I love proving different things on mathematics, I mean, I love knowing where math theorems, methods and formulas come from. But most math books don't prove or show that kind of things. Do you know any book that could satisfy my wish? Obviously, there are lots of branches of mathematics, but I'm asking you to tell me, for example, "Oh, I know that X book proves all calculus theorems", "I've got a book called X that explains where all geometry formulas come from", etc.
Thank you
On
Proofs from the Book by Aigner and Ziegler is a book which covers a broad range of mathematical fields. I would say it is a good book if you are after learning the proofs for famous theorems, but not so good if you want to practice proof writing for yourself - it depends what you are looking for.
If I understand you well, you have not one, but two questions.
The first one is about proving theorems. This one is fairly simple... I would say that all serious math books prove theorems! Then it is difficult to be more specific as it highly depends on the domain you're looking for (algebra, calculus...) and your level.
The second one is about history of theorems. Here, it is more difficult.
The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (Sterling Milestones) is pretty good, but very broad. I think that if you want to touch at a more specific area, you need again to be domain specific (number history, geometry...).