How should you respond when a professor answers your question with "It's obvious!"?

Question

I had a math question and I went to my professor's (now a professor at Harvard) office hours (this was a really long time ago). I asked him and he said, "It's obvious!" I sort of said, "OK." I never did figure out the answer to the question...

Answer 1

You can act in two alternative ways:

1. Tell the professor: "Sorry, maybe it's obvious, but I cannot really get it: could you please explain it to me anyway?"
2. Accept that the professor might want you to understand this independently, and go home and bang your head over it until you understand it, whatever time it takes.

About the second point, sometimes students think that if they cannot understand a concept in a few minutes, they have to ask. I sometimes ask my students when they come with a question: "How long did you think about it?". When I was a student, I'd chew over certain concepts for weeks before grasping them, but the reward was a better understanding of those concepts, something that I wouldn't have achieved if I had gone to the professor as soon as I couldn't understand.

Answer 2

Your professor was a jerk.

When someone comes to me with a question they seek an answer to - I do my best to answer it. I may skip some parts and highlight the need to review them (from this we get X, you can check by yourself with the Mologof conjecture, but let's assume that we do have it now. From there ...) but I always guided the student, "bootstrapping" his journey to the solution so to speak.

Now to your question about how to answer that: there is no good way. The bad way is what I did once in a very similar situation (It is obvious for very intelligent people like you, but for the more stupid ones it is not. I am not sure, though, that they are intelligent enough to be able to explain it - or something like that). We had a complicated interaction afterward.

If you really want an answer I would go to someone else because at this point the conversation won't go well.

Answer 3

It probably means: "You should be able to figure that out by yourself". Whether the professor is right about that or not, we cannot know. In any case it looks like they do not wish to answer, so your best bet is to ask your question elsewhere.

Of course, instead of responding with "OK" you could have tried to get an answer by responding with:

• "It is not obvious to me, could you put me on the right track?" (indicating that you really need a hint), or something like:
• "I read X, Y and Z, but could not understand the part where they derived A from B." (demonstrating that you did your best and have a very specific question)

But, obviously (pun intendend), it is impossible to tell from here how they would respond.

Answer 4

Deep knowledge in mathematics (and I suppose other fields) depends on insight, not just facts. What is "obvious" to someone with insight may not be to someone else who hasn't yet gained that insight. This was always my experience studying math. And it takes a lot of hard work to gain that insight. Some of it frustrating until you can say "A Ha".

Perhaps he is suggesting that you think deeper about the issue and come up with your own solution.

You can also, perhaps, tell him that it isn't obvious to you and would he give you a hint. A hint is better than an answer since it might lead you to the insight you lack.

Of course, he might also be wrong.

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See this for an apocryphal story about what is obvious/trivial and what is not in math.

Answer 5

I am late to this question and the other asnwers are great. However, I had a friend who shared with me a realization he had that I think might be helpful to you. If a mathematician thinks something is truly obvious or trivial, they will state it as fact. When they say something is "obvious" or "trivial" what they really mean, is that it is obvious and trivial, now that you know it is obvious. That is, you can show it by doing something naive. So it is okay that you don't find it immediately obvious. Your professor just thinks that if you attack the problem with the fundamentals, you can figure it out. So go back to definitions, basic properties, and/or key theorems, and you'll be able to figure it out!

Answer 6

First of all, the professor should not have said that. It can sometimes be helpful to indicate in a paper or lecture that something follows directly rather than following in less clear way (there's still probably better words for this than "obvious"), but it's never appropriate to answer a question by saying "it's obvious."

That said, I think the best follow-up question to ask here that's most likely to get a good answer is to simply ask:

Why is it obvious?

Hopefully this will not only get you an answer to your original question, but will also get an explanation of what bit of meta knowledge you're missing that's supposed to make it straightforward to work out. It's good to learn why it's true, but it's even better to learn why it's supposed to be obvious.

Answer 7

Grow a Thicker Skin

I know how that answer sounds, but hear me out: I've been in that same situation.

Early in my undergrad, I struggled with basic chemistry. The large-lecture freshman chem was taught by a kind, energetic, and engaging man who consistently won awards for "best professor" from students. For mostly-extracurricular reasons, I flunked.

The off-cycle class was instead taught by a professor who was, shall we say, significantly less well regarded. He clearly spent more time doing research than teaching, and his lecture skills had atrophied. In retrospect, I think he didn't look at any examples ahead of time either. Instead, he would show up to class, talk (briefly) about something current that he found interesting, explain the theory of what he was covering, then spend a large portion of class solving the first half of each of a series of example problems diligently and with careful detail. Often he made some remark like "...and from there the answer is obvious" when he stopped.

In a subject which I had previously found difficult, this approach was somewhat distressing.

What I did after a few weeks was, essentially, what the title says: grow a thick skin. When he stopped solving a problem halfway through, I would (politely) ask him to show us how to solve from there. He would give this look, like I had asked "But Professor, how do you solve '2x=4'?", but he would also solve each one out, with the same diligence and detail as the first half.

It felt terrible to be asking those questions, and to be subject to those looks. But I couldn't afford to repeat the class again, so I had to keep asking. After doing that for a while though, a few things became clear. One, everyone else was struggling just as much with his style, and were very glad to have me (or anyone!) asking for more details. Two, he simply didn't know what parts were hard. I assume that basic chemistry had just been part of his professional life so long that it was all trivial. Either way though, I think he was struggling with what to emphasize as much as the class was struggling to learn.

Ironically, that ended up one of my favorite classes. The initial hump of asking those questions was very difficult (at least for me). But ultimately, it was also empowering to participate much more actively. And once I was already demanding explanations for the examples I didn't understand, asking for explanations of the material was no harder. So, because I was forced to constantly ask for clarifications, the second half of that class ended up being among the clearest and easiest to understand classes I have taken. Learning how and when to push for more details also helped immensely in future classes and in my professional life.

Assume your professor is operating in good faith, and that he wants to teach, and be polite and persistent until you get a satisfactory answer.

Answer 8

One explanation that other answers here have not raised I believe, is very common: Intimidation as a defensive mechanism. People who do not know why something holds, or have a difficulty articulating a clear argument, usually defend themselves by saying things like: "it's obvious", so to intimidate others from questioning them or demanding an explanation.

The professor might be well accomplished in his area, but this doesn't mean he knew the answer or how to explain the argument. Some scholars are good and quick intuitive and effective thinkers, but completely lack the ability to rigorously understand some arguments from first-principles.

In this case, you should simply insist on an explanation, but not too much, as this may offend the professor who is probably trying to conceal their deficiencies. A slightly provocative answer may be: "Yes, this is probably obvious, so I bet it should be very easy to explain!".

Answer 9

Answers to questions addressed to a professor are in general only "obvious" to people who have the relevant background. The professor is being rude and unprofessional and a terrible teacher with that response, but a diplomatic follow up would be something like

It's not obvious to me, so it seems like I am missing some of the prerequisite perspective needed to see the obvious answer. Could you help me identify and fill in that gap in my understanding?

Answer 10

I would reword what XavierStuvw has already said more strongly.

Obvious means easy to explain.

To expand on this... Landau and Lifshitz' Course of Theoretical Physics is INFAMOUS for the overuse of "obvious" to the degree of spawning an entire barrage of meta-jokes. I could offer several takes on it:

• (Professor teaching us QED, rather strong scientist in their own regard): What was obvious to Landau is not obvious to us mere mortals. If you can not explain it in simple and accessible terms, it is not obvious.
• (An amazing professor of analytical mechanics, answering my inquiry about whether I should use Landau's book on the subject as the main course material): Those are books which are good when you already know the subject to gain deeper insight. Do not use it for your first exposure.
• (My own experience studying QM using their books): Feels like attacking a brick wall, you sit there perplexed staring at a single page for quite literally several hours until it indeed becomes obvious to you as well. It feels like a major victory; in hindsight, though, you are not quite sure if it is just your brain tricking you into being convinced just to end the torture. I do believe it actually worked for me, but for me, intuition beats rigor so it is definitely not everyone's cup of tea. But at least at the end of the day I could explain it to others without resorting to "this is obvious".

So this is a judgement call, after all: if your professor thinks that sitting in front of the textbook meditating and becoming one with the subject is THE way to master it, you are out of luck here and would be better off seeking help elsewhere (your peers taking the same course, other professors or even the Internet). Looking it up before bothering other people is a habit you start developing by the end of the university, so if this exchange happened on your 4th year or some such, it might be they are just expecting you to work it out on your own (and that "obvious" is a politesse for "not worth spending my time explaining it to you").

If this is not their general demeanor, well, just ask to elaborate; there are many ways to do so such as "In this case, I am obviously missing something trivial" or "I don't see it" or "Could you outline the actual proof, please?".

I know I parrot Louic and Massimo quite a bit in this answer as well but uh, your question just so happened to attract personal experience-style answers not fitting into comments :)

Answer 11

"Exactly because it is obvious, would you mind it to show me that?" or, at the meta level, "Would you explain what obvious means in this context?".

Explaining obvious things should entail an easy explanation, otherwise it is not obvious.
Consider also the meaning 1 of the entry https://www.merriam-webster.com/dictionary/professor.

My two cents.

Answer 12

My bet is the answer was obvious to any student who should proceed with a mathematics curriculum and you were being evaluated. The fact that you never figured out the answer speaks volumes about whether you should be hired. You might not like that and I'll probably get downvoted, but employers want people who can solve problems even if they can't ask somebody. I was just on a job during which I solved a problem in a day that the rest of the existing team could not over the prior few months. The team had actually solved it, they just didn't know it and did not execute on it - the answer was "obvious".

Anyway, if you want answers from somebody smarter than you, you need to ask the question in such a manner that they feel its worth their time answering.

And lastly, just read through a lot of SO Q&A and enjoy the answers that are like "google is your friend" and "already answered here" and "vote to close as a duplicate" and ... and ... The more you think and that thought is evident in your question (which can be more than one sentence), the more likely you'll get an answer.

[Edit] The subject matter here is mathematics, I didn't see anywhere stated that it was Calculus, trig, or whatever, but math (it is singular) is a "head game", its thinking, its learning how to think. The best way to learn anything is by doing, so the best way to learn how to think mathematically is to think mathematically. The instructor knows this and wants to see it in his students.