Here are a few notes about the specific types of questions you mention: > "Why and how the author explained conceptX this way?" Questions like this will rarely have a good answer unless the author happens to be available for providing it (the rest of us can at most speculate on his reasons). This is not to say that it may not turn out to have a good answer in some special cases (sometimes, the reason will be clear to people with more experience in the field), but it means you need to be a bit careful with them. > "What if we reject definitionY?" It depends on what you mean by "reject". If you mean "do not accept as the definition" then that is not really a question about math (technically, you can define things precisely how you want). > "What is the logic behind assumptionZ?" The answer to a question like this will almost always be "look through the proof and see where it is used", though sometimes there might be some subtlety involved, in which case it can make for a good question. > "The definitionX′ can be proved from the definitionY′ so why the author quote X′ as a definition?" Definitions cannot be proved, so I don't quite see how a question like this could arise. > "How the author deduced the statementY from the statementX" These are generally good questions, and the more specific you can be about which step in a given proof seems like it is missing detail, the better. All in all, if you keep the above comments in mind, I think you will find that your questions will be well received, and that you should be able to learn a lot from using this site.