Memories of Paul Koebe

Huber Cremer (1897-1983) studied at the University of Berlin for his doctorate, advised by Ludwig Bieberbach, and was awarded the degree in 1927 for his thesis Zum Zentrumsproblem. He was then Paul Koebe's assistant in Leipzig for four years. He tells of his time with Koebe in 'Erinnerungen an Paul Koebe', Jahresbericht der Deutschen Mathematiker-Vereinigung 70 (1968), 158-161. We give a translation of this article below:

Memories of Paul Koebe
by H Cremer in Merzhausen near Freiburg im Breisgau

I am happy to respond to the request of the editors of the annual report to share some personal memories of Paul Koebe. I was an assistant to him for four years (1927-1931) and had such a good opportunity to get to know him both on and off the job. Koebe was not only an important mathematician, he was also a personality of great calibre and a man with great humour. A very lovable nucleus was hidden in his rough shell, which only those who could be with him for longer could see.

My first encounter with Koebe, which soon led to my job as an assistant to him, was quite amusing. At that time (1927) I had just finished my doctorate and worked that morning in the library room of the mathematics seminar at Berlin University, which also served as a place for assistants to stay. At that time there were no separate lounges or even separate rooms for assistants. When the assistants went to a number theory lecture from Schur, one said to me:

"Mr Cremer, this stupid dental technician who is imagining that he has solved the squaring of the circle will certainly come back soon, please brush him off." "What does he look like?" I asked. "He's unmistakable," said the assistant, "not exactly slim, not dressed like the Prince of Wales, quite unmistakable. When you see him, you will know that it is the man." "Thank you," I said, looking forward to the announced visitor like the servants in Schiller's "Walk to the Iron Hammer".

A man came ten minutes later, and I was convinced that the description would fit in every way. He came in and without further ado he asked: "Is there any ordinary professor here?" - "No," I said, "everyone is travelling abroad." "Isn't there at least one assistant?" he asked further. "No," I remarked, "they're all in Schur's number theory V". "Do you read number theory here in a five-semester cycle?" "In a twelve-semester cycle," I replied. "When is the lecture over?" he wanted to know. "Schur lectures four hours in a row," I explained, "the lecture only ends after 2 p.m. and then there is usually still an hour of discussion." "Very strange," he said. I already hoped that he would leave, when he suddenly said: "Because I'm Koebe". "What! are you the Koebe?" I cried and all the clouds fell away. As a function theorist, of course I knew a lot about the great Koebe, but I had never seen him before. Now everything was different in one fell swoop. A long conversation about our great love, functional theory, concluded our first encounter.

A few weeks later, Koebe wrote asking me whether I wanted to come to Leipzig and become his assistant. I became it at the beginning of the 1927 winter semester.

During the negotiations to take over the assistant position, he showed me his collection of offprints and emphasised that it was the largest private collection of offprints in Germany and maybe even in Europe. It was really huge and spanned two large rooms.

I had no inkling of anything good because it was clear to me that as an assistant I would be responsible for keeping this collection in order. So I asked, "What is the point of having such a large collection of offprints?" "Well," replied Koebe, "we now have an appointment in Leipzig (it was the ordinary professorship that van der Waerden was appointed to later), so I just let my assistant pick out the special offprints and put them on the desk, then I know immediately how much the gentlemen have written." "Pardon me", I said, "do you do that in Leipzig by weight?" "Oh no," Koebe replied ambiguously, "of course we also take the quality of the paper into account."

Koebe was a mathematician with all his heart and soul. He had the gift of being able to get others excited about mathematics, especially for function theory, that he loved more than anything.

Koebe's seminars were very lively. Here we got to know in particular his great work on the theory of uniformization. There was a lot of discussion and every single step was discussed. Koebe himself always took part in the seminars personally and tried to give even the less gifted students a deeper understanding of the difficult issues.

His lectures were also very lively. He outlined the big picture. He kept emphasising that every analytical function is an "organic whole". As the lion can be recognised by the smallest piece of its claw, the entire function of an analytical function is already given by a functional element.

In September 1921 the annual meeting of the Deutsche Mathematiker-Vereinigung took place in Jena. Koebe introduced his major presentation as follows:

"There are many areas in mathematics where you earn yourself rightful merit by discovering new results. They are mostly long and steep mountain slopes for bleating goats. But the theory of functions can be compared to a lush marshland, especially suitable for large cattle!"

Koebe wrote his scientific work all by himself. His assistants were not involved in this, not even when carrying out secondary calculations, and were hardly ever used to make corrections. So they were in no way forced to work exactly in Koebe's direction, but were allowed to pursue their own inclinations.

Koebe was not interested in applications. "I was told that my distortion rate could make a million dollars in the aerospace industry," he said. But he never tried to earn this million or even a thousandth part of it. He remained a pure mathematician who found the applicability of mathematics profane.

Koebe could occasionally become sarcastic, so that he might appear to others as "a bigwig". But he certainly was not. You could strike back, he expected that, and he enjoyed it. In any case, I have occasionally taken great liberties that have not harmed me in any way.

Once he had asked me to do a certain calculation. But I had not got round to it and wanted to make excuses for not doing it, that it had been more difficult than expected, and I was not finished yet. Koebe gave me a long hard look and said: "Tell me, Mr Cremer, did you have such arithmetic problems at elementary school?" That hit hard. The next morning, Koebe's calculation was completed to his satisfaction.

But I soon had the opportunity to reciprocate. One thing Koebe had in mind was the so-called "Göschenkultur". In particular, he found that the "Little Knopp" was in no way sufficient as the only textbook for the students. "Now our students come, read the "Little Knopp" and then think they have learned function theory!" After he had said this again very emphatically in a lecture, the next morning I found Koebe intensely busy with the "Little Knopp" shortly before nine o'clock. He used it to prepare his lecture. "What, you, Professor," I said, "are you reading Little Knopp?" "What does that have to do with you," growled Koebe gruffly. "Nothing," I countered, "and yet I can say here with Mephistopheles: I find my pleasure in it, too."

That's how I got to know Koebe up close for four years. After becoming a lecturer at the University of Cologne in 1931 and a professor at the Technical University in Breslau in 1940, I only saw Koebe occasionally at congresses and during visits to Leipzig, for the last time in autumn 1944.

Paul Koebe deserves to continue living as a person in the memory of mathematicians. Perhaps I can contribute a little with these lines.

Last Updated September 2020