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Learn German, Interestingly @LGcommaI
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#germanculture
Today is the 124-th #birthday of #German #mathematician Heinz Hopf(1894-1971). By ISBN 3-05-500402-7,page 173, Hopf in 1925 became one of only ten men during the 124 years from 1810-1933 whom the #mathematics faculty of #Berlin gave the grade of 'summa cum laude'..
.. for his doctorate. Hopf's relatively old graduation age of 28.5 years (which is old in mathematics, esp. in Hopf's time) is clearly due to #WorldWarOne: at age 18, Hopf volunteered to serve in the #German army, which he did(as a low-ranking officer) for a full four years..
.., in particular participating in the Battle of #Verdun of 1916,in which he was wounded. While on furlough in 1917, Hopf attended mathematics lectures, in particular by Erhard Schmidt, in his hometown of #Breslau (then still a #German town), which impressed him greatly. During..
..the #war, Hopf won the 'Iron Cross' decoration twice: an Iron Cross 2nd Class (pictured below on the left) was awarded on 1916-02-08; an Iron Cross 1st Class (below on the right) was awarded on 1918-06-17(less than three months before the end of the war). Remarkably, his mind..
.. and body were sufficiently unaffected for Hopf to resume his studies in mathematics at the relatively ripe age of 22, in #Breslau and later in #Berlin (Hopf followed his teacher E. Schmidt to Berlin in 1920). Hopf attended lectures by at least the following mathematicians ..
.. (as evidenced by handwritten lecture notes preserved in archives of the ETH Zurich):

Ludwig Bieberbach (1885-1982),
Hans Driesch (1867-1941; not a mathematician),
Georg Feigl (1890-1945),
Richard Hönigswald (1875-1947; not a mathematician),
Adolf Kneser (1862-1930),
..
..
Hans-Otto Kneser (1901-1985),
Carl August Koehler (1855-1932),
Oskar Perron (1880-1975),
Heinrich Rickert (1863-1936; not a mathematician),
Erhard Schmidt (1876-1959),
Friedrich Schur (1856-1932),
Issai Schur (1875-1941),
Ernst Steinitz (1871-1928).
It was especially ..
.. Heinrich Schmidt's influence which brought Hopf to work in topology. By Hopf's own account, Schmidt suggested that Feigl give a lecture series on the (then new) 'Analysis Situs' of Poincaré (»Im Jahr 1920 folgte ich Erhard Schmid an die Universität #Berlin. Unter den vielen..
..Anregungen, die von ihm ausgingen, hebe ich hier nur diejenigen hervor, die direkt die Topologie betrafen: wie schon 1917 in #Breslau einige der Brouwerschen Arbeiten; seinen eigenen Beweis des Jordanschen Kurvensatzes (Preuss. Akademie d. Wiss. 1923), einen Beweis, der zwar..
.. wohl nicht verallgemeinerungsfähig, aber an Eleganz kaum zu überbieten ist; und schließlich regte er an, daß sein damaliger Assistent G. Feigl einen Vortragszyklus über die großen Arbeiten zur "Analysis Situs" von Poincaré hielt. Schmidt ermutigte mich, weiter Topologie zu..
..treiben« Hopf's 1925 dissertation had the title "Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten". Reviewers were Schmidt and Ludwig Bieberbach. Schmidt recommended the very rare grade 'eximium' for the thesis. Bieberbach concurred. The oral exam would..
.. result in the slightly lesser average grade "summa cum laude", mostly because philosopher Max Wertheimer awarded Hopf a mediocre grade for the philosophy-exam. (I will describe the oral exam later.) Only three men were ever awarded an 'eximium' average in mathematics by..
.. University of Berlin: Friedrich Prym in 1863, Hermann Schwarz in 1864, Franz Mertens in 1865.

I will now transcribe and translate Schmidt's review of Hopf's thesis, using the reprint in ISBN 3055004027, page 335-338. Biermann says that the original is written by typewriter,..
.. has handwritten corrections, and handwritten signatures by Schmidt and Bieberbach. The review is dated 1925-02-25. I now start the transcription/translation, using numbered hashtags #SROHT-n, where 'SROHT' is for 'Schmidt's Review Of Hopf's Thesis' and n is a natural number..
.. counting the sentences.

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