Other useful theorems and quotes of the kind very intelligent people without realising how they come across...
Theorem "If it's worse than square root of 51 then you've done it wrong"
"Going from 1 to 2 is one of the most important and most difficult steps in the whole of mathematics"
"The output equation is what we put on the end so that we get the right answer"
"This proved by Cayley & Hamilton - the Patron Saints of Linear Algebra"
"We then hit this expression with out Cayley & Hamilton hammer"
"A matrix with repeated eigen values is not something we talk about in decent society"
"a function is a sausage machine"
"by the end of this course you will be able to tell the difference between an orange and a doughnut"
Proof by "if you stare at it long enough you will be able to see that it is true"
Theorem "Every function is continuous and differentiable unless it obviously isn't"
"This is the garbage in - garbage out principle"
Proof "because we use a reasonable sensible function, we're not talking pathological functions here"
Proof "on the assumption that the functino isn't that stupid"
"stuff minus same stuff =0"
"If we stand back and look at this more closely"
"I see that we have minus one minutes left so in that time I'll..."

Ideas of Proof

I've been meaning to write this up for about a decade.
During my university maths lectures our lecturers used to prove different things using different methods - some of them less rigorous than others - some of the ones that made me laugh I wrote down.
These are all absolutely genuine quotes from 2000/2001 attributed to unnamed lecturers of the School of Mathematics, Cardiff University.
(Thank you dear lecturers for making studying a maths degree more fun than I could ever have imagined!)

Proof by "it just ought to be true"
Proof by "the proof is long and boring so I'll not prove it"
Proof by "I've said it three times already therefore it must be true"
Proof by "ommision"'
Proof by "in the next lecture"
Proof by "It's obvious"
Proof by "here's a picture"
Proof by "Trust me, it's true"
Proof by "I promised we wouldn't do any more proofs"
Proof by "This doesn't work for all numbers but it's easier"
Proof because "just in case we bump into it on a dark applied mathematical night"
Proof by "phoning the cosmic mathematical answering service"
Proof "Quickly because it would be unfair to put it in the exam"
Proof justified by "d/dx x^2 = 2x, d^2/dx^2 x^2= x" ...on 'correction' "=1", d^3/dx^3 = 0  ... so it does make sense"
Proof explained by "If a grapefruit was a kipper it would still be a fish"
Proof including "much as I like complex numbers - I'd like everything to be nice and real"
Proof because "I simply can't resist telling you"
No proof because "I won't be able to prove it"
Proof by "similarly"
Proof "either by solving equations or by 'light of nature' "
No proof because "I'm not going to tell you"
Proof by "we just have to understand it"
Comment on proof "if any paragraph starts with 'consider' it's going to be a trick"
Proof "start any proof by 'given any epsilon>0' "
Proof for "next time a man in the street / pub asks you..."