Euler and the structure of mathematics
The aim of this paper is to investigate Euler's reorganization of mathematics centered around analysis. The author emphasizes three features of Euler's conception: First, the notion of analysis changed the concept of mathematical theory and made its later development possible. Secondly, the crucial aspect was the rebuilding of the edifice of the mathematical science. Thirdly, his conception concerned the foundations of analysis. His foundations proved to be inadequate to include the new apparatus in a coherent theory and were rejected by mathematicians of the nineteenth century. Thus, the author demonstrates that the use of the term `analysis' in Pappus's sense disappeared from Euler's papers in the middle of the 1730s. Analysis became the science of abstract quantities. The principle of the generality of analysis was the cornerstone of Euler's understanding of analysis. Geometry and mechanics were transformed into a branch of applied analysis.
scientific article; zbMATH DE number 7188915
scientific article