INTRODUCTION
(T. VÁMOS)
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.
