The notes that Marx took have been collected into four independent treatises: On the Concept of the Derived Function, On the Differential, On the History of Differential Calculus, and Taylor's Theorem, MacLaurin's Theorem, and Lagrange's Theory of Derived Functions, along with several notes, additional drafts, and supplements to these four treatises.
These treatises attempt to construct a rigorous foundation for calculus and use historical materialism to analyze the history of mathematics.
Since their publication, Marx's independent contributions to mathematics have been analyzed in terms of both his own historical and economic theories,[1] and in light of their potential applications of nonstandard analysis.
"[6] However, Marx was evidently disturbed by the implications of this, stating that "The closely held belief of some rationalising mathematicians that dy and dx are quantitatively actually only infinitely small, only approaching 0/0, is a chimera".
[10] Yesterday I found the courage at last to study your mathematical manuscripts even without reference books, and I was pleased to find that I did not need them.
[13] Joseph Dauben speculates that Marx's developments in calculus may have also contributed to an interest in nonstandard analysis among Chinese mathematicians.