I am writing an undergraduate thesis on local and global class field theory from a classical (i.e., non-cohomological) approach and am hoping to obtain copies of the early groundbreaking publications in the field. I am primarily interested in finding English translations of articles from Weber, Hasse, Hilbert, Kronecker, and Takagi from 1850 to around 1935 as possible. A fairly comprehensive list of them is found in Hasse's "History of Class Field Theory" in Cassels & Frohlich's ANT, and I can provide a list if needed. Any recommendations for sites that provide translated back issues of Mathematische Annalen and/or Gottinger Nachrichten from these time periods would be of great utility.


Thank you all for responding! You're answers will definitely help me develop the historical portion of my thesis. In response to several comments, I realized when posting that it was probably naive to assume that English translations of all these works were available but presented the question in the above manner for the sake of brevity.


I actually found your cfthistory.pdf file while googling the subject early in my research and have benefited from it greatly! Small world! :)

I would be fine with library copies of the works, of course, but my university would have to order copies from other institutions. As such, I thought I'd first make sure there wasn't some large repository of translated articles from Hilbert et al. online somewhere.

I can't thank you enough for this list of sources, too! I will definitely attempt to get my hands on as many as possible.

Thanks again for helping and posting your history of CFT online!

@Ben Lenowitz:

Thank you for pointing me to the Gottingen database. I haven't been in awhile and not while searching for these articles. I will give it a shot.

  • $\begingroup$ Have their collected works been translated into English? $\endgroup$ Feb 24, 2010 at 1:51
  • $\begingroup$ Haven't a lot of Emil Artin's papers on the subject been translated? I would think he's as good a source as any of those you've listed. $\endgroup$ Feb 24, 2010 at 2:10
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    $\begingroup$ You might find the answers to this question useful: mathoverflow.net/questions/8351/… $\endgroup$ Feb 24, 2010 at 2:14
  • $\begingroup$ Hilbert's Zahlbericht has been translated into English. :amazon.com/Theory-Algebraic-Number-Fields/dp/3540627790/… $\endgroup$ Feb 24, 2010 at 2:17
  • $\begingroup$ The French version is freely available at numdam.org. Serach for Auteur=Hilbert and Journal=Annales de la faculté des sciences de Toulouse. $\endgroup$ Mar 4, 2010 at 2:18

5 Answers 5


First, there's no need to focus on online copies, as asked for in the question. We used to have things called libraries which contain journal articles in them. :) Try looking there.

More seriously, I think your task is to a large extent hopeless. Most of those works were never translated into English. But there are numerous English language sources which describe some aspect of how class field theory was originally developed and you should start there.

Here are some:

G. Frei, Heinrich Weber and the Emergence of Class Field Theory, in ``The History of Modern Mathematics, vol. 1: Ideas and their Reception,'' (J. McCleary and D. E. Rowe, ed.) Academic Press, Boston, 1989, 424--450.

H. Hasse, ``Class Field Theory,'' Lecture Notes # 11, Dept. Math. Univ. Laval, Quebec, 1973. [This is basically adapted from his paper in Cassels and Frohlich, but has some nuggets that were not in C&F.]

K. Iwasawa, On papers of Takagi in Number Theory, in ``Teiji Takagi Collected Papers,'' 2nd ed., Springer-Verlag, Tokyo, 1990, 342--351.

S. Iyanaga, ``The Theory of Numbers,'' North-Holland, Amsterdam, 1975. [The end of the book has a nice exposition of how alg. number theory developed up to class field theory.]

S. Iyanaga, On the life and works of Teiji Takagi, in ``Teiji Takagi Collected Papers,'' 2nd ed., Springer-Verlag, Tokyo, 1990, 354--371.

S. Iyanaga, Travaux de Claude Chevalley sur la th\'eorie du corps de classes: Introduction, Japan. J. Math. 1 (2006), 25--85. [Are you OK with French?]

M. Katsuya, The Establishment of the Takagi--Artin Class Field Theory, in ``The Intersection of History and Mathematics,'' (C. Sasaki, M. Sugiura, J. W. Dauben ed.), Birkhauser, Boston, 1995, 109--128.

T. Masahito, Three Aspects of the Theory of Complex Multiplication,
``The Intersection of History and Mathematics,'' (C. Sasaki, M. Sugiura, J. W. Dauben ed.), Birkhauser, Boston, 1995, 91--108.

K. Miyake, Teiji Takagi, Founder of the Japanese School of Modern Mathematics, Japan. J. Math. 2 (2007), 151--164.

P. Roquette, Class Field Theory in Characteristic $p$, its Origin and Development, in ``Class Field Theory -- its Centenary and Prospect,'' Math. Soc. Japan, Tokyo, 2001, 549--631.

H. Weyl, David Hilbert and His Mathematical Work, Bull. Amer. Math. Soc. {\bf 50} (1944), 612--654. [Hilbert's obituary]

I did write up something myself about a year or so ago on the history of class field theory just to put in one place what I was able to cobble together from these kinds of sources. See


which contains the above references as the bulk of the bibliography (I did not just type all those articles references above by hand!) The main thing which had baffled me at first was how they originally defined the local norm residue symbol at ramified primes. I give some examples of how this was determined in the original language of central simple algebras.


There is no reason to expect that any of these articles have been translated. As pointed out in comments and the linked threads there are some books that have been translated and some secondary sources in English. But for the articles themselves you'll have to read them in German. For my undergrad thesis I translated one of Artin's articles. You might want to try translating one article you want too.

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    $\begingroup$ Just a note - You will probably be able to find most of the articles that were published in German journals at the GDZ website: gdz.sub.uni-goettingen.de $\endgroup$
    – user1073
    Feb 24, 2010 at 3:05

As a starting point for online sources for those of us without a thing called library nearby I recommend Rehmann's list.

BTW I think that Furtwängler's name is missing from your list; he proved the existence and all the main properties of Hilbert class fields between 1902 and ca 1910.

Finally, the letters between Hasse and Artin, along with quite a lot of comments, are available here (as a free pdf file; unfortunately it is in German).

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    $\begingroup$ "unfortunately it is in German" : Maybe learning some German is not a bad investement if someone is interested in the history of class field theory ! $\endgroup$ Mar 3, 2010 at 14:26

Recently I found that some of Takagi articles were published in a Botany journal (?!) called "The journal of the College of Science, Imperial University of Tokyo, Japan".

Iyanaga, in his "The Theory of Numbers", cites three articles by Takagi published in this journal:

[1] Über die im Bereiche der rationalen komplexen Zahlen Abelscher Zahlkörper, J. Coll. Sci. Tokyo 19 (1903), Article 5, 1-42.

[2] Über eine Theorie des relativ-Abelschen Zahlkörpers, J. Coll. Sci. Tokyo 41 (1920), Article 9, 1-133.

[3] Über das Reziprozitätsgesetz in einem beliebigen algebraischen Zahlkörper, J. Coll. Sci. Tokyo 44 (1922), Article 5, 1-50.

All three of them are available in the links above.

Actually, there are some nice illustrations in the Botany articles :)

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    $\begingroup$ It was not a botany journal. As the name suggests, it was a journal that accepted articles from many areas of science. $\endgroup$
    – S. Carnahan
    Apr 19, 2018 at 2:20
  • $\begingroup$ Dear @S.Carnahan. The name also confused me, but wikipedia and another page indicated that it was a Botany journal. Perhaps it published mainly Botany articles. Anyway, please edit my answer if I'm wrong. $\endgroup$
    – efs
    Apr 19, 2018 at 13:10

Latest document to become available online :

Chevalley, Claude (1934): Sur la théorie du corps de classes dans les corps finis et les corps locaux.


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