"Let's draw the same graph in some sort of devil worship kind of way."

"Can you waddle from anywhere to anywhere?"

"I hope it's clear that we're dead now."

"Given a tree - a nice concrete thing..."

"And maybe you have to utter the words 'contradiction' or something."

"The longest path in the world..."

"It proves itself for you."

"There's a happy tree."

"Trees are nice, friendly things."

"An advertisment for the power of having a leaf."

"There's a footprint of induction in here somewhere."

"That might not work, but nothing else could possibly work."

"For the same boring reasons..."

"A useless-looking question."

"I'm doing two proofs because they're both morally sound."

"A and Γ(A) versus rest of world."

"Then we will pray that we can check..."

"These are quite expensive edges."

"An advert for max flow min cut."

"New, fictitious points."

"If there's some bad set somewhere..."

"It's got a very Hally sort of feel."

"Obviously, it's daft to look at disconnected graphs."

"Sad example, as usual..."

"...waddle along to x, hop into H and hop back out again."

"This point's got degree huge."

"A whopping n/2 - 1."

"So we're done - we can go home."

"Why does this board keep escaping? Is it scared?"

"I'll now draw my exciting curly A."

"Co-lex will say, 'Keep your world down.'"

"The basic idea about compression is that you're as lazy as possible."

"When we say, 'Stomp on your set'..."

"The ultimate 'rabbit out of a hat' proof."

"Why don't we give a reason, instead of saying, 'waffle, it's obvious'."

"Let's throw ourselves away."

"This is a sort-of-maths course."

"We dared to call it maths."

"Apologies for the devil-worshipping thing again."

"We don't need to have turquoise spectacles."

"Theorem 1 - which was called Ramsey's theorem - and theorem 3 is called Ramsey's theorem as well. We've got two theorems next time, which are also called Ramsey's theorem."

(on finding that there was no red chalk in the room) "No! The red chalk has gone! The lecture has to stop - there's no red chalk."

(about a minute later) "Okay, purple will be red for today."

"A fantastic red r-set..."

"There'll be r's, brackets, and a's and b's flying around."