Marx versus Engels on infinitesimals: Chimera or triumph?

Abstract

We document the evolution of Karl Marx's take on infinitesimals. We contrast his initial favorable stance with later criticisms, and examine the differing perspectives of Marx and Engels on the subject. Marx's favorable assessment was based on his study of Sauri's textbook. Later, influenced by Boucharlat's textbook, Marx reversed his position to an unfavorable stance, describing belief in infinitesimals as a `chimera'. Marxist scholar Guglielmo Carchedi claims that ``Marx differentiates with the eyes of the social scientist, of the dialectician'' but fails to note dialectician Engels' endorsement of infinitesimals. Struik linked Marx to Abraham Robinson, but missed the fact that the link passes via ... Fermat. Namely, there may be an affinity, as per Struik, between Marx's comments on the calculus and Robinson's nonstandard analysis, but the kernel of such an affinity resides in the techniques already found in the context of Fermat's adequality. To adapt Carchedi's metaphor, we could say that Marx may have differentiated with the eyes of adaequo of Pierre de Fermat. The first editor who worked on some of Marx's mathematical manuscripts in the mid-1920s was Emil J. Gumbel, though he is not mentioned in either the 1933 or the 1968 Soviet edition of Marx's mathematical manuscripts.