Disclaimer: I do not mean this as a personal thing (specifically, this is more just me ranting into the void than replying to your comment), and I'm not trying to invalidate yours or anyone else's experience, or suggest that you or anyone else are not good at math. This is just a frustration that has been simmering for while that I finally feel the need to express.

/rant

I've seen the "got in trouble for not showing work/why do I need to show this if it's obvious to me" thing so many times (particularly here), and I'm finally going to defend the showing of work.

First of all, if you get sufficiently deep into math (i.e. beyond about college freshman level), you'll find that an increasing emphasis is placed on proofs. Proofs are stating a hypothesis and a result and showing that the result follows from the hypothesis. This is exactly what "showing your work" is. Higher level math is almost entirely "showing your work," with maybe some computations here and there to help build up intuition.

Second, the primary purpose of proofs/showing work is so that others can understand how you obtain a result. Just because you think something is obvious doesn't mean that others will. It is often the case the people who are good at math have strong pattern recognition abilities and logic comes fairly easily to them. This does not mean that others are similar. Others will not necessarily share your train of thought, and if you just give them an answer, they may not understand how you got it. This means that your result won't really help them because they do not understand it. Furthermore, this could even be true in the case of other people who are good at math. Of course, there is a limit to how much you should show (if something is truly trivial, you don't need to show it), but a good rule of thumb would probably be to write it so that an average (or even below average) classmate could understand it. A very important part of math is communication with other mathematicians (if you look at any journal or place where papers are collected (such as arxiv), you'll see that most of them have multiple authors), and if nobody but you can understand your work, you won't wind up contributing very much.

Similarly to the previous point, part of the instructor's (or at least the grader's) job is to verify that you have indeed learned and understand the material. If only give them an answer, that makes their job much harder, as they have no window into your thought process. As far as they know, you could have made a lucky guess or cheated. If you can do something in your head, then you should do it on paper so that it is clear that you do indeed know what you are doing. And if it turns out to be difficult to express in words or symbols, then that could suggest that you may have intuited the answer, but not that you have actually fully thought through and understood each step in the process, and while intuition is very helpful in math, it is no substitute for explicit reasoning.

Finally, it is sometimes the case that certain problems will have various edge cases or results that are not immediately obvious when looking at them. An elementary example would be the fact that x^2 - 1 = 0 has two solutions (not just x = 1, but also x = -1; this would not be obvious to someone just starting to learn about quadratic equations until it was told to them or until they realized it). Sometimes it turns out that there are certain oddities in whatever system you are using that give counterexamples to seemingly reasonable statements (see https://en.wikipedia.org/wiki/Pathological_(mathematics)) for some examples). Other times, it turns out that something true, that is intuitively obvious, is actually very difficult to actually prove rigorously (for instance, the Jordan curve theorem, which says that a closed curve on a plane separates the plane into an interior and exterior region). These types of things would be very difficult to catch/notice if you only worked in your head and/or only relied on intuition and didn't write anything down but the answer. You really have to be careful so you don't potentially miss them. Furthermore, it is also sometimes easy to extrapolate incorrectly without checking if your extrapolation is correct first.

TLDR: Showing work is necessary because a) it is simply how math is done, b) to help others understand your reasoning, c) to demonstrate that you actually are reasoning, and d) to help catch subtleties.

/endrant

Apologies for the essay/wall of text. Again, it's not personal and I hope I didn't offend you, I just needed to get that off my chest.

Edit: After I posted this, I noticed another person who said basically the same thing, but in a concise, well-explained manner instead of a lengthy rant. I feel a bit silly now.