And worth a shirt "After much thinking, the solution is obvious."

There was an old joke. University math class. Professor writes a huge formula on the board. Says, "and from this, it is obvious that," and writes another very different large formula on the board. He stands for a second, says "hm...", and walks out of the lecture hall. He returns 30 minutes later, throws a stack of papers freshly-covered in writing unto the desk, mutters "yeah, that indeed was obvious", and continues the lecture.

My dad actually did a form of this, at the encouragement of a teacher.

He was working out the proof to a problem in college and got stuck half way through. He had the problem and the answer, so he worked it from both ends and got stuck in the middle. He had to present the process in class, so he went to the professor for help.

His professor (who had done it originally) couldn't remember how anymore, and told him when he got to that point, he should say "and from this, it's obvious that..." and just jump to the next step.

That's exactly what he did, and no one in class (half hour into the class) even noticed.

"It is obvious that..." usually means "with large amounts of algebra but very little actual thinking" when properly used in a math textbook or lecture. It has its utility.

Write down the problem. Think real hard. Write down the solution.

(The Feynman method—described by someone who observed him, though, not the man himself).