## 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.

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.