Hi, I'm the author. If you find any particular claim of "obviousness" unclear, submit an issue request!

But please don't confuse "straightforward" with "obvious". Sometimes I deliberately gloss over mechanical details because I think they're a distraction from the main point. I'm NOT claiming that you should immediately know how to fill in the details; I'm claiming that filling in the details is boring.

I would agree that words like "obvious" or "trivial" can be disheartening to a learner.

If it's obvious to the reader, they know it whether or not you tell them it's obvious. If it's not obvious to them, then they will try to figure it out. Telling this person "it's obvious" only serves to make them feel bad about not getting it right away.

I felt that way when studying math in college, but after sometime I actually came to like the use of "clearly" and the like as it can be used as a check on whether you've spent enough time internalizing the previous information. It's one thing to have a text or a person hold your hand through algorithms or theorems, it's another to be able to do it yourself. So getting hit with a "clearly" that feels unjustified is often a signal to let go of the guiding hand and go back and review until the statement in question does become clear.

Sometimes this is th'e case, yes, sometimes it is not.

An example: http://jeffe.cs.illinois.edu/teaching/algorithms/book/Algori... Page 15

> It’s quite easy to show that the singing time is Θ(n2); in particular,the singer mentions the name of a gift ∑ni=1i=n(n+1)/2times (counting thepartridge in the pear tree).

I'm pretty sure that I still remember how to read the formula and I even know what does Θ(n2) means, but it's still unclear for me how do we get n^2 and this formula from the "NDaysOfChristmas(gifts[2..n]):" example.

I agree as well. Maybe it serves to alert the reader to when they are missing a piece of prerequisite knowledge, but there are ways to do this that don't create as much friction.

Now that is something mathematician quickly learn to not be bothered about:

the proof is easy and left as an exercise

The main takeaway I got from Polya's How to Solve it is that properly conceptualizing the problem in your head before attempting to solve it is key.