nLab John von Neumann

Selected writings

John von Neumann (German: Johann von Neumann; Hungarian: Neumann János Lajos) was a Hungarian mathematician.

He defended his PhD thesis in 1925 advised by Lipót Fejér, with the title Az általános halmazelmélet axiomatikus felépítése (Axiomatic construction of general set theory), which introduced the NBG set theory, as well as classes and von Neumann ordinals.

Selected writings

On set theory:

  • J. v. Neumann, Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik 154 (1925), 219–240. doi.

PhD thesis (journal version):

  • J. v. Neumann, Die Axiomatisierung der Mengenlehre, Mathematische Zeitschrift 27 (1928), 669–752. doi.

On Hermitian operators and introducing the formal definition of Hilbert spaces:

On the mathematical foundations of quantum mechanics based on Hilbert spaces of quantum states:

Proving the Stone-von Neumann theorem:

Co-introducing Jordan algebras as algebras of quantum observables:

On quantum logic:

Introducing the theory of what came to be known as von Neumann algebra factors:

The classification of factors into types I, II, III and the construction of examples not of type I:

Discussion of traces on these factors:

On isomorphism of factors and proof of a single isomorphism class of approximately finite type II 1II_1 factors:

On decomposing von Neumann algebras as a direct integral of factors:

Recollection of the history which made von Neumann turn to discussion of these “factors”, motivated from considerations in the foundations of quantum mechanics and quantum logic:

  • Miklos Rédei, Why John von Neumann did not Like the Hilbert Space formalism of quantum mechanics (and what he liked instead), Studies in History and Philosophy of Modern Physics 27 4 (1996) 493-510 [doi:10.1016/S1355-2198(96)00017-2]
category: people

Last revised on December 2, 2023 at 17:25:53. See the history of this page for a list of all contributions to it.