Table Of ContentKARL MARX AND MATHEMATICS
This collection of various texts on Karl Marx and Mathematics is the revised and
extended second edition of the Special Supplement to Karl Marx, Mathematical
Manuscripts (1994; Calcutta: Viswakos) titled Marx and Mathematics. A part of
the additional information included in the present collection has evolved during the
last 25 years. Some of the relevant developments of this period have been indicated
in the Translator's Note to the revised second edition of Karl Marx, Mathematical
Manuscripts (2018, Delhi: Aakar Books). The remaining part of the information
indicated in this introduction and collection existed but was either inaccessible to
most people before the emergence and development of the World Wide Web or,
was neglected by the earlier editors, including the present author. The sources of the
texts included in the three parts of this collection and, some biographical information
about their respective authors have been indicated at the end of each text.
The emergence and development of the Ethnomathematics movement continue
to change our understanding of the history of evolution of plural mathematics
on planet earth since the Neolithic age. Rediscovery and study of some of the
neglected source texts have further energized investigations on the subsequent
history of mathematical cultures, including those on the histories of algebra and
analysis in some of the ancient and medieval languages of Asia, like Sanskrit,
Arabic and Malayalam. Consequently, it is now possible to indicate some of the
larger gaps in the dominant understanding of history of mathematics not only in
Marx's time, but also at the time of editing Marx's mathematical manuscripts in
the twentieth century, and even today. Finally, the emergence and development of
mathematical and statistical software packages are vigorously reshaping our ways of
conceptualizing and doing mathematics towards an unknown future. It is time now
for taking yet another look at all mathematical text from the past and that includes
the mathematical manuscripts of Marx.
These texts have been divided into three parts. Part one contains some topical
texts related to the history of emergence, development, editing, publication and
reception of the mathematical manuscripts of Karl Marx. Part two contains a
selection of five articles reflecting some of the investigations inspired by these
manuscripts in Russia, India and France. Part three contains five articles on plural
mathematics before and after Karl Marx (1818-1883). The texts in this collection
are followed by two appendices containing two bibliographies: one on Hegel and
mathematics and, the other on mathematics and semiotics.
Pradip Baksi (1948-), translator and editor of the first Bengali and English editions
of these manuscripts (1994) and, of some texts of Rammohun Roy (1998), and of
Karl Marx (1999) on India.
KARL MARX AND MATHEMATICS
Edited by
Pradip Baksi
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LONDON AND NEW YORK
AAKAR
First published 2021
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SIGN AND ABBREVIATIONS
Words, clauses or sentences within < > brackets indicate subsequent insertion for the
present volume.
MEGA: Marx-Engels-Gesamtausgabe (1975- ).
Berlin: Dietz-Verlag/ Akademie Verlag/ De Gruyter Akademie Forschung.
MECW: Karl Marx/ Friedrich Engels, Collected Worb (1975-2005), Moscow: Progress etc.
Contents
Introduction, 2019 Vll
Acknowledgements XXX
Introduction, 1994 XXXI
Part One: History
EXCERPTS FROM LETTERS 3
Marx to Engels:
11 January 1858
6 July 1863
Engels to F.A. Lange:
29 March 1865
Marx to Engels:
31 May 1873
Engels to Marx:
18 August 1881
21 November 1882
Marx to Engels:
22 November 1882
EXCERPTS FROM REMINISCENCES 8
Engels':
Speech at Marx's funeral, 17 March 1883
Preface to the second edition of Anti-Diihring, 23 September 1885
Paul Lafargue: 1890 9
A note on the history of collecting, deciphering, editing and
publication of Marx's mathematical manuscripts, 1994 - Pradip Baksi 10
Notes to references in the preceding pages 13
VI Karl Marx and Mathematics
BIBLIOGRAPHY 14
Different editions of Karl Marx's mathematical manuscripts
Books and articles on Karl Marx's mathematical manuscripts
Additions to the Bibliography
Emil Julius Gumbel (1891-1966): The first editor of the mathematical
manuscripts of Karl Marx - Annette Vogt 22
Part Two: Investigations
The Concept of Differential according to Marx and Hadamard
- Valery Ivanovich Glivenko 37
Marx's "Mathematical Manuscripts" and development of history of
mathematics in the USSR - Vladimir Nikolayevich Molodshii 46
On the logical apparatus working in Karl Marx's Capital and
Mathematical Manuscripts - Vasily Ivanovich Przhesmitsky 53
On the problem of situating Marx's mathematical manuscripts in the
history of ideas - Pradip Baksi 61
The differential calculus, mathematicians and economists in the nineteenth
century: K. Marx and H. Laurent, readers of J.L. Boucharlat - Alain Alcouffe 76
Part Three: Plural Mathematics
Mathematics and its history in retrospective
- Adolph-Andrei Pavlovich Yushkevich 95
Nonstandard analysis and the history of classical analysis
- Feodor Andreevich Medvedev 132
The new structural approach in mathematics and some of its methodological
problems - Georgi Ivanovich Ruzavin 140
Reflections on seven themes of philosophy of mathematics
- Vladimir Andreevich Uspensky 151
Emergence and development of the concept of constructivisability in
mathematics - Nikolai Nikolayevich Nepeyvoda 191
Appendices: Two Bibliographies 201
Appendix I. A bibliography on Hegel and mathematics
Appendix II. A bibliography on mathematics and semiotics
Subject Index 205
Name Index 209
Introduction, 2019
This collection of various texts on Karl Marx and Mathematics is the revised and
extended second edition of the Special Supplement to Karl Marx, Mathematical
Manuscripts (1994; Calcutta: Viswakos) titled Marx and Mathematics.
A part of the additional information included in the present collection has
evolved during the last 25 years. Some of the relevant developments of this period
have been indicated in the Translator's Note to the revised second edition of Karl
Marx, Mathematical Manuscripts (2018: xxxiv-xxxvi; Delhi: Aakar Books). The
remaining part of the information indicated in this introduction and collection existed
but was either inaccessible to most people before the emergence and development of
the World Wide Web or, was neglected by the earlier editors, including the present
author. The sources of the texts included in the three parts of this collection and,
some biographical information about their respective authors have been indicated
at the end of each text.
Today, digital copies of the source texts studied by Marx, and those of his
mathematical notes, excerpts and manuscripts are available in the public domain.
Though currently postponed sine die, these manuscripts, notes and excerpts remain
slated to be published within the Marx-Engels-Gesamtausgabe (MEGA2) as MEGA2
1/28 and IV/30. Studies in the history of Marx/Engels editing and publishing, and of
its role in the emergence and development of the ideologies like Marxisms, Leninism,
and Stalinism etc. continue to register progress [Leckey, 1995; Marxhausen, 2006;
Mosolov, 2010; Sperl, 2005 and 2016].
The emergence and development of the Ethnomathematics movement continue
to change our understanding of the history of evolution of plural mathematics on
planet earth since the Neolithic age. Rediscovery and study of some of the neglected
source texts have further energized investigations on the subsequent history of
mathematical cultures, including those on the histories of algebra and analysis in
some of the ancient and medieval languages of Asia, like Sanskrit, Arabic and
Malayalam. Consequently, it is now possible to indicate some of the larger gaps
in the dominant understanding of history of mathematics not only in Marx's time,
but also at the time of editing Marx's mathematical manuscripts in the twentieth
century, and even today.
Vlll Karl Marx and Mathematics
Finally, the emergence and development of mathematical and statistical
software packages are vigorously reshaping our ways of conceptualizing and doing
mathematics towards an unknown future. It is time now for taking yet another look
at all mathematical text from the past and that includes the mathematical manuscripts
of Marx.
The present introduction has three parts, pertaining to some aspects of: 1) the
history of editing and reception of Marx's mathematical manuscripts; 2) the past
history and present developments of mathematics within which the said manuscripts
were and are being edited and studied; and, 3) some of the present and possible
future issues of interest to the students of Marx and mathematics.
EDITING AND RECEPTION
The first editor of Marx's mathematical manuscripts during the years 1925-27 and
1930, Emil Julius Gumbel [1891-1966] is known as the principal architect of the
statistical theory of extreme values, as a fearless crusader against political murder
by the Nazis in Germany, and as a German-American statistician and pacifist:
<https ://www .encyclopediaofmath.org/images/a/ad/EmilJu liusG UMBEL. pdf>
For a narrative on this first period of editing of the mathematical manuscripts
of Marx, see: Vogt, 1995.
In a communication published in 1927, Gumbel noted that Marx had mainly
studied some of the mathematical texts known towards the end of the eighteenth
century and, that his choice of texts was influenced by that of Hegel. Hegel
mentioned the same works of Euler, Lagrange, Landen and Newton that Marx used
or mentioned and, that like Hegel, he too was preoccupied with the foundations of
differential calculus, and with the process of deduction of derivatives. He pointed
out further, that Marx had no direct acquaintance with preceding or contemporary
mathematical literature, such as the works of Carl Friedrich Gauss [1777-1855] or
those of Bernard Bolzano [1781-1848] (Gumbel, 1927: 59).
Gumbel's statement on the interrelationships of Hegel and Marx in the domain
of mathematics needs reexamination in the light of subsequently published literature;
for a bibliography on Hegel and Mathematics see: Appendix I.
Gumbel was entrusted with the task of editing Marx's mathematical manuscripts
by David Borisovich Riazanov [1870-1938], the founder-director of the Institute of
K. Marx and F. Engels [IME, 1921-1931] in Moscow:
<http://rjazanov.shpl.ru/>
Towards the end of Stalin's campaign against his adversaries within the leadership
of the ruling party of USSR and, at the very beginning of the emergence of his cult
in 1931, Riazanov was removed from his job at that institute, expelled from the
party, and arrested. He was shot dead at Saratov in 1938, formally rehabilitated in
1958, and politically rehabilitated in 1989.
Sometime after Riazanov' s arrest in 1931, the editorial responsibilities related
to Marx's mathematical manuscripts were handed over to Sofya Aleksandrovna
Introduction, 2019 IX
Yanovskaya [1896-1966], a member of the Bolshevik party since 1918, a former
commissar of the Red Army during the Civil War, a Professor of the Moscow
State University, the Institute of Red Professors and the Academy of Sciences of
the USSR since 1931 and, one of the principal architects of the study of philosophy
and history of mathematics and, mathematical logic in the USSR:
<http:// www-groups. des. st -and. ac.uk/history/ Bio graphies/J anovskaj a.html>
<http:// www-groups. des. st -and. ac. uk/history/ References/J anovskaj a.html>
At that time the Institute of Marx and Engels [IME] had already become the
Institute of Marx, Engels and Lenin [IMEL, 1931-1954], on its way to becoming
the Institute of Marx, Engels, Lenin and Stalin [IMELS, 1954-1956]; and finally, the
Institute of Marxism-Leninism [IML, 1956-1991]. These changes reflect the shifting
ideological stances and priorities of the rulers of USSR, over the last 60 years of
the existence of that state.
A year before becoming the second editor of Marx's mathematical manuscripts,
Yanovskaya wrote that there were very few "mathematician-marxists" in the USSR;
that the students working to obtain doctorate degrees in mathematics-if not loudly,
then at least noiselessly-called the courses on history and philosophy of the
natural sciences that were organized for them to be "red theology"; and, that the
old professors of the "Moscow School" of mathematics spared no efforts to save
the autonomy of "pure" mathematics from the malicious assaults of the partisans of
materialist philosophy. Even the word "Comrade" was not permitted in the Institute
of Mathematics and Mechanics, within the Mathematical Society and, in their journal
the Matematicheskii sbornik [Mathematical Collections], as quite a significant
percentage of its members were white emigres (Yanovskaya, 1930: 88). She further
reported that at that time in the Mathematics Department of the Faculty I of Physics
and Mechanics of the Moscow State University there were only 2 full members and
1 candidate member of the ruling party and, only 3 members of the Komsomol, all
about to pass out (ibid.: 90). Throughout this article she lamented the lack of, and
offered her proposals for, nurturing mathematically well-trained and ideologically
well-fortified marxist-leninist cadres for the "mathematical front". To trace the
evolution of some of her ideas as a party ideologue embedded within the academic
bureaucracy of mathematics in the USSR in the 1930s, see: Y anovskaya, 1931
and 1936. For some overviews of the history of interrelationships of mathematical
theories, applied mathematics, religion, ideology, philosophy and politics in Russia
and the Soviet Union, see: Vucinich, 1999, 2000 and 2002; Lorentz, 2002; Seneta,
2004; Graham and Kantor, 2009; Hollings, 2013; and, Demidov and Levshin, 2016.
In 1932, Y anovskaya studied the mathematical manuscripts of Karl Marx
in collaboration with Dmitri Rykov of Moscow and A.E. Nahimovskaya from
Minsk (Rosenfeld, 1996: 74). In a long footnote attached to an article published
in 1933 Yanovskaya acknowledged that the "photocopies of Marx's mathematical
manuscripts were available at the Institute of Marx-Engels since 1925" and, that "a
significant part of the said manuscripts were quite scrupulously deciphered by 1927"
(Yanovskaya, 1933: 75-76, footnote 2). However, she noted that "the materials
chosen for deciphering and their presentation were not that satisfactory" (ibid.).
