When should people ask naive questions?

Question

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:

1. Ask my adviser or some grad students.

2. Do as thorough an Internet search as possible. Look for the answer in papers that may provide a clue.

3. Ask my questions on MathStackExchange. If I don't get an answer there ask on MathOverflow.

4. 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.

Answer 1

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.

Answer 2

To build on what Buffy said: my experiences have been that people don't mind questions, even 'naive' ones. What they mind are questions being asked that show you've done no effort on your part to find an answer. Based on the fact that you have an algorithm to find answers, I cannot imagine that you fall into that second category! If anything, it sounds like you are worried you've gone too far out the other side: that is, are you spending too much time doing your own research when you can get the needed information faster. That's a bit more of a personal decision, so I can't tell you about you, only about me.

I don't think people (as whole) or academics (in particular) have any idea how complicated ideas get. For most any grad-school-level topic, there's a ton of background information that goes into it that most experts forget that they had to acquire. (what I consider "the expert's blindspot" but wikipedia has listed as "the curse of knowledge".) I have found that experts who are reminded of the level of complexity of background information respond to questions (that some might think are naive) quite well. It's when experts still have that blindspot that they think a question is 'stupid / foolish / naive' (etc.)

By showing that you have done some research on your own, you help remind the experts that learning is hard and involves a lot of steps and that you are trying. I can be prone to the idea of "oh, I don't want to bother so-and-so", but I have learned to overcome that (to some degree). As long as I have shown some level of research on my part, I have found that answers are not hard to come by, as long as I am willing to ask them. (Lastly, most experts love to talk about their topic. Getting an expert to talk about their area of expertise is usually pretty dang easy!)

Answer 3

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.

Reputations tend to develop based on facts. If you want to develop a reputation as knowledgeable, then get knowledgeable, by asking questions when you don't know something. In other words, you are doing the right thing by asking questions. Don't worry if it is a "naive" question, of if you are afraid you will look silly. If you don't know the answer, and you can't figure it out yourself, then ask for help. You are a student after all! Gradually you will develop more knowledge, and your reputation will eventually reflect that knowledgeable state. Professors are much more impressed by a grad-student who is hungry for knowledge and unafraid of embarrassment than one who covers up their lack of knowledge by being afraid to ask 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 enthusiastic response, or uncertainty from experts as to the answer.

"It's obvious" is a shitty answer, and whoever told you that is a shitty teacher. If it's not obvious to you at graduate level then it is probably not obvious, and your professors should attempt to elucidate it for you. If you are having trouble with exercises assigned to you then this may reflect a lack of preliminary knowledge in techniques needed to solve those problems, so try to solve it as an exercise and come back for more help when you've hit a wall. If the experts are uncertain then that means you are approaching the level of problem where things are getting pretty difficult. Keep asking questions and bringing tenacity to your problems and eventually they will crack.

A postdoc friend confided in me that he doesn't post questions because he's worried he'll look stupid.

That approach is what looks stupid to me. I learn really fast because I ask a lot of dumb questions that make me look stupid. You'd be surprised how much you learn when you do that.

Answer 4

I advise to stick with your process. Yes it is less efficient for you but the world of mathematics professors does not owe you a duty of personal tutoring. ALSO, you may find some tangential gains along the way.

It's not so much that you are scared to bother the great men but that you need to build your own muscles also. That said, I would be a little more direct and quick to ask questions of professionals at your institution (versus letters out of the blue to people offsite). Over time you will build up a directory of people inclined to help you, knowledge of the library, benefits of Dover paperbacks, etc.

Also anyone who is teaching you, you should mercilessly exploit. Even if they get prickly or try to brush you off..let that roll off your back like duck water and just keep grinding. Go to every office hour and wear them down.

Answer 5

Your algorithm lacks non-Internet literature search. Even in this age, the best-organized mathematical expositions are still in books and in pre-Internet papers. By excluding pre-Internet resources, you are missing on opportunity to learn the "common" background.

You should browse your library shelves (preferably physical, but virtual also work). You should search papers not simply on Internet, but on MathSciNet/Zentralblatt first.

And don't stop asking questions.