Edition of a Large Selection of

Foundations of Mathematics and Natural Science

Hilbert's reputation as one of the greatest mathematicians is well established; but already in his lifetime Hermann Weyl and Otto Blumenthal lamented that many of his deepest ideas were presented in lectures and never formally published, or published only in fragments -- with the consequence that an accurate overview of his thought cannot be obtained from published sources alone.

The Hilbert *Nachlaß* held in the University of Göttingen
, divided between the Universitätsbibliothek
and the Mathematisches Institut, thus assumes unusual importance for students
of Hilbert's thought. This *Nachlaß *is remarkably complete.
It covers his entire professional career, from his first days as a student
in Königsberg to the time of his death in Göttingen more than
sixty years later. In addition to scientific notebooks, drafts of articles,
reading notes, and an abundant correspondence, the *Nachlaß*
contains some 126 protocols of Hilbert's lectures. These protocols range
in length from 50 to 500 pages. Some are manuscripts; others are polished
typescripts. Several are in Hilbert's hand; most were written up by his
assistants (among them figures of the stature of Ackermann, Born, Bernays,
and Courant), corrected by Hilbert, bound, and deposited in the library
of the Mathematics Institute. Hilbert lectured on topics that were central
to his research, and these protocol volumes provide a detailed record, semester
by semester, of the development of his scientific interests and thought.

We propose to publish, in six volumes, the most important of Hilbert's unpublished writings on the foundations of mathematics and of physics. We hope thereby to accomplish two things: first, to present a fuller and more balanced picture of Hilbert's actual views than has thus far been available; second, to trace the development of his thought on foundational questions, and thereby show how he arrived at some of his most influential ideas.

Our edition will focuses on that part of Hilbert's *Nachlaß *which
touches directly on foundational issues, and which forms only a part of
the entire corpus of writings, large though this part is. Nevertheless,
the foundational part is enough to shed valuable new light on Hilbert's
scientific contributions and to correct some widespread misconceptions.
The 'standard picture' of Hilbert holds:

1. That he was a 'formalist' -- i.e. a mathematical purist who believed mathematics is ultimately nothing but a game played with meaningless symbols.

2. That his program for the philosophy of mathematics was decisively refuted by the Gödel incompleteness theorems.

3. That his interest in physics was marginal, and restricted to the precise mathematical formulation of of well-established theories.

4. That once he had finished working on one area, he would abandon it totally and move on to the next, devoting to it his full attention.

This picture has been encouraged by Hilbert's own habits of publication. His published writings are somewhat ascetic, and present only his technical conclusions: missing is any account of how he came to his results, of the broader ideas that drove him, or of how the numerous aspects of his work are interrelated. His work on physics, indeed, he left largely unpublished, and it is therefore easy to overlook his his deep involvement with the fundamental contributions to relativity theory, quantum mechanics, statistical mechanics, and thermodynamics and the classical theories of continua and electrodynamics.

In contrast to the published works, the protocols in the Nachlaßin extenso in the *Nachlaß* protocols, and in turn
call into question the extent to which Gödel's theorems 'refuted Hilbert.'
Certainly they refuted *parts* of his technical program; but (as Gödel
himself was careful to point out) they do not in any obvious way refute
the program itself, let alone the underlying philosophy of mathematics.

The publication of this *Nachlaß* material will thus accomplish
several things:

1. It will make available for the first time the bulk of Hilbert's unpublished
work on the foundations of mathematics and natural science.

2. It will shed new and interesting light on way Hilbert saw the intimate
relationship between mathematics and natural sciences, a relationship that
became paradigmatic for the development of science in our century.

3. It will make essential a reconsideration of Hilbert's views in the
philosophy of mathematics, and in particular of the philosophical significance
of Gödel's theorems; and it will make available for the first time
a complete and accurate picture of Hilbert's work on the foundations of
mathematics.

4. It will shed light on the relationships between Hilbert and some of
the central figures of twentieth-century science -- notably Klein, Minkowski,
Poincaré, Zermelo, Weyl, Russell, Einstein, Born, Sommerfeld, von
Neumann, Bernays and Gödel.

5. It will shed light on the way in which Hilbert came to some of his
central ideas, thus providing a rare glimpse into the workshop of a mathematician
of the highest rank. In addition, it will illuminate the entire fabric (or
*Fabrik*!) of mathematics and mathematical physics in Göttingen
in the first three decades of the twentieth century.

The Hilbert-Edition should thus be of interest to scholars from a number of different disciplines, and should assist a reappraisal both of the substance of Hilbert's work, and of its relationship to the work of his contemporaries.

We propose to produce a critical, annotated edition in six volumes, each
of some 500 pages. The provisional oragnisation is as follows:

Volume 1: Foundations of Geometry. [**Link 2: detailed list of contents
of Vol.1**]

Volume 2: Foundations of Logic and Arithmetic (early works). [**Link 3:
detailed list of **contents of Vol.2]

Volume 3: Foundations of Logic and Arithmetic (later works). [**Link 4:
detailed list of **contents of Vol.3]

Volume 4: Foundations of Natural Science (classical theories, including
electrodynamics). [**Link 5: detailed list of contents of Vol.4**]

Volume 5: Foundations of Natural Science (relativity theory and quantum
mechanics). [**Link 6: detailed list of contents of Vol.5**]

Volume 6: Varia (selections from diaries; popular lectures and lecture-courses).
[**Link 7: **detailed list of contents of Vol.6]

The Hilbert-Edition has been in preparation since 1990, and the editorial work has been proceeding at full pace since 1993, under a long-term grant from the Deutsche Forschungsgemeinschaft. It is based at the Institut für Wissenschaftsgeschichte at the University of Göttingen in Germany.

The address to write to is:

Hilbert-Edition

c/o Dr. Ralf Haubrich

Institut fuer Wissenschaftsgeschichte

Universitaet Goettingen

Humboldtallee 11

37073 Goettingen, Germany;

Electronic contact can be made via e-mail at: rhaubri@gwdg.de. Dr. Haubrich can be reached by telephone at (+49 551) 39 8117; the Institute's fax number is (+49 551) 39 9748.

We would be grateful for any relevant information concerning oral reports, handwritten, typewritten, or printed material (e.g., letters, lecture notes, notes on talks, biographical notices) concerning Hilbert's activities. We would be most grateful, if such information could be sent to Dr. Haubrich at the above addresses, conventional or electronic.

The first volume on Hilbert's geometrical writings is nearing completion. We hope that the remaining volumes can follow at intervals of two to three years.

It is also the intention, once the Hilbert-Edition is well under way, and
given a better understanding of the entirety of the *Nachlaß,*
to produce a volume of English translations of selections from the Hilbert-Edition.
This volume will be aimed primarily at students, and will contain relatively
non-technical material dealing with general themes in the philosophy of
mathematics and natural science. A second English volume containing selections
from the more technical works is not out of the question.

William Ewald (University
of Pennsylvania)

Michael Hallett (McGill University)

Ralf Haubrich (University of Göttingen)

Ulrich Majer (University of Göttingen)

Wilfried Sieg (Carnegie Mellon University)

with the cooperation of

Helmut Karzel (Technische Universität München)

and

Tilman Sauer (Max Planck Institut für Wissenschaftsgeschichte, Berlin)
[**Link 14: **

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