The mathematical manuscripts of Karl Marx are a manuscript collection of Karl Marx's mathematical notes where he attempted to derive the foundations of infinitesimal calculus from first principles.
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.
Marx's contributions to mathematics did not have any impact on the historical development of calculus, and he was unaware of many more recent developments in the field at the time, such as the work of Cauchy. However, his work in some ways anticipated, but did not influence, some later developments in 20th century mathematics. These manuscripts, which are from around 1873–1883, were not published in any language until 1968 when they were published in the Soviet Union alongside a Russian translation. 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.[2]