**Paul Koebe** was a German mathematician who worked on complex functions. His colleagues found him brilliant but difficult.

- Hermann Koebe set up a metal foundry with a copper smithy for pump manufacture in Poststrasse, Luckenwalde in 1878.
- Hermann Koebe products have been used worldwide.
- Koebe's pump "Triumph" can be blown out and blasted on in a few seconds by one man without any physical exertion.
- Koebe received his elementary school education in Luckenwalde and then attended the Joachimsthalsches Gymnasium in Berlin.
- The course, which was based more on practical applications than that of the more academic gymnasium, still qualified Koebe to enter university.
- Koebe was awarded his secondary school certificate in 1900.
- There he attended lectures by the physicists Ludwig Claisen (1851-1930) and Philipp Eduard Anton von Lenard (1862-1947), and the mathematicians Goetz Martius (1853-1927), and Paul Stäckel.
- The additional examiner for the oral on his thesis was Friedrich Schottky who had been appointed to Berlin in 1902 while Koebe was in the middle of his studies.
- Koebe was awarded his doctorate from the Friedrich-Wilhelms-Universität of Berlin on 24 June 1905.
- Koebe also studied for three semesters at the Charlottenburg Technische Hochschule.
- Koebe undertook research at Göttingen for his habilitation presenting his thesis in 1907.
- Koebe never tired of composing new variations on this theme.
- Abandoning this unwieldy instrument, Koebe and Poincaré now reached their goal by combining H A Schwarz's idea of the universal covering surface with simple estimates of the Harnack type for harmonic functions.
- It was in 1907 that Koebe achieved this most famous result on the uniformization of Riemann surfaces, it being a major contribution to Hilbert's Twenty Second Problem.
- Koebe resolved the problem in the one-dimensional case.
- Shortly after 1900 Koebe had established the general principle of uniformization which had been originally conceived by Klein and Poincaré.
- Ludwig Bieberbach was nearly five years younger than Koebe who was a docent at Göttingen during the time that Bieberbach was undertaking research for his doctorate advised by Felix Klein.
- Koebe proved to be a major influence on the direction of Bieberbach's research.
- Paul Koebe had proved an earlier theorem about bounds on the distortions caused by such maps, and Bieberbach's introduction to his paper in volume 4 of the 'Mathematische Zeischrift' (1919) explicitly said that Koebe's "distortion theorem" contributed nothing to his "rotation theorem." There are two questions here: the existence of bounds of a certain type (the qualitative question), and obtaining explicit, perhaps best possible, bounds (the quantitative question).
- In 1920, in volume 6 of the same journal, Koebe ...
- In 1921 (same journal, volume 9) Bieberbach publicly replied, sort of admitting Koebe was right, but saying that quantitative results were his aim, and anyway, both Koebe's theorem and his rotation theorem flowed directly from another theorem of his: "My conjecture that my 'surface theorem' is the true root of all results known up until now about the behaviour of univalent mappings has thus found complete confirmation." In 1922 Edmund Landau took up the matter in his advanced seminar and wrote Koebe and Bieberbach a joint letter.
- Although clearly an outstanding mathematician, nevertheless, Koebe had a reputation for stealing the ideas of others, particularly younger colleagues.
- Koebe was considered a conceited and disagreeable man with a reputation for picking up the ideas of younger people and, because he was so quick, being able to finalise and publish them first.
- Koebe rushed off a paper on the same subject and thus claimed independent credit for the result.
- Then Koebe showed up at a seminar where Courant was scheduled to speak on his thesis and by virtue of seniority took the position of speaking first.
- They rigged up an elaborate apparatus and hid it in a chamber pot under the lectern of a class Koebe was teaching.
- An alarm sounded at erratic intervals as Koebe lectured.
- Another famous mathematician whom Koebe seems to have stolen ideas from was L E J Brouwer.
- The introductory lecture by Klein, which gave a general orientation, was followed by the lectures and presentations by Brouwer, Koebe, Bieberbach and Hilb.
- After the session, a discussion took place which Koebe did not accurately describe in his report, rather turning it to his advantage.
- However, already at that time several warning voices said to me: 'All that, you have explained now to Koebe, you will only with the greatest effort be able to claim as your property, as soon as he has understood you', and indeed Koebe displayed some symptoms that seemed to bear out those voices.
- All the same, it is important to me to answer here, for your information, Koebe's objections against my note .
- Here Koebe is moving around in a circulus vitiosus: for on the one hand he demands me to praise his as yet unpublished work extensively, on the other hand he tries to prevent me from learning its contents.
- After it was published Brouwer realised that there had been changes to one of his footnotes, the changed footnote giving Koebe much greater credit than his original did.
- People at the time believed that Koebe himself had made the change in Brouwer's note.
- To a trustworthy friend of mine who years later asked him about this incident, Koebe explained it as a trick somebody played on him.
- The above quotes give a very negative impression of Koebe as a person, and this does appear to be the general view of his colleagues at the time.
- There is, however, a more positive view expressed by Huber Cremer (1897-1983) who was Koebe's assistant from 1927 to 1931.
- Koebe was appointed to Leipzig University in 1910 as an extraordinary professor of mathematics.
- Koebe's style was pompous and chaotic and, as we have shown above, Koebe anecdotes were famous in Germany between the two wars.
- Freudenthal, who like Koebe was born in Luckenwalde, also tells us that Koebe's life-style was, as his mathematics, chaotic.

Born 15 February 1882, Luckenwalde, Germany. Died 6 August 1945, Leipzig, Germany.

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Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive