On Hilbert's 13th Problem

TL;DR

This paper discusses Hilbert's 13th problem, demonstrating that any continuous multivariable function can be expressed as a superposition of continuous univariate functions and addition, highlighting a fundamental property of continuous functions.

Contribution

It proves that continuous functions of multiple variables can be decomposed into superpositions of univariate functions and addition, advancing understanding of function representation.

Findings

Any continuous multivariable function can be represented as a superposition of univariate functions and addition.

The result provides a constructive way to decompose complex functions into simpler components.

This work confirms a key aspect of Hilbert's 13th problem regarding function superpositions.

Abstract

Every continuous function of two or more real variables can be written as the superposition of continuous functions of one real variable along with addition.