How to ask dumb questions

Keep asking the dumb questions! It is better to look like a fool, than to be one.

You worry that many speakers are annoyed at the `elementary' questions. Some speakers do it because they are stressed about public talking, and any question upsets them. For some, communication of mathematics is not the aim of the talk; they give it because it is a condition of travelling to the venue, or simply because everyone else gives the talks. Instead of feeling joy at an opportunity to clear the confusion, they might get annoyed at having to do the extra work of explaining some of the background. The annoyance has no long-term effect --- nobody holds grudges for asking dumb questions. To give up actually understanding math for such a petty reason is just not worth it.

There is only one situation in which you should refrain from asking a question. That is when you are representative neither of the actual audience nor of the intended audience. So, if you are graduate student at your department's colloquium, it is OK to ask anything. If you are a graduate student at a seminar in your field, it is OK to ask anything. If you are at a seminar in another field, and there are several other students in your field in the room, again it is OK to ask anything. Only if you a lone outsider at a seminar or a conference that is not in your field, there is a reason not to ask questions.

Before asking a question, ask yourself the following:

If I get a nice detailed and understandable answer to this question, will I be able to understand a significant part of the rest of the talk?

If the answer is "no", then you should probably not ask the question even if there really is some ambiguity that could be cleared up, because chances are that asking the question will not benefit anyone (i.e. that those who are able to understand the talk would also be able to answer the question themselves).

If the answer is "yes", then that is a good start. In that case you should probably ask the question unless it is something you really ought to know (if you don't know that it is something you should know, then that is usually good enough). Of course you don't want to become known as "that annoying grad student who keeps asking trivial questions", but you also don't want to miss out on learning something from the talk because you are missing some small detail, and usually the above will limit the number of questions you ask sufficiently that people should not be annoyed.

There is no such thing as a dumb question is a good adage for the classroom, where our mission is to teach students, and we have a number of weeks to accomplish the learning objectives. We use this maxim to encourage students to ask questions rather than fall behind.

However, there is such a thing as an annoying question can be an equally true corollary, particularly in a conference setting where someone is trying to cram months worth of research into a 45-minute talk in front of presumed experts in the field. In such cases, it might be preferable to not derail the speaker's presentation.

How can I tell if my question is "dumb" (i.e. the answer is well-known or searchable), or if it addresses legitimate ambiguity?

Really, there's no way to tell for sure during the talk. However, if you venture to ask your question, you can preface it with something like:

"I'm sorry if I'm asking something obvious here, but..."

So far, my answer doesn't really differ from some of the other advice you've gotten in other answers. However, I want to address the professional etiquette part of your question. While you are asking your question, and in the immediate wake of getting the question out of your mouth, pay careful attention to the body language of the audience at large. If you see several heads nodding affirmatively, that might be a good indication that you were brave enough to ask something that was nagging in the minds of everyone else, and the speaker has made some erroneous assumptions about what was presumed to be fundamental or obvious. However, if you notice some sideways glances accompanied by grimaces or eye-rolls, then maybe you've touched on something that would be better left until the end of the session, or until the next break, in which case you can quickly add:

"If you'd rather discuss that with me off-line, that's okay."

In summary, be aware of your environment:

• What is the purpose of the talk?
• Who is the intended audience?
• What are the speaker's time constraints?

Moreover, be cognizant of non-verbal audience reaction to your initial question, and use that as a barometer before venturing to ask follow-on questions. In my experience, people are rather forgiving the first time a presentation is interrupted by an elementary question, but they begin feeling exasperated when that one question transforms into a hijacking of the presentation as a whole.