Hermann Weyl

Hermann Weyl (November 9th 1885 - December 8th 1955) is one of the most influential mathematicians of the twentieth century, one of the first to combine the General relativity with the laws of the electromagnetism. Its research in mathematics related primarily to the Topologie and the Géométrie (mainly the geometry riemannienne). Weyl also published many work on the space, the Temps, the Matière, the Philosophie, the Logique, and the Histoire of mathematics. It carried out research in quantum Mécanique and Théorie of the numbers.

Biography

Born with Elmshorn near Hamburg in Germany, Weyl studied 1904 with 1908 with Göttingen and Munich, mainly interested by mathematics and physics. Its doctorate was constant in Göttingen under the direction of Hilbert and Minkowski. In 1910, it obtained a post of teacher like deprived reader with Göttingen. He taught mathematics with the federal Polytechnic school of Zurich in Suisse in 1913.

Then open a stable period of its life, favourable with mathematical research. It is during this period that it made its principal discoveries in mathematics (to read Recherche). Episodically, he was a professor invited to the Université of Princeton in 1928 and 1929. He left the polytechnic school of Zurich in 1930 to succeed Hilbert with Göttingen where he took the pulpit of mathematics. The rise of the National Socialism in Germany in 1933 obliged Weyl to accept a station with the Institut of the Advanced Studies (IAS): his wife, Hella was Jewish and underwent the racist legislation of the Nazi regime.

It is in Princeton that he worked with Einstein. Weyl sought a Unification Gravitation and electromagnetism. This research gave explanations of the violation of nonthe conservation of the parity, a characteristic of the weak interactions.

Weyl continued to work with the IAS until its retirement in 1952; he died in Zurich.

June 25th 1936 -->

Work

Geometry

In 1913, Weyl publishes Die Idee der Riemannschen Fläche ( the concept of surface of Riemann ) where it provides a unified treatment of the surfaces of Riemann. It was the first to formalize, on this occasion, the definition of what is a surface. This remarkable work is often regarded as one of its principal contributions.

In 1918, it introduces the concept of gauge, first stage of what will become the Théorie of gauge. Actually, its vision was an attempt not successful to model the fields electromagnetic and gravitational like geometrical properties of the space time. With final, the Tenseur of Weyl in Géométrie riemannienne has a considerable importance to release the properties in conformity .

Of 1923 with 1938, Weyl studied the compact groups, in terms of matric representation. It establishes in particular a formula for the characters of a compact Groupe of Dregs . This work proved fundamental to include/understand the symmetry of the laws of quantum mechanics. It posed the bases of them, giving rise to the Spineur S, become familiar around the years 1930. The noncompact groups and their representations, the following the example of the Group of Heisenberg, have also one of its subjects of concern. Consequently, the groups of Dregs and their algebras of Dregs became a branch with whole share of the Géométrie and Theoretical physics.

The book “the traditional groups” recover the symmetrical groups, the linear groups, the orthogonal groups and the groups symplectic. It is besides Hermann Weyl in person who chose the term symplectic to avoid any complex confusion with .

Bases of mathematics

See also: Bases of mathematics

In the Continuum , by using work of Bertrand Russell, Weyl was able to develop the traditional analysis, without using neither the proof by contradiction, neither the infinite whole of Cantor, nor the Axiome of the choice. A little later Weyl changed point of view, being attached to the Intuitionnisme Brouwer. It published an controversial article protesting at the sides of Brouwer “We are the revolution”. The article in question popularized much the intuitionalist point of view of that had not done it original work of Brouwer.

George Polya and Hermann Weyl made a bet about the future of mathematics at a mathematical meeting in Zurich in February 1918. For Weyl, in the twenty years to come, the mathematicians would admit the vague character of notions like the Corps of the real numbers, the Ensemble S and the Dénombrabilité, wondering at the same time if the truth or the falseness of the Propriété of the upper limit, had the same contents as the interrogation on the assertions of Georg Hegel in philosophy of nature. The existence of this bet was discovered in 1995 by Yuri Gurevich.

A few years later, Weyl estimated that the intuitionalism of Brouwer was a too narrow point of view and joined, at least partially, the position of Hilbert. In the last years of its life, it adopted the point of view of Ernst Cassirer; but it published very few articles defending this new position.

Relativity

Weyl followed closely the development of the Relativité in physics. Its approach was based on the phenomenologic philisiphie Edmund Husserl, and in particular on its test of 1913, Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch: Allgemeine Einführung in die queen Phänomenologie .

Quotations

the problems of mathematics are not problems of the vacuum.
In thesis days the angel off topology and the devil off abstract will algebra fight for the off drunk every individual discipline off mathematics.
My work always tried to unit the truth with the beautiful, goal when I had to choose one gold the other, I usually thing the beautiful.

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