On the Kolmogorov-Arnold representation theorem for continuous functions

Abstract

In 1900 at the International Congress of Mathematicians in Paris, D. Hilbert posed 23 questions that later became known as Hilbert's 23 problems. Number 13 remained unresolved for over half a century until 1956 and 1957 when A. N. Kolmogorov and his student V. I. Arnold, in a series of three papers, provided the solution. In this paper, I present Hilbert's 13th problem as well as give my interpretation of Kolmogorov's solution to this.