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.
On set theory:
PhD thesis (journal version):
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:
Von Neumann’s 1927 Trilogy on the Foundations of Quantum Mechanics (annotated translations by Anthony Duncan) [arXiv:2406.02149]
David Hilbert, John von Neumann, Lothar W. Nordheim, Über die Grundlagen der Quantenmechanik, Math. Ann. 98 (1928) 1–30 [doi:10.1007/BF01451579]
Proving the Stone-von Neumann theorem:
John von Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren, Mathematische Annalen 104 (1931) 570–578 [doi:10.1007/BF01457956]
John von Neumann, Über Einen Satz Von Herrn M. H. Stone, Annals of Mathematics, Second Series 33 3 (1932) 567-573 [doi:10.2307/1968535, jstor:1968535]
Mathematische Grundlagen der Quantenmechanik (German) (1932, 1971) [doi:10.1007/978-3-642-96048-2]
Mathematical Foundations of Quantum Mechanics Princeton University Press (1955) [doi:10.1515/9781400889921, Wikipedia entry]
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 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:
Last revised on June 5, 2024 at 19:39:33. See the history of this page for a list of all contributions to it.