Two Efforts To Remove The Mystery Of Calculus

Calculus still lacked rigidity in the very long time after its establishment. Since 1950's to his death, Marx had been paying attention to differential calculus and trying to overcome the crisis in the foundations of differential calculus. Marx had made much comment on calculus, and Engels also had expressed his opinions on differential calculus. In fact, Marx and Engels, the two non- mathematicians, had put forward the methods to the crisis in differential calculus respectively, but their solution was inconsistent with others. For long time, there is much research about the differential calculus thought of Marx and Engels, but there is hardly a literature which pointed out the difference between the differential calculus thought of Marx and Engels definitely. This paper tried to collect, collate and analyze all the statement of Marx and Engels which they had published and tried to discuss the differences between the differential calculus thought of Marx and Engels further.From this study, Marx's development track of the differential calculus thought can be divided into the following three stages: learning stage, commenting stage and method stage for developing his own idea, while his corresponding thought also shows three following characteristics: (1) the internal logic of his method is consistent and tight;(2)He searches for the philosophic explanation of the problem which can't be resolved during his research in the differential calculus;(3)He adopts the explaining way that is the dynamic state from philosophy concept rather than the mathematician pursue of static state during the process of the differential calculus analysis. In a word, Mark's study on the differential calculus is always in mathematic field and independent of other realms, that is to say, Mark always thinks about these attacks to the differential calculus from the inner part of Mathematics. However, Engels doesn't carry on a specialized mathematics research in the differential calculus, and he always treats the differential calculus as an example to prove the dialectics. Different from Marx, Engels' thought not only depends on his research in dialectics but also in the dialectics theories system. The purpose of Engels' statement on the differential calculus is for the sake of the epistemology study.By contrasting, we find that there is significant differences between the differential calculus thought of Marx and Engels, although both of them always searches for philosophical explanations of the question from Mathematics. On the surface, these differences are characterized by different foundations of differential calculus, different understanding of the concept of infinitesimal, different solution of the crisis in the foundations of differential calculus, the differences between reading, citation and writing style. However, on deep-seated level, these differences are concretely characterized by different starting point of reaching differential calculus, different theory which is used to discuss the problem from differential calculus, different treatment dialectical thinking and formal logic used in Mathematics.