On the history of analysis. The formation of definitions

TL;DR

This paper traces the historical development of mathematical analysis and definitions from the 17th century to the early 20th century, highlighting shifts in conceptual understanding and the emergence of descriptive set theory.

Contribution

It provides a historical overview of the evolution of definitions in analysis, emphasizing the transition from classical to descriptive and structural approaches.

Findings

Distinction between concept volume and structure established in 17th century

Introduction of descriptive definitions in Cantor's set theory

Development of descriptive set theory in Moscow in early 20th century

Abstract

The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou l'art de penser". They were the first, who distinguished between the volume of the concept and its structure. They created a tradition which was strong in math till XIX century, especially in France. The definitions were in binomial nomenclature mostly, but another type of definition appears in Cantor theory - it was the descriptive definition. As it used to be in human sciences, first the object had only one characteristic, then as the research continued it enriched with new characteristics so we have full-fledged conception. In this way the mathematics acquired its own creativity. In 1915 Lusin laid down a new principle of the descriptive theory: a structural characteristic is done, the analytical form had to be found. New schools of descriptive set theory appeared in Moscow in the first half of the 20th century.