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    $\begingroup$ The "P vs. NP" aspect of "obvious" results is discussed by Scott Aaronson in reference to Huang's recent proof of the sensitivity conjecture (mentioned above) here: scottaaronson.com/blog/?p=4229 $\endgroup$ Commented Aug 11, 2019 at 22:07
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    $\begingroup$ In the same spirit as the post I would like to add "Do not confuse difficulty of the exposition with difficulty of the underlying maths". It seems that a substantial chunk of mathematics is made more difficult than necessary because of how its exposition is written and structured, whether this being intentional or not. $\endgroup$ Commented Aug 12, 2019 at 12:38
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    $\begingroup$ "The important parts of the proof are the key ideas, which sometimes are quite small in comparison to the rest of the work." ― this hits the nail on the head. Great answer overall as well! $\endgroup$ Commented Aug 12, 2019 at 17:30
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    $\begingroup$ Perhaps I shouldn't comment, but the case-check in 3-primes is by far the most trivial part - it's not even the more interesting computational part, by far. Neither is it the part that takes longest to describe; it is one page out of hundreds. $\endgroup$ Commented Nov 9, 2019 at 6:33
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    $\begingroup$ @PaceNielsen But that's not how the proof works. The point is to come up with a better analytical treatment (which still inherits the basic insights of Vinogradov and Hardy-Littlewood), so that the number of cases to check is small (in comparison with today's computational resources) rather than hyperastronomical (really $\text{exp}(\text{astronomical})$, if we are talking about Vinogradov's original proof). $\endgroup$ Commented Nov 11, 2019 at 15:56