What math 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 are 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 will leave out everything but the conclusion. (You can't question 'em if you can't see 'em.)
• Briefly: I am running out of time, so I will just write and talk faster.
• Proceed formally: Manipulate symbols by the rules without any hint of their true meaning. Proof omitted: Trust me, it is true.