Works of Karl Marx, 1881

Marx's Mathematical Manuscripts

Written: 1881;
Source: Marx's Mathematical Manuscripts, New Park Publications, 1983;
First published: in Russian translation, in Pod znamenem marksizma, 1933;
Transcribed: Andy Blunden and Gabriel Silva.

Table of Contents

Publisher’s Note
Preface to the 1968 Russian edition
Letter from Marx to Engels, May 20, 1865
Letter from Engels to Marx, August 10, 1881
Letter from Engels to Marx, November 21, 1882
Letter from Marx to Engels, November 22, 1882

The Manuscripts

Two Manuscripts on Differential Calculus

‘On the Concept of the Derived Function’
On the Differential

Drafts and supplements on the work ‘On the Differential’[33]

First Draft
Second Draft
‘Third Draft’
Some Supplements

On the history of Differential Calculus49

A Page included in Notebook ‘B (Continuation of A) II’
I. First Drafts
II. The Historical Path of Development
III. Continuation of Extracts

Taylor's Theorem, MacLaurin's Theorem and Lagrange's Theory of Derived Functions

1. From the Manuscript ‘Taylor's Theorem, MacLaurin's Theorem, and Lagrange's Theory of Derived Functions’
2. From the Unfinished Manuscript ‘Taylor's Theorem’

Appendices to the Manuscript
‘On the History of the Differential Calculus’ and
Analysis of D’Alembert's Method

On the Ambiguity of the Terms ‘Limit’ and ‘Limit Value’
Comparison of D’Alembert's Method to the Algebraic Method
Analysis of D’Alembert's Method by Means of Yet Another Example

Appendices by the editors of the Russian edition

Appendix I. Concerning the Concept of ‘Limit’ in the Sources consulted by Marx
Appendix II. On the Lemmas of Newton cited by Marx
Appendix III. On the Calculus of Zeroes by Leonard Euler
Appendix IV. John Landen's ‘Residual Analysis’
Appendix V. The Principles of Differential Calculus according to Boucharlat
Appendix VI. Taylor's and MacLaurin's Theorems and Lagrange's theory of Analytic Functions in the source-books used by Marx

Additional material

E. Kol’man. Karl Marx and Mathematics: on the ‘Mathematical Manuscripts’ of Marx
Hegel and Mathematics by Ernst Kol’man and Sonye Yanovskaya
Hegel, Marx and the Calculus, Cyril Smith | Review of the New Park Publications Edition, Andy Blunden, June 1983.

Hegel on Calculus

The Differential
Calculus Deduced from its Application
Infinitesimal Magnitudes

PDF version of the entire New Park Publications book

This file has been copied from The Maoist Internationalist Movment website. It is a photocopy of the same New Park book used for the above texts, but includes the full text, including indexes, preface, etc., in a single, large file.

PDF version


49 With his manuscript ‘On the Differential’, Marx fulfilled a promise to write a specialized piece shedding light on the historical path of the development of differential calculus. In sketches preceding this letter [‘On the Differential’ was a letter to Engels - Trans], he expressed an intention to illustrate the history of differential calculus by means of the history of the theorem on the differential of a product. Obviously Marx succeed in carrying out neither of these intentions completely. Only the tentative drafts contained in the notebook ‘B (continuation of A)’, where they alternate with Marx’s computations for his work on the differential, have survived. These drafts begin, appropriately for Marx’s primary purpose, with an explanation of the methods of Newton and Leibnitz in the example of the theorem on the differential of a product. For the same reason, only the beginning goes like this and not the concluding section explication the method of d’Alembert. Later Marx passes to a more detailed discussion and critique of the methods of Newton and Leibnitz in general. This brings him to the general periodisation of the history of differential calculus, in which three periods are distinguished: 1) the mystical differential calculus of Newton and Leibnitz, 2) the rational differential calculus of d’Alembert, and 3) the purely algebraic differential calculus of Lagrange, the characterisation of which comprises the second part of the extant drafts of the history of differential calculus. It was this part which Marx apparently decided to develop into a third letter to Engels. The concluding part of the historical drafts presents a more detailed exposition of the general ideas contained in the first part. The drafts are published in full with the exception of notes whose content refers to the work ‘On the Differential’, which are omitted.


Hegel, Marx and the Calculus, Cyril Smith
Review of the New Park Publications Edition, Andy Blunden, June 1983.