On the \(3n+1\) problem (Q5953269)

The ``Collatz'' problem (or ``3n+1''- or ``Hasse''- or ``Syracuse''- or ``Kakutani''-problem) is to prove that for every \(n \in \mathbb N\) there exists a \(k\) with \(T^{(k)}(n)=1\) where the function \(T(n)\) takes odd numbers \(n\) to \((3n+1)/2\) and even numbers \(n\) to \(n/2\). In the paper under review the author gives a very readable introduction into this field, starting with Collatz-graphs and the connection to equivalent statements in other than number-theoretic or discrete problems, for example in complex analysis. Finally, various open questions and conjectures about the chaotic structure of predecessor sets are discussed.