«Priority Dispute» between Cauchy and Maclaurin or the History of a Mistake.

Abstract

Both students and specialists have to master a large volume of mathematical information mainly through books and manuals, which generally concerns the accepted definitions and proved theorems. However, it is rather difficult to find out texts tracing the genesis of a definite mathematical statement or the life of a certain mathematician. The paper attempts to achieve the balance by describing the invention process of a mathematical theorem. Apart from the activity-production dualism, the paper illustrates the fact that any mathematical statement development demands quite complicated and even contradictive illogical approaches, and only thereafter it gets a rigorous didactic proof (inductive-deductive dualism). The author also elicits the interrelation between an individual and society, the mutual influence of a mathematician and his colleagues - both the close and remote ones in distance and time. Therefore, the analysis of such process as a theorem invention can reveal the fundamental didactic characteristics inherent to mathematics, as well as any other scientific discipline. 

The paper is addressed to teachers, postgraduates and students specializing in natural sciences and technical disciplines related to mathematics.