A. Beardon

- on proofs and isometries

Part IA, Algebra and Geometry


"A matrix on a plate..."

"No, I haven't done the proof, I made a clear statement."

"I can simply wave my hands and say, 'by induction'."

"If it's not obvious to you, you'll learn nothing by going through rigorous proofs."

"Writing and copying doesn't actually get it into your mind."

"Swings and roundabouts..." = transpositions and disjointness

"I can change the number I've got in a perverse way."

"Have you turned the plane over or not?"

"You put your 4 cards on the table and do what you do anyway, and that's my proof."

"How pathological, how peculiar can they be?" (isometries)

"You must judge how persuasive I am here."

"All sorts of isometries could be going on on the table."

"I think the Schedules insist I say something about conics."

"By shifting the origin, you can kill off all the terms."

"Kill off the n's, one by one."

"Can we have a vote on it?"

"whenever two are the same, I kill them off."

"Hit it on the left with the tau."

"The proofs that are deeper are usually short."

"The usual business with a donkey on a rope..." (finding a circle on a weirdly curved surface)

"Throw away all the terms you don't want." 1