Leopold Kronecker’s conception of the foundations of mathematics

Abstract

Kronecker’s views on the foundations of mathematics are often reduced to jokes and regarded as an outdated set of ill-assorted ideas. A closer look however shows that they constitute an original and coherent doctrine justified by epistemological convictions. This doctrine appears in the article On the concept of number, published in the Journal of Crelle (1887) and, especially, in the last course taught by Kronecker, in Berlin in the summer semester of 1891. This article would attempt to state the principles and insights of Kro-necker’s doctrine by comparing it to other foundation schools of thought so as to underline its originality and show the influence this doctrine exerted on Kronecker’s own mathematical work.