How to refer to a theorem in a book of which I don't know the source?
Contrary to intuition, it is often inappropriate to try to cite well-known and foundational material to its original source. The reason is that you did not actually learn the material in its original form but instead from some modern reinterpretation of that material (e.g., in a standard textbook).
To see why, try reading the original for something like Newton's Laws of Motion. First of all, it's in Latin. Even if you get a translation, however, you'll find that the notation is strange and difficult to comprehend. That is because even though the fundaments of Newtonian physics have not changed in the centuries since it was discovered, we have improved greatly in our ability to understand and teach the material, as well as in how we integrate it with other material.
In short: if it's textbook material, it is most honest to cite a textbook as your source. Two modifying notes, however:
- It doesn't have to be the textbook that you personally learned from---any good presentation will do.
- You only need to cite a textbook if some of your audience may be unfamiliar with the material. In a computer science paper, the halting problem needs no citation; in an interdisciplinary paper expected to be read by e.g., economists or biologists, it does need a citation.
I'm not sure how things are done in math, but if these theorems are "quite standard" and common knowledge, I would think you could mention them, and say something along the lines of "for a reference" or "for further discussion" see XYZ textbook