How do I find the original paper of each famous theorem?

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?

Solution 1:

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!!!)

Solution 2:

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.