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. 

OBVIOUSLY: I hope you weren't sleeping when we discussed this earlier,  
because I refuse to repeat it. 

RECALL: I shouldn't have to tell you this, but for those of you who erase  
your memory tapes after every test... 

WLOG (Without Loss Of Generality): I'm not about to do all the possible  
cases, so I'll do one and let you figure out the rest. 

IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should be able  
to prove this without me holding your hand. 

CHECK or CHECK FOR YOURSELF: This is the boring part of the proof, so you  
can do it on your own time. 

SKETCH OF A PROOF: I couldn't verify all the details, so I'll break it 
down into the parts I couldn't prove. 

HINT: The hardest of several possible ways to do a proof. 

BRUTE FORCE (AND IGNORANCE): Four special cases, three counting arguments,  
two long inductions, "and a partridge in a pair tree."

SOFT PROOF: One third less filling (of the page) than your regular proof,  
but it requires two extra years of course work just to understand the
terms. 

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. 

CANONICAL FORM: 4 out of 5 mathematicians surveyed recommended this as
the final form for their students who choose to finish. 

TFAE (The Following Are Equivalent): If I say this it means that, and if
I say that it means the other thing, and if I say the other thing... 

BY A PREVIOUS THEOREM: I don't remember how it goes (come to think of it
I'm not really sure we did this at all), but if I stated it right (or at
all), then the rest of this follows. 

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. 

LET'S TALK THROUGH IT: I don't want to write it on the board lest I make
a mistake. 

PROCEED FORMALLY: Manipulate symbols by the rules without any hint of
their true meaning (popular in pure math courses). 

QUANTIFY: I can't find anything wrong with your proof except that it
won't work if x is a moon of Jupiter (Popular in applied math courses). 

PROOF OMITTED: Trust me, It's true. 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 Once upon a time, when I was training to be a mathematician, a group of
us bright young students taking number theory discovered the names of the
smaller prime numbers.

2:  The Odd Prime --
        It's the only even prime, therefore is odd.  QED.
3:  The True Prime --
        Lewis Carroll: "If I tell you 3 times, it's true."
31: The Arbitrary Prime --
        Determined by unanimous unvote.  We needed an arbitrary prime in
        case the prof asked for one, and so had an election.  91 received
        the most votes (well, it *looks* prime) and 3+4i the next most.
        However, 31 was the only candidate to receive none at all.
41: The Female Prime --
        The polynomial X^2 - X + 41 is prime for integer values from 1 to 40.
43: The Male Prime - they form a prime pair.

Since the composite numbers are formed from primes, their qualities
are derived from those primes.  So, for instance, the number 6 is "odd
but true", while the powers of 2 are all extremely odd numbers.