Those forced out included Hermann Weyl ( who had taken Hilbert's chair when he retired in 1930 ), Emmy Noether and Edmund Landau.

The first complete mathematical formulation of this approach is generally credited to John von Neumann's 1932 book Mathematical Foundations of Quantum Mechanics, although Hermann Weyl had already referred to Hilbert spaces ( which he called unitary spaces ) in his 1927 classic paper and book.

The American theoretical physicist John Archibald Wheeler coined the term wormhole in 1957 ; however, in 1921, the German mathematician Hermann Weyl already had proposed the wormhole theory, in connection with mass analysis of electromagnetic field energy.

As noted above, Dirac initially thought that the hole might be the proton, but Hermann Weyl pointed out that the hole should behave as if it had the same mass as an electron, whereas the proton is over 1800 times heavier.

Despite difficulties solving the differential equation for hydrogen ( he had later help from his friend the mathematician Hermann Weyl ) Schrödinger showed that his non-relativistic version of the wave equation produced the correct spectral energies of hydrogen, in a paper published in 1926.

Around the same time Weyl also found his relativistic equation, which also had spinor solutions.

Michael Atiyah, in particular, has commented that whenever he examined a mathematical topic, he found that Weyl had preceded him ( The Mathematical Intelligencer ( 1984 ), vol. 6 no. 1 ).

Einstein had a lasting influence on Weyl who became fascinated by mathematical physics.

However, within a few years Weyl decided that Brouwer's intuitionism did put too great restrictions on mathematics, as critics had always said.

The " Crisis " article had disturbed Weyl's formalist teacher Hilbert, but later in the 1920s Weyl partially reconciled his position with that of Hilbert.

After about 1928 Weyl had apparently decided that mathematical intuitionism was not compatible with his enthusiasm for the phenomenological philosophy of Husserl, as he had apparently earlier thought.

Some decades later the rather abstract view coming from category theory was tied up with the approach that had been developed in the 1930s by Hermann Weyl ( in his book The Classical Groups ).

In 1930, Emil was offered a professorship at ETH ( Eidgenössische Technische Hochschule ) in Zürich, to replace Hermann Weyl, who had moved to Göttingen.

His now-famous Foundations of Constructive Analysis ( 1967 ) aimed to show that a constructive treatment of analysis is feasible, something about which Weyl had been pessimistic.

The term " Lie algebra " was introduced in 1934 by Hermann Weyl, for what had until then been known as the algebra of infinitesimal transformations of a Lie group.

Theodore Roosevelt was the star of many early pieces in TNR, but by December 1914, Roosevelt had a falling out with Croly, Lippmann, and Weyl.

Weyl extended Schur's method to complex semisimple Lie algebras by showing they had a compact real form.

The last Komtur of the Teutonic Knights, Freiherr Beat Conrad Reuttner von Weyl, had a new castle built by the official architect of the Teutonic Knights, Franz Anton Bagnato, between 1794 and 1796.

But in this address Weyl " while defending Brouwer against some of Hilbert's criticisms ... attempts to bring out the significance of Hilbert's approach to the problems of the foundations of mathematics.

The Institute has been the workplace of some of the most renowned thinkers in the world, including Albert Einstein, Paul Dirac, Kurt Gödel, Clifford Geertz, T. D. Lee and C. N. Yang, J. Robert Oppenheimer, John von Neumann, Freeman J. Dyson, Hassler Whitney, André Weil, Hermann Weyl, Harish-Chandra, Joan W. Scott, Frank Wilczek, Edward Witten, Albert O. Hirschman, Nima Arkani-Hamed, George F. Kennan, and Yve-Alain Bois.

Weyl published technical and some general works on space, time, matter, philosophy, logic, symmetry and the history of mathematics.

* In connection with the Weyl – Polya bet, a copy of the original letter together with some background can be found in George Polya's article, " Eine Erinnerung an Hermann Weyl ", ( Regrettably, this charming article was omitted from Polya's collected works.

If v belongs to some Weyl chamber, no root lies in v < sup >∧</ sup >, so every root lies in v < sup >+</ sup > or v < sup >−</ sup >, and if α lies in one then − α lies in the other.

Strauss later added more music, and Weyl needed to change some of the words.

This means that in general relativity, the Einstein curvature at some event is entirely determined by the stress-energy tensor at that event ; the other piece, the Weyl curvature, is the part of the gravitational field which can propagate as a gravitational wave across a vacuum region.

A third equivalent condition follows from the Ricci decomposition of the Riemann curvature tensor as a sum of the Weyl curvature tensor plus terms built out of the Ricci tensor: the Weyl and Riemann tensors agree,, in some region if and only if it is a vacuum region.

We can think of a fourth rank tensor such as the Weyl tensor, evaluated at some event, as acting on the space of bivectors at that event like a linear operator acting on a vector space:

A Weyl tensor which has type I ( at some event ) is called algebraically general ; otherwise, it is called algebraically special ( at that event ).

If the Weyl tensor is algebraically special at some, there is a useful set of conditions, found by Lluis ( or Louis ) Bel and Robert Debever, for determining precisely the Petrov type at.

In some ( more or less ) familiar solutions, the Weyl tensor has the same Petrov type at each event:

Some time latter, Hermann Weyl introduced the Weyl curvature tensor, which measures the deviation of a Lorentzian manifold from being conformally flat, i. e. with metric tensor having the form of the product of some scalar function with the metric tensor of flat spacetime.

where α is some conformal factor which is yet to be determined ( see Weyl rescaling ), we get the desired velocity restriction.

Dirac tried to argue that this was due to the electromagnetic interactions with the sea, until Hermann Weyl proved that hole theory was completely symmetric between negative and positive charges.

Among his 69 Ph. D. students in Göttingen were many who later became famous mathematicians, including ( with date of thesis ): Otto Blumenthal ( 1898 ), Felix Bernstein ( 1901 ), Hermann Weyl ( 1908 ), Richard Courant ( 1910 ), Erich Hecke ( 1910 ), Hugo Steinhaus ( 1911 ), and Wilhelm Ackermann ( 1925 ).

Indeed Hilbert would lose his " gifted pupil " Weyl to intuitionism — " Hilbert was disturbed by his former student's fascination with the ideas of Brouwer, which aroused in Hilbert the memory of Kronecker ".

" The foundations of mathematics ," with comment by Weyl and Appendix by Bernays, 464 – 89.

The mathematician Hermann Weyl began corresponding with him in 1918.

Weyl brought the early period of the development of the theory of Lie groups to fruition, for not only did he classify irreducible representations of semisimple Lie groups and connect the theory of groups with quantum mechanics, but he also put Lie's theory itself on firmer footing by clearly enunciating the distinction between Lie's infinitesimal groups ( i. e., Lie algebras ) and the Lie groups proper, and began investigations of topology of Lie groups ( Borel ( 2001 ), ).

Predicativism was first studied in detail by Henri Poincaré and Hermann Weyl in Das Kontinuum, where they showed that much of elementary real analysis can be conducted in a predicative manner starting with only the natural numbers.

As noted by Weyl, Formal logical systems also run the risk of inconsistency ; in Peano arithmetic, this arguably has already been settled with several proofs of consistency, but there is debate over whether or not they are sufficiently finitary to be meaningful.

In 1920 Weyl, Hilbert's prize pupil, sided with Brouwer against Hilbert.

Chapter Five: " Hilbert to the Rescue " wherein Davis discusses Brouwer and his relationship with Hilbert and Weyl with brief biographical information of Brouwer.

Weyl also showed how to use exponential sums in diophantine approximation, with his criterion for uniform distribution mod 1, which was a fundamental step in analytic number theory.

By 1949, Weyl was thoroughly disillusioned with the ultimate value of intuitionism, and wrote: " Mathematics with Brouwer gains its highest intuitive clarity.

Thus, by expressing quantum mechanics in phase space ( the same ambit as for classical mechanics ), the Weyl map facilitates recognition of quantum mechanics as a deformation ( generalization ) of classical mechanics, with deformation parameter ħ / S, where S is the action of the relevant process.

In 1932 he went to Princeton University for a year as a Rockefeller Fellow, where he worked with Hermann Weyl, Oswald Veblen, and Solomon Lefschetz.