TABLE OF CONTENTS
Descriptive Summary
Biographical Note:
Scope and Contents
Organization
Restrictions
Index Terms:
Administrative Information
Description of Series
General correspondence:
The Mathematical Apparatus for QuantumTheories:
Books (unpublished):
Articles (published):
Articles (unpublished):
Lectures:
Grants:
Subject files and notes:
Personal:
Publications by others:
At SRH:

A Guide to the Otton Martin Nikodym Papers, 19252012





Creator: 
Nikodym, Otton Martin, 1887 

Title: 
Otton Martin Nikodym Papers 

Dates: 
19252012 

Abstract: 
Collection documents the career of
Otton Martin Nikodym (18871974) at the University of Warsaw and Kenyon College.
Correspondents include J.L. Destouches, N. Dunford, H. Hasse, V. Klee, G. Ludwig,
C. Paue, and W. Sierpinski. Material includes correspondence, subject
bibliographies, and photographs. 

Extent: 
12 ft.; manuscript, typescript,
printed, photographic. 

Language: 
Material is written in English, French, Italian, and Polish. 

Repository: 
Dolph Briscoe Center for American History, The
University of Texas at Austin 
Otton Martin Nikodym was born August 13, 1887, in Zablotow, Poland. He was educated
at the Universities of Lwow and Warsaw, and the Sorbonne. Nikodym taught at the
Universities of Cracow and Warsaw and at the High Polytechnical School in Cracow. He
came to the United States in 1948 to join the faculty of Kenyon College. He retired
in 1966 and moved to Utica, N.Y., where he continued his research. Nikodym died in
1974.
Nikodym worked in a wide range of areas, but his bestknown early work was his
contribution to the development of the LebesqueRadonNikodym integral. His work in
measure theory led him to an interest in abstract Boolean lattices. His work after
coming to this country centered in the theory of operators in Hilbert space, based
on Boolean lattices, culminating in his The Mathematical Apparatus for
QuantumTheories. He was also interested in mathematics teaching.
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The papers contain notes and drafts for unpublished works on affine geometry, algebra
of fields, Fréchet and abstract Riemann integrals, measure theory, and logic;
together with notes, drafts, and proofs for several published works. Material used
in preparing volume 1 (published) and volume 2 (unpublished) of The Mathematical
Apparatus for QuantumTheories is included. Volume II is virtually complete,
requiring final editing. There are notes for lectures and courses, and drafts of
textbooks on algebra and geometry. The collection includes Nikodym's bibliography
and reprints, together with his library (annotated) and reprint collection. Papers
are in English, French, Italian, and Polish. Correspondents include J.L.
Destouches, N. Dunford, M. Fréchet, H. Hasse, V. Klee, G. Ludwig, C. Paue, and W.
Sierpinski. The papers, except for Nikodym's reprints, largely postdate his arrival
in the U.S. (1948). Material includes subject bibliographies, photographs, and
paintings by Stanislawa Nikodym of the Nikodyms' home in Gambier, Ohio, and of
European scenes.
Forms part of the Archives of American Mathematics.
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Organization 

Organized into 11 series: 




General Correspondence 


The Mathematical Apparatus for QuantumTheories 


Books (unpublished) 


Articles (published) 


Articles (unpublished) 


Lectures 


Grants 


Subject Files and Notes 


Personal 


Publications by Others 


At Sid Richardson Hall (Photographs) 
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Use Restrictions
The majority of this collection is stored remotely at CDL. Advance notice required
for retrieval. Contact repository for retrieval.
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Subjects (Persons) 


Nikodym, Otton Martin 


Nikodym, Stanislawa 

Subjects 


Fields, Algebraic 


Functional analysis 


Hilbert space 


Lattice theory 


Linear operators 


Logic, Mathematical and symbolic 


Mathematics  Study and teaching 


Measure theory 


Quantum theory 
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Otton Martin Nikodym Papers, 19252012, Archives of American Mathematics, Dolph
Briscoe Center for American History, University of Texas at Austin.
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General correspondence: 
Box 
8644/1 


A  D 



E  G 



H  L 



Kenyon College 



M  S 



Nikodym, Stanislawa, letters of condolence,
1974 



Offprint requests 



Springer Verlag, 196478 
Box 
8644/2 


T  Y, and unidentified 
Box 
2014103/1 (SRH math office) 


Correspondence with mathematicians, mostly photocopies,
19471967 
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The Mathematical Apparatus for QuantumTheories: 
Box 
8644/2 


Notes on work of various physicists, including Bohm, DeBroglie,
Ludwig, Weyl 



Notes on mathematical physics 



Notes on mathematical physics: Green's formula 



Drafts for v. I and II, Calculus of variations in the
large 



Manuscripts and notes, Destouches: A general theory of
predictions 
Box 
8644/3 


The Mathematical Apparatus for QuantumTheories, v.
I: 




Manuscripts used in v. I(?) 




Chapters: W' (Jubilee of H. Hasse), R', S, T, N, F, S,
J 




Chapter: R', List of notions and symbols 




Chapters H, K, and unlabeled 




Typescripts: 





Fragments; Pp. 1214 





Pp. 225288; Chapter A 
Box 
8644/4 




Typescript chapters: 






A' 





B, B', C 






C', D 





D', E 






H, J, K, L, M, N 
Box 
8644/5 





J, J', K, L 





M, N, P 





P, P', Q, Q' 






P', Q, Q', R 






R, R', T, U 
Box 
8644/6 





R', S, T, U 






W, W' 






W, W' 




Page proofs: 





Pp. 1448 





Pp. 449942 
Box 
8644/7 




Corrected page proofs, Pp. 1560 





Corrected page proofs, Pp. 561941 




Reviews 



The Mathematical Apparatus for QuantumTheories, v.
II: 




Notes and drafts 





Chapter list, Chapters , , , and unlabeled 




Rund (Account of infinities), Mean value, Differentiation of
Fourier integral: 





Saturated tribes, Operators, Lagrangeextremals, Partial
and double summation on the Cartesian product,
Cantorization 





Chapters I or I, I, KIII, and unlabeled 





Plan of v. II, Chapter or, and unlabeled 
Box 
8644/8 




Chapters I, I, and unlabeled 





Last chapter of Book II, Lemma on Stieltjes
integrals 





Chapters II, I, IV, IV, FourierPlancherel theorem, and
unlabeled 




Auxiliary chapters, and unlabeled 





Chapter plan, Auxiliary chapter II 




Drafts arranged by chapter  Chapters: 





I, IV, I, I, Outline of v. II 





IV, I, II(?), III, II, I, I, I, I, III 
Box 
8644/9 




IV, IV, IV, appendix, appendix, wIII, I, III,
7III 





Appendix, I, III, III, III, II, II, III, III, IV, II, and
unlabeled 





III, I4.9/8644/V 





III, III, III, III, III, III, III 





II, II, II, II 
Box 
8644/10 




I, I 





I, I 





I, I 





I, I, I 




Manuscript and typescript drafts: Pp. 9911195 
Box 
8644/11 


Typescript drafts: 










Pp. 1  343 





Pp. 344  761, Chapter lists 





Pp. 762  990 





Pp. 991  1195, Chapter lists 




Completed typescript 
Box 
8644/12 


Completed typescript (cont.) 
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Books (unpublished): 
Box 
8644/12 


Affine geometry 
Box 
8644/13 


Algebra of fields 



Elementary college mathematics text 



Geometry 
Box 
8644/14 


Geometry (cont.) 



Let us Look in the Depths of Thought (originally radio lectures,
Warsaw, 1938), with correspondence, 197677 
Box 
8644/15 


Understanding College Algebra 
Box 
2014103/1 (SRH math office) 



Introduction (annotated),
undated 
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Articles (published): 
Box 
8644/15 


Bibliography 



Reprints (reprints follow order of the bibliography: not strictly
chronological): 




192528 




1929 




1930 




192833 
Box 
8644/16 



1937 




1938 




193949 




194854, 1957 




195560 




1959, 1964 
Box 
8644/17 



195665 
Box 
2014103/1 (SRH math office) 



Sur une généralisation des intégrales de M. J. Radon,” by
Otton M. Nikodym, 1929 




“Sur l’extension des corps algébriques abstraits par un
procédé généralisé de Cantor,” by Otton M. Nikodym and Stanislawa
Nikodym, December 1954 
Box 
8644/17 


Correspondence, 195270 



"Theorems on divisibility of
cardinals" (1957), with related letters from Paue and
Suss. 



"Summation of quasivectors on Boolean tribes
and its application to quantumtheories, I," annotated
(1959) 



"Studies of some items of the lattice theory
in relation to the HilbertHermite space" (1969) 



"A study in Lagrange's variational problem
considered in the large" (1970) 
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Articles (unpublished): 
Box 
8644/17 


Fréchet integrals, VitaliHahnSaks theorem, abstract Riemann
integrals 
Box 
8644/18 


Algebra 



On generalized Cantorextension device in abstract fields (with
S. Nikodym), 1954 



Remarks on formal structure of mathematics 
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Lectures: 
Box 
8644/18 


Correspondence, announcements, 194670 



Advanced lectures at Kenyon: 




Projective geometry 




Topology, geometry, and other topics 



Lecture at DeBroglie's seminar on Jacobi's theory concerning
movement of a material point 
Box 
8644/19 


Lectures on measure theory, Naples
(1965) 
Box 
8644/20 


Popular lectures on logic 



"Sur les absurdites respectables dans les
mathematiques et sur leur cure  avec application a la fameuse
fonction delta de M. Dirac" 



Lectures in Pittsburgh: Hilbert space, Boolean tribes, complex
approximation 
Box 
2014103/1 (SRH math office) 


Announcement posters, 19471959,
undated 
Box 
AAMOS/1 


Wall charts on quantum theory work 
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Grants: 
Box 
8644/20 


National Science Foundation, correspondence, applications,
reports 




195364 




196572 



Other agencies, correspondence, applications, 195269 
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Subject files and notes: 
Box 
8644/20 


Bibliographies: 




Boolean tribes, Orderings and lattices, Measure
integrals 
Box 
8644/21 



Functional calculus, Hilbert space 




Nelson Dunford bibliography 




Destouches, J. L., "Ancienne
theorie des quanta" 




Fourier integrals, differential equations, and other
topics 




Groups and rings 




Hilbert space (includes correspondence: G. Ludwig),
1965 



Notes: 




Nonmathematical notes: Chemistry, atomic structure,
languages 
Box 
8644/22 



Research notes (unidentified) 
Box 
2014103/1 (SRH math office) 



Mathematical notes, in English and French,
undated 
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Personal: 
Box 
8644/22 


Biographical items, curriculum vitae, newspaper
clippings 



Official documents, financial records, addresses,
notes 



Organization memberships (with correspondence), 194767 
Box 
2014103/1 (SRH math office) 


Curriculum vitae, January 1968 
Box 
8644/23 


Paintings by S. Nikodym 
Box 
AAMOS/1 


Paintings by S. Nikodym 
Box 
8644/23 


The Rape of Cinderella, by Eugene Paul Nassar (dedicated to O. M.
Nikodym) 
Box 
2014103/1 (SRH math office) 


Tributes to Nikodym, in English, Polish, and German,
19741985 



Correspondence  letters to Stanislawa Nikodym and Eugene
Nassar after O. M. Nikodym’s death, 19741990 
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Publications by others: 
Box 
8644/23 


Reprints: 




A  C 




D  G 




H  J 
Box 
8644/24 



K  O 




P  S 




T  Z 



Colloque de Topologie Algebraique
(1947) 



Stanislawa Nikodym, bibliography and reprints 



"Beginnings of the Mathematical Research
Institute Oberwolfach of the CountrySeat 'Lorenzenhof'" by
I. Suss. 
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At SRH: 
Box 
4RM224 


Photographs and photocopies of photographs, circa 19471964, undated 
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