Toeplitz joined a group of young people working with Hilbert: Max Born, Richard Courant and Ernst Hellinger, with whom he collaborated for many years afterward.

During this period he also published a paper on summation processes and discovered the basic ideas of what are now called the Toeplitz operators.

In 1929, he cofounded "Quellen und Studien zur Geschichte der Mathematik" with Otto Neugebauer and Julius Stenzel.

The book introduces the subject by giving an idealized historical narrative to motivate the concepts, showing how they developed from classical problems of Greek mathematics.

[1] Here is how Gottfried Köthe, who was Toeplitz's assistant in Bonn, described their collaboration: Otto liked to take walks and talk about scientific questions.

In his protocols of mutual meetings, sometimes it is marked that the results as drafted were found at a walk along the Rhine river ...As we advanced with our joint work, naturally, new questions arose, and we became more daring, setting ourselves higher goals.