Editing Vladimir Arnold (section)

=== Hilbert's thirteenth problem ===
{{see also|Kolmogorov–Arnold representation theorem}}
The problem is the following question: can every continuous function of three variables be expressed as a [[function composition|composition]] of finitely many continuous functions of two variables?  The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of [[Andrey Kolmogorov]]. Kolmogorov had shown in the previous year that any function of several variables can be constructed with a finite number of three-variable functions. Arnold then expanded on this work to show that only two-variable functions were in fact required, thus answering the Hilbert's question when posed for the class of continuous functions.<ref>{{Cite web|first=Stephen|last=Ornes|date=14 January 2021|title=Mathematicians Resurrect Hilbert's 13th Problem|url=https://www.quantamagazine.org/mathematicians-resurrect-hilberts-13th-problem-20210114/|website=[[Quanta Magazine]]}}</ref>