Hermann Weyl

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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.

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Biography

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

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

In 1913, Weyl published Die Idee der Riemannschen Fl�che which unified analysis, geometry and topology in the standard model. He produced the first gauge theory in which the electromagnetic field and the gravitational field appear as geometrical properties of spacetime.

George Polya and Weyl, during a mathematicians gathering in Z�rich (February 9, 1918), made a bet concerning the least upper bound property. This discussion was on the completely vaguenes of the concepts concerning the construction of the real numbers, sets, and countability [and that the phrases of the least upper bound property is false]. What was in debate was that it may be irrelevant asking about truth of the least upper bound property, other than the basic assertions of Georg Hegel. When the friendly bet ended, the individuals gathered cited Polya as the victor (with [[Kurt G�del]] 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 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 Z�rich, Switzerland, in the year of 1930 and he became Hilbert's successor at [[G�ttingen]] where he held the chair of mathematics. The rise of the National Socialist Germany, in 1933, resulted in Wyel going to the Institute for Advanced Study at Princeton University. There Weyl worked with Einstein.

Here, Weyl reaserched a grand 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 the first dimension. This is part of the theory for complex manifolds and for differential manifolds.

Weyl worked at the IAS till retirement. He retired in 1952. Weyl died in Z�rich, 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

See also

Main: Weyl group, Weyl's postulate, Weyl tensor, Weyl spinor, Peter-Weyl theorem

Mathematical / Physics: Almost periodic function, Diophantine approximation, Dirac equation, Dirac sea, Embedding, Multilinear algebra, Timeline of black hole physics

People: Edmund Husserl, Gerhard Gentzen, Jean-Pierre Serre

Lists: List of mathematical topics, List of mathematicians, List of astronomical topics, List of physics topics

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


References

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