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BRÓDY, F. - VÁMOS, T. (eds): The Neumann compendium


More than 30 years after the publication of the six volumes of John von Neumann's papers edited by A. H. Taub, we selected some basic papers and excerpts of books which are, in our view, most relevant to the present, either still being the basic resources of an up-to-date progress in science or fundamental in the historical view of the evolution of thoughts. All are standards in elucidation of ideas, for any scientist, at any time.

We have divided this volume into sections and each section starts with introductory note by Hungarian researchers. All of these notes are short except that in the section on Operator Algebra. The reasons for this exception are: (i) the heightened interest in the results on operator algebra; (ii) the highly abstract nature of the subject calls for a more detailed explanation, even for mathematicians who are not working in this field.

Section 1 is on Quantum Mechanics, one of the first great subjects of Neumann's activities, developing a firm mathematical basis for the theories of Heisenberg, Schrödinger, Jordan and Dirac, generating many further ideas, especially in operator algebras, and establishing his lifelong relation with physics. Though quantum mechanics is not so much a continuation of Neumann's line as operator algebras are, his disquisitions are classical and still contribute to a basic conundrum of physical reality. The main part of this section is taken from Chaps. V and VI of Mathematical Foundations of Quantum Mechanics followed by two papers related to the implications : concerning logics-another subject still in revolution.

Section 2 is on Ergodic Theory. In some aspects this basic mathematical and philosophical problem is still open, but Neumann's contribution is crucial in relation to his work in quantum mechanics and operators and to the achievements of Haar, Riesz and Halmos.  Problems of ergodicity are still being investigated both in the abstract-mathematical direction and by the extensive use of computers.

Section 3 is on Operator Algebra. As we mentioned earlier, this section plays a distinctive role.

Section 4 consists of papers on Hydrodynamics. One of Neumann's most fundamental contributions was his analysis of detonation processes and his techniques of utilizing numerical methods to analyze theoretical problems. (The need for his analysis has led to his involvement in computer invention/design/development; although the computers he wished for were only available after the war.)

The other great digression, besides physics, is Economics, our fifth section. Theory of games is still a basic paradigm of any cooperative activity, the theory and practice follow Neumann's ways of thought. His work was best described by himself, in the book written with Morgenstern, from where we extent the introductory parts, which are of interest not solely with respect to their subjects taken in the narrow sense but for their implications for general mathematical methodology (e.g., axiomatics).

Section 6 on Computers, comprises a selection of papers that
demonstrate the brilliant ideas and their presentation.

The seventh section collects his most important speeches and papers on general problems of science and society. He had a highly acknowledged personality, an accepted authority in thinking about present and future, and he accepted this role with intellectual pleasure and a full awareness of his responsibility. The questions discussed, as well as the method, the ethical attitude and the wisdom of their discussion, retain their validity up till today.

All of the papers collected are originally in English with two exceptions: The chapters from "Mathematische Grundlagen der Quantenmechanik" are taken from the English edition of 1955, translated by R. T. Beyer, and the paper "Zur Algebra der Funktionaloperatoren und Theorie der normalen Operatoren" has been translated for this volume by R. Lakshminarayanan.

The bibliography, compiled with the cooperation of  F. Nagy and  Ms. Kiss, is based on Neumann's autobibliography completed in 1953, and on Ulam's and Taub's bibliographies. Entries for works that surfaced in the meantime have been added, and all items have been checked and verified. There are a lot of materials unpublished: manuscripts, lecture notes, memoranda, and a huge correspondence, scientific and otherwise, with a broad circle of acquaintances, among them many of the most brilliant scientists of the epoch; apparently an area for further research.

A facsimile of his "Lebenslauf" (Curriculum Vitae) submitted to the Berlin University, a facsimile of a letter to L. Fejér, and a transcript of an interview for the Radio "Voice of America" in 1955 have been included in this volume to make it complete.
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