1918), made a bet concerning the future direction of mathematics. Weyl predicted that in the subsequent 20 years, mathematicians would come to realize the total vagueness of such as notions as real numbers, sets, and countability, and moreover, that asking about the truth or falsity of the least upper bound property of the real numbers was as meaningful as asking about truth of the basic assertions of Georg Hegel on the philosophy of nature. The existence of this bet is documented in a letter discovered by Yuri Gurevich in 1995, and it is said that when the friendly bet ended, the individuals gathered cited Polya as the victor (with Kurt Gödel not in concurrence).

From 1923 to 1938, Weyl developed the concept of continuous groups in terms of matrix representations. Weyl analysis topics included matrix algebras, semigroups, commutators, and spinors. These are important in understanding the group theory's structure of quantum mechanics. Weyl established a group-theoretic basis for quantum mechanics. Weyl's analysis covered symmetric groups, full linear groups, orthogonal groups, and symplectic groups and the results of the invariants and representations. Weyl also showed how to use exponential sums in diophantine approximation, with his criterion for uniform distribution mode 1, which was fundamental step in analytic number theory. In 1928 and 1929, he was a visiting professor at Princeton University.

Weyl leaves the professorship at the Technische Hochschule in Zürich, Switzerland, in the year of 1930 and he became Hilbert's successor at Göttingen where he held the chair of mathematics. The rise of the National Socialist Germany, in 1933, resulted in Weyl going to the Institute for Advanced Study. There Weyl worked with Einstein.

At Princeton Weyl researched a unification of gravitation and electromagnetism. Weyl tried to incorporate electromagnetism in the geometrical formalism of general relativity. Weyl's research of Riemann surfaces and the associated definition of the complex manifold in one dimension. This is part of the theory of complex manifolds and of differential manifolds.

Weyl worked at the IAS till retirement in 1952. He died in Zürich, Switzerland.

Personality

Weyl's own comment, although half a joke, sums up his personality.

My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.

Quotes

"The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization." -- Hermann Weyl (Gesammelte Abhandlungen)

"The problems of mathematics are not problems in a vacuum ... " -- Hermann Weyl

"[Impredicative definition's] vicious circle, which has crept into analysis through the foggy nature of the usual set and function concepts, is not a minor, easily avoided form of error in analysis". -- Hermann Weyl

"In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics."

Published works

Weyl, Hermann, "The Continuum : A Critical Examination of the Foundation of Analysis". 1918. ISBN 0486679829
Weyl, Hermann, "Mathematische Analyse des Raumproblems". 1923.
Weyl, Hermann, "Was ist Materie?". 1924.
Weyl, Hermann, "Gruppentheorie und Quantenmechanik". 1928.
Weyl, Hermann, "Space Time Matter". June 1952. ISBN 0486602672
- original title : "Raum, Zeit, Materie"
Weyl, Hermann, "On generalized Riemann matrices". Ann. of Math. 35, Vol. III, pp.~400--415, 1934.
Weyl, Hermann, "Elementary Theory of Invariants". 1935
Weyl, Hermann, "Symmetry". Princeton University Press, 1952. ISBN 0691023743
Weyl, Hermann, "Philosophy of Mathematics and Natural Science". 1949.
Weyl, Hermann, "The Concept of a Riemann Surface" Addison-Wesley, 1955.
Weyl, Hermann (and Herausgegeben von K. Chandrasekharan ed), "Gesammelte Abhandlungen". Vol IV. Springer 1968.

Weyl, Hermann, "Classical Groups: Their Invariants And Representations". ISBN 0691057567

External links and references

The MacTutor History of Mathematics archive, "Hermann Klaus Hugo Weyl ". School of Mathematics and Statistics, University of St Andrews, Scotland
Weisstein, Eric W., "Weyl, Hermann (1885-1955)". Eric Weisstein's World of Science.
Bell, John L., "Hermann Weyl on intuition and the continuum " (PDF)
Y. Gurevich, Platonism, Constructivism and Computer Proofs vs Proofs by Hand, Bulletin of the European Association of Theoretical COmputer Science, 1995.
Kilmister, C. W. Zeno, "Aristotle, Weyl and Shuard: two-and-a-half millennia of worries over number." 1980.