The notion of Natural Numbers among Germanic Mathematicians during the Second Half of the 18th Century

Abstract

While the idea of the naturalness of the positive integers is ancient, the idea of the naturals as the foundation of our number system is not. This latter idea, along with other factors, eventually led to the abstract definitions of natural numbers at the end of the 19th century. But, what led to such an idea that was already present among Germanic mathematicians in the first third of the 19th century? This article examines the tensions around the notion of number among the Germanic mathematicians of the second half of the 18th century with the aim of contributing to a better understanding of some of the factors that explain the
emergence of such a different approach to naturals.