First translation into English of Frobenius' 1893 obituary for Leopold Kronecker. Part 1.

71441 = 199 x 359 days ago, the important #German -Jewish #mathematician Leopold Kronecker (1823-1891) was born in
Legnica (now Poland; at the time, overwhelmingly a German town). His parents were merchants in the part of western #Poland which now is not part of #Germany anymore (Lower Silesia).

Already in 'Gymnasium' (~high-school), Kronecker came into scientific contact with another great German mathematician: Ernst Eduard Kummer (1810-1893), then still a young high school teacher. The friendship between Kronecker and Kummer was a curious one, perhaps unique in the history of #Academia in the following sense: let A and B be persons such that:

• A is a teacher of B in high-school,
• A is full professor at a university U where B studies as a student,
• B succeeds A when he retires from his chair.

The above constraints are satisfied with A=Kummer, B=Kronecker.

Kronecker studied mathematics (and some philosophy and physics) in #Bonn, #Breslau (now: Wrocław), but mostly in #Berlin, and submitted his thesis 𝘋𝘦 𝘶𝘯𝘪𝘵𝘢𝘵𝘪𝘣𝘶𝘴 𝘤𝘰𝘮𝘱𝘭𝘦𝘹𝘪𝘴 in 1845. Kronecker's thesis is considered a good piece of work, but wasn't an outstanding scientifc achievement (which is a rare occurrence for a PhD thesis anyway) like e.g. Heinz Hopf's thesis was. Dirichlet was enlisted as a reviewer (even though by 1845 Dirichlet was not a full professor and needed special permission to participate in PhD procedings). Biermann writes the following interesting passage on p. 48 of ISBN 3‐05‐500402‐7: »Kronecker, nachmals der erste Berliner Ordinarius, der in Berlin selbst promoviert hat, ist bekanntlich in seiner Dissertation „De unitatibus complexis“ zu Methoden und Resultaten gelangt, die mit der wenig später von Kummer geschaffenen Theorie der idealen Zahlen eng zusammenhängen, aber noch nicht bis zu ihr vordringen. Frobenius hat daher die Kroneckersche Arbeit mit einer Chemie ohne atomistische Hypothese verglichen [Fußnote 5:] G. Frobenius: Gedächtnisrede auf. Leopold Kronecker. In: Abhandlungen der Königlichen Preußischen Akademie der Wissenschaften zu Berlin. 1893, S. 1--22.« My translation: ›Kronecker, who later became the first full professor at Berlin who had obtained his doctorate at Berlin itself, has (as is well-known) discovered methods and results in his dissertation 'De unitatibus complexis' which are intimately connected with the theory of ideal numbers created by Kummer, but which did not yet quite reach that far. Therefore, Frobenius has compared Kronecker's dissertation with chemistry without the atomistic hypothesis. [Footnote 5:] Commemorative address for Leopold Kronecker. In: Proceedings of the Royal Prussian Academy of Sciences of Berlin. 1893, p. 1--22.‹

I will now reproduce the above-cited commemorative address by Frobenius, together with my own English translation, using hashtags of the form #FAFK-𝑛, where 'FAFK' is for 'Frobenius' address for Kronecker', and 𝑛 is a positive integer indicating the sentence in the official 1893 edition of (the print-version of) Frobenius' address.

To the best of my knowledge, my translation is the first translation of Frobenius' obituary for Kronecker; I have published it already on Twitter, under the hashtag #FAFK. (See e.g. https://twitter.com/LGcommaI/status/1071172657964560384).

The German text (without translation) of the obiturary was (besides the original publication) republished in the book Print ISBN 9783211958421.

BEGINNING OF PART 1 OF MY TRANSLATION

"Gedächtnisrede auf Leopold Kronecker \ von Georg Frobenius"
My tr.: 'Commemorative Address for Leopold Kronecker By Georg Frobenius'

"Gehalten in der öffentlichen Sitzung am 29. Juni 1893 [Sitzungsberichte St. XXXII. S. 641]. Zum Druck eingereicht am gleichen Tage, ausgegeben am 13. Juli 1893."
My tr.: 'Presented in the public session on 1893-06-29. Proceedings, part 23, p. 641. Submitted to the printer on the same day, distributed 1893-07-13.'

"Für den Verlust, den die mathematische Section der Academie in den funfziger [sic] Jahren durch Jacobi's [sic; this is not the correct possessive form according to contemporary #German orthography LG,I] Tod, durch Dirichtlet's Weggang erfuhr, fand sie bald glänzenden Ersatz in drei Männern, deren Namen die Geschichte der Mathematik stets unter den ersten nennen wird."
M.t. 'The mathematical section of the [Berlin] Academy soon found a briliant replacement for the loss that it had suffered in the 1850s through the death of Jacobi and the move of Dirichlet, namely in the person of three men whose name the history of mathematics will always mention among the very first.'

"Jeder Mathematiker rühmt Kummer's bahnbrechende Schöpfungen in der Zahlentheorie und ist mit seinen schönen Untersuchungen in der Liniengeometrie vertraut."
My tr.: 'Every mathematician praises Kummer's pathbreaking creation in number theory, and is acquainted with his beautiful investigations in line geometry.'

Vocabulary.
'der':the,
'rühmen':to laude/praise,
'Untersuchung': research/investigation(literally: under-search).

"Jeder kennt die grundlegenden Arbeiten von Weierstraß in der Theorie der Functionen und würdigt seine fruchtbare kritische Durchmusterung des gesammten Feldes der Analysis."
My tr.: 'Everyone knows the fundamental work of Weierstrass in the theory of functions und appreciates his fertile and critical survey of the entire field of analysis.'

Remark. 'theory of functions' is a traditional German name for what now is called 'Complex Analysis'.

"Ungleich schwerer ist es, Kronecker's Stellung in der Wissenschaft kurz und zutreffend zu kennzeichnen, weil die weittragenden Entdeckungen, die ihm dauernden Ruhm sichern, nicht in dem Rahmen einer einzelnen mathematischen Disciplin Platz finden."
My tr.: 'It is disproportionately more difficult to characterize Kronecker's position within science concisely and accurately, for the far-reaching discoveries (which secure him lasting glory) do not fit into the frame of a single mathematical discipline.'

"An Vielseitigkeit des Talents, an Schärfe des Urtheils und an der Fähigkeit sich rasch in einen neuen Gedankenkreis eiinzuarbeiten hat ihn keiner übertroffen."
My tr.: 'No one has surpassed him in versatility of talent, in acuity of judgement, and in ability to work oneself into a new circle of thoughts.'

"Aber so hervorragend auch seine Leistungen auf den verschiedensten Gebieten der Größenforschung sind, so reicht er doch in der Analysis an Cauchy und Jacobi in der Functionentheorie an Riemann und Weierstraß, in der Arithmetik an Dirichlet und Kummer, in der Algebra an Abel und Galois nicht ganz heran."
My tr.: 'However excellent his achievements in diverse domains of quantitative research may be, he doesn't quite match Cauchy and Jacobi in analysis,nor Riemann and Weierstrass in complex analysis, nor Dirichlet and Kummer in arithmetic, nor Abel and Galois in algebra.'