Collatz's 1957 paper with Ulrich Sinogowitz,[1] who had been killed in the bombing of Darmstadt in World War II,[2] founded the field of spectral graph theory.

In the war years he worked with Alwin Walther at the Institute for Practical Mathematics of the Technische Hochschule Darmstadt.

[3] From 1943 to 1952, Collatz held a chair at the Technische Hochschule Hannover (now Leibniz University Hanover) .

From 1952 until his retirement in 1978, Collatz worked at the University of Hamburg, where he founded the Institute of Applied Mathematics in 1953.

For his many contributions to the field, Collatz had many honors bestowed upon him in his lifetime, including: He died unexpectedly from a heart attack in Varna, Bulgaria, while attending a mathematics conference.