Lately, I writing some essays whose topics are mathematics-heavy. Even though they are not research papers and will never be published, I just want to give proper references to each famous theorem/ideas.

However, finding the original source of each theorem proves to be a much more difficult task than I thought. This brings me to my question

How, in general, do I find the original papers of each famous theorem?

Specifically, how do I find Caratheodory's paper on the extension theory that now bare his name?

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    $\begingroup$ Let me emphasize this point a little. For me, finding the entire paper is not necessary (but I'd good if I can, though), the main point I want is finding the reference source. $\endgroup$ – BigbearZzz Aug 24 '16 at 22:33
  • $\begingroup$ I'd good $\to$ it'd be good $\endgroup$ – BigbearZzz Aug 24 '16 at 22:43
  • $\begingroup$ Are you sure you need these? Given that these results are usually known by their originator's name, the role of the reference as giving credit to the same is void (and further, credit can be addressed in the text). What's important then is to provide the readers with a source that presents the proofs in a language, and with standards of rigour, that the target audience expects. e.g - I think it's lame to refer to Newton/Leibniz when talking about derivatives, since their phrasing is archaic and impenetrable to most. A ref. to the undergrad calculus textbook du jour would be far more useful. $\endgroup$ – stochasticboy321 Aug 25 '16 at 1:22
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    $\begingroup$ @stochasticboy321 I think if you are writing an essay about history of calculus it'd also be appropriate to give the reference to Newton&Leibniz original publications on derivative. Similarly, since I am writing about development in measure theory, I think it'd great to include the reference to Caratheodory's paper. I don't think it's lame at all. $\endgroup$ – BigbearZzz Aug 25 '16 at 8:10
  • $\begingroup$ Yes, I would happily concede in that case, with a lame appeal to the fact that it didn't appear in the body of the question . My rant was more about if, for instance, one was writing notes that folks might refer to later. Oh, and apologies if I seemed too brusque above, the char. limit and caffeine deprivation make one do odd things. $\endgroup$ – stochasticboy321 Aug 25 '16 at 10:57

As you observe, in many cases the most celebrated results are viewed as being so widely known and diffuse that no reference is given. Yes, a bit ironic.

A way to try to circumvent that is to look at as-old-as-possible textbooks/monographs, from times within few decades of the developments you'd want to trace back. Things would seem different to those people... For example, the Whittaker-and-Watson "Modern Analysis" will give (dangit-awkwardly-footnoted-buried...) references to many things that were new then, but not now...

Jesper L-umlaut-utzen's 1984 essay on "Sturm and Liouville's..." gives many original refs.

There is an AMS-published volume "History of Analysis..." which has many original refs.

The quasi-encyclopedic two volumes edited by I. Grattan-Guiness (sp?) are marvelous, with nearly-infinitely-many original references.

(And, if you have the time/energy to double-check, Wiki!!!)

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    $\begingroup$ C's 1918 book mentioned in arxiv.org/pdf/1103.6166.pdf $\endgroup$ – Will Jagy Aug 24 '16 at 22:45
  • $\begingroup$ Thank you very much. I also agree that it's funny when the most famous results are those that are hardest to trace down. $\endgroup$ – BigbearZzz Aug 24 '16 at 22:47
  • $\begingroup$ Ah, good, @WillJagy! Thx. Though I notice that the literal title was mangled, presumably by typo or incomprehension of German: the "ber" is surely something else, maybe "bei", in the title of C's article as cited there. A person could probably check to confirm... $\endgroup$ – paul garrett Aug 24 '16 at 22:48
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    $\begingroup$ It was uber with u umlaut. I put a link (to a preview) in an answer $\endgroup$ – Will Jagy Aug 24 '16 at 22:49

You should find a modern research paper or book citing this theorem. If it gives a reference for it (if not, try another reference), then go to the bibliography and check the reference. Repeat this process with this new reference: this should converge!

Edit: for this kind of theorem (which can be cited in advanced undergraduate courses which never give any reference like this), it's more difficult but in your case https://arxiv.org/pdf/1103.6166 may help.

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    $\begingroup$ I tried it twice, but it seems that the theorem (Caratheodory's) is so famous that the authors don't think they need to put that into the bibliography :P $\endgroup$ – BigbearZzz Aug 24 '16 at 22:33
  • $\begingroup$ Maybe my edit above can help. $\endgroup$ – paf Aug 24 '16 at 22:40
  • $\begingroup$ Interesting! Thank you very much, that might actually works. $\endgroup$ – BigbearZzz Aug 24 '16 at 22:42
  • $\begingroup$ You're welcome! $\endgroup$ – paf Aug 24 '16 at 22:45
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    $\begingroup$ I see, same arXiv piece I found. Their typing was faulty, the second word in the title of C's 1918 book is über .. I meant uber with a u umlaut. Umlauts do not work as well as in answers. $\endgroup$ – Will Jagy Aug 24 '16 at 22:46

Better: they also have his collected works in five volumes,


This link ought to show the same results it showed me, a few dozen items with author Caratheodory:


This would probably not be the very earliest publication, but some recent papers on the arXiv refer to

Carath ́eodory, C, Vorlesungen über reelle Funktionen, 1st e d, Berlin: Leipzig 1918


which would be an entire book. There were later editions and reprints.

Here is the link at the UCB library


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    $\begingroup$ That was amazing! May I ask you which method did you use to search? $\endgroup$ – BigbearZzz Aug 24 '16 at 22:48
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    $\begingroup$ (Good work! ...) $\endgroup$ – paul garrett Aug 24 '16 at 22:50
  • $\begingroup$ @BigbearZzz If I find something relevant I look in the references. The book was a reference, I searched for the title and author. They also have his collected works oskicat.berkeley.edu/record=b14596125~S1 in five volumes. $\endgroup$ – Will Jagy Aug 24 '16 at 22:59

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