When should people ask naive questions? I'm a graduate student in math and I usually have lots of questions about papers I read. Sometimes my questions are about technical things but a lot of questions I have are about "well-known" facts that I didn't learn from courses or from my background reading. I do think about my question to make sure I can't quickly figure out the answer. What is a litmus test or rule of thumb for asking experts naive questions? Over the years the responses I have gotten were: "It's obvious," "Exercise" (when I never figure out the answer due to lack of knowledge), an ethusiastic response, or uncertainty from experts as to the answer.

I don't want experts to think, "How do you not know this?" I want to develop a reputation as a knowledgeable grad student who has potential as a researcher. A postdoc friend confided in me that he doesn't post questions because he's worried he'll look stupid. And I also don't want to annoy people with lots of trivial questions. But I also know that I have to learn from them, and that it's usually way faster to ask someone in person about their paper than to hit a roadblock in their paper and keep thinking about it.

My algorithm so far goes as follows: 


Ask my adviser or some grad students. 
Do as thorough an Internet search as possible. Look for the answer in papers that may provide a clue.
Ask my questions on MathStackExchange. If I don't get an answer there ask on MathOverflow.
If MathOverflow answers are unclear or I don't get responses, either discuss the answers with my adviser or email an expert out of the blue.


What would be a more efficient algorithm for asking possibly naive questions, if there is one? The main drawback I have encountered is that an expert can sometimes answer my question right away, whereas independent search would take too much time.
Perhaps you are overthinking the effect that asking questions has. Perhaps you are misjudging which questions are "naive". They don't sound naive to you, I think, but you worry that they are naive to others. 

I went to school long ago - mathematics. Before the internet. Before personal (or many) computers. But my solution to having a question was to ask it. I asked a lot of questions. I didn't bother people in their offices for simple(ish) things, but in class I pretty much always had my hand up. My mother was often exasperated with me for asking so many questions as a child, but I never got that sense that my professors were. 

But the effect was that almost everyone thought I was very smart. Smarter, probably, than I really am. It turns out that I was just bold enough to ask the questions that other students were afraid to ask. Some of the questions I asked, of course, were the result of errors made by the prof in lecture and he/she would then correct them, but most were just gaps. 

But the best answer isn't always a direct answer, but a hint as to how/where the answer can be found. The simple answer doesn't usually give the context you need. The "answer to life, the universe, and everything is 42" may be correct or not, but it isn't enlightening. It is the connections between things that are important, everywhere, but especially in mathematics. 

Some may think that you are asking things you "should" already know, but everyone will see you as engaged, rather than complacent. 

It turns out that, just as in a course, in grad school you probably aren't there to prove to people that you don't need to be there. Ask and ye shall receive.