The Dictionary: What Mathematics Professors Say and What They Mean by it:
Clearly:
I don't want to write down all the "in-between" steps.
Trivial:
If I have to show you how to do this, you're in the
wrong class.
It can easily be shown:
No more than four hours are needed to
prove it.
Check for yourself:
This is the boring part of the proof, so you
can do it on your own time.
Hint:
The hardest of several possible ways to do a proof.
Brute force:
Four special cases, three counting arguments and two
long inductions.
Elegant proof:
Requires no previous knowledge of the subject
matter and is less than ten lines long.
Similarly:
At least one line of the proof of this case is the
same as before.
Two line proof:
I'll leave out everything but the conclusion, you
can't question 'em if you can't see 'em.
Briefly:
I'm running out of time, so I'll just write and talk
faster.
Proceed formally:
Manipulate symbols by the rules without any
hint of their true meaning.
Proof omitted:
Trust me, It's true.