TY - JOUR

T1 - Marx versus Engels on Infinitesimals: Chimera or Triumph?

AU - Katz, Mikhail G.

AU - Kuhlemann, Karl

AU - Кутателадзе, Семен Самсонович

N1 - Katz, M. G. Marx versus Engels on infinitesimals: chimera or triumph? / M. G. Katz, K. Kuhlemann, S. S. Kutateladze // HOPOS. – 2026. – V. 16. - № 1. - Pp. 108-131. – DOI 10.1086/739306. – EDN JQAFEC. We are grateful to historian of mathematics Annette Vogt for helpful comments. The influence of Hilton Kramer (1928–2012), who pursued and exposed the mendacity of the marxist ‘long march’ in academia and the arts with mathematical rigor, is obvious throughout.

PY - 2026

Y1 - 2026

N2 - 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. Marx differentiates with the eyes of the social scientist, of the dialectician. –Carchedi

AB - 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. Marx differentiates with the eyes of the social scientist, of the dialectician. –Carchedi

UR - https://www.scopus.com/pages/publications/105032542257

UR - https://elibrary.ru/item.asp?id=86677904

U2 - 10.1086/739306

DO - 10.1086/739306

M3 - Article

VL - 16

SP - 108

EP - 131

JO - HOPOS

JF - HOPOS

SN - 2152-5188

IS - 1

M1 - 4

ER -