And the use of "it can be shown that" usually means it is difficult to show that...

"There certainly are readers to whom it is not easy." Is it easy to see that? Is it even certain that there are readers other than the author and the referee? I wouldn't be surprised if any reader who reaches a certain point, say halfway through the paper, will find a certain statement easy to see. On the other hand, I don't advocate writing "it is easy to see" because it often signals that the author hasn't thought about this point carefully enough.

And the use of "note that", as if everything else could be safely ignored.

See this question and the many other questions linked in comments.

Possible duplicate of Is it acceptable to use the word "trivial" in lecture?

Basically just means a.) you should try it for yourself (see Hardy, Course in Pure Mathematics) or b.) I can't be bothered to write down the details as they are tedious and annoying (see Perelman's proof of the Poincaré conjecture).

@StephanKolassa That question is about lectures, not papers, and is a different (but related) phrase. A duplicate question it is not.

Yes, there is. It makes bug hunting a lot easier :)

Imagine an entire paper that said "it is easy to see that our results are completely correct" and ends there.

Is there any good reason to write “it is easy to see”? ... Well, yes, obviously.

My math lecturer: 'It is intuitively obvious'. It almost never was.

This question was asked previously on a different SE site: math.stackexchange.com/questions/54431/….

Yes, there is one good reason. I like to call it "proof by intimidation".

@penelope, sorry, no. That one is usually phrased as "As I'm sure you will agree...".

At my first job years ago I was sent to a class on writing proposals. One point made was that if you were tempted to write "it is obvious (easy to see)" you should replace it with "you dummy" and see how it reads.

Finding the cases where it's appropriate to use "it's easy to see" has been left as an exercise for the reader

@Buffy How about "recall that"?

No one ever says "no doubt" unless they are unsure of their facts. Some of these phrases mean the opposite of what they say. "It is easy to see that" means "I'm not going to explain this": ostensibly because the explanation is not needed, but quite possibly because the explanation is not easy.

@JollyJoker "recall that" can be used to refer to some details in an earlier part. That sounds pretty legitimate

I never take good lighting for granted, and I don't want my students to do it either.

@Tom or 3) I did not understand or bother to try but everyone says that it is easy

@Buffy To me, using any of the phrases "it's (easy to see/obvious/trivial)" comes across as "If you (reviewer) don't find it easy/obvious/trivial, you're not as smart as I, to whom this is easy, so therefore it is easy to see, and even obvious, that you should accept my paper without questioning the logic of one smarter than you, you dummy." I'm happy to include your "As I'm sure you will agree" to my list of "proof-by-intimidation" key-phrases, but I've ready plenty papers using easy/obvious/trivial that come across as trying to bully the reader into believing them.