T. W. Körner

Part IA, Analysis I



"I say this function is continuous. And you say 'Oh no it isn't!' And I say 'Oh yes it is!' And this goes on for a few minutes."

"Once you've seen a tiger (irrational point), how many other tigers are there?"

"You can always convert porridge into water with bits of porridge floating in it, if you add enough water." (referring to 'diluting' the syllabus)

"I say an tends to a.
You say here is an ε > 0.
I say n0(ε).
You check and say OK."

"Here is the fundamental axiom of analysis. Da dah!"

"I don't know what to set n3(ε) equal to." (whispered) "Between you and me, I actually do."

"I don't have to go through life remembering what n3(ε) is."

"You have to admit that I'm better than you."

"In some sense, I haven't the foggiest idea how to do it."

"And now, I'm going to do something really clever."

"I WIN." (written in place of QED)

"Overuse of the ratio test makes you blind."

"It's like checking that the car is actually there before getting into it."

"A dyed-in-the-wool user of calculus."

"The supremum is like defining the current King of France."

"If your head is bursting from the first three lectures..."

"This is a proof of the bleeding obvious."

"L.u.b is such a nasty thing."

After asking the audience a question and getting no reply:
"I've lectured to graveyards which had more life in them."

"So what you have is not one piece of furniture, but four pieces of furniture, which is easier to deal with."

"Clint Eastwood goes through the last door and disappears." (if you try to use the Fundamental Theorem of Analysis with the rationals)

"Even if I got it wrong, I know the answer is right."

"You can't just sit by the roadside, weeping."

"You've got a point (alpha), which is peculiar. But is it peculiar enough?"

"If you want, you can go to sleep."

"A is having a champagne supper, and saying, 'These convergent sequences have nothing to do with me!'"

"That concludes the armaments phase of the lecture course."

"You don't believe me, do you?"

"This is terribly clever. Yes it is."

"Let us return to our chickens."

"While it's quite fun to show that x2 is continuous directly..."

"Small changes in x produce small changes in x."

"The next bit writes itself, which is good of it."

"It's like a party several blocks away, and as you get closer you can hear the noise of shouting, and smashing of glass... and you burst in and say, 'Stop! Stop!' And you discover it's a nun reading a devotional text. And you say, 'So sorry.'"

"Every minute of the day, someone somewhere says, 'Bolzano-Weierstrass'."

"It did not spring like Athena from the head of Zeus..." (definition of differentiability)

"A de-gearing process, in which you take a Rolls-Royce and use it to drive a budgerigar."

"My mother warned me about the wolves in the forest, about ladies of uncertain virtue - and not to divide by zero."

"The ratio group sweeps the errors under the carpet."

"In the name of all authority, I say that the only solutions of f'..."

"The proof is one where, on either side, crocodiles lurk."

"There's always a suspicion that, when someone says wlog, that they're trying to fiddle something."

"When I look over this side, I can see all the way upwards, so I must be looking downwards."

"You won't have any mathematicians to kick around."

"There is a dreadful, sinful place called Trinity..."

"You're in the position of a man in an Escher diagram. And you go up and up the stairs, and you end up beneath where you started. And you're terribly unhappy."

"Wlog - a very useful word."

"It's all too easy to muck up this proof."

"Mathematics is not about a deeply felt internal... feeling."

"As usual, we're at the wrong time at the wrong place."

"This will probably not arrive precisely where I want it to go."

"Let me spend ten minutes talking at random."

"It looks like a lot of letters have escaped from a dictionary."

"It should be a surprise when Taylor's theorem works - kind of like a birthday present."

"What I do now is... well, what do I do now?"

"Apart from getting the constant wrong, and the sign wrong, it's all trivial."

"You should always do the first thing that comes into your head, see what happens, then throw it away."

"It goes to zero like a bat out of hell."

"The real numbers are there, offstage, waiting to appear."

"The real numbers and the complex numbers are extravagantly special."

"You wander along, and generalise and generalise until you fall over a cliff."

"If you're in R, and you're afraid of being mugged..."

"This proof really requires you to be awake - and since I'm not awake, we may have problems."

"I've proved them stone dead."

"It's very naff to use ln. It shows you're not sophisticated."

"We have all seen logs that it is harder to fall off." (after talking about exp(a log y)...)

"It has to be said, it slips down like butter." (a proof)

"The axe method - keep hacking at it until we get the answer we want."

"Do not open mouth until mind is in gear." (said after he made several mistakes while writing a proof)

"Exercise for students: correct the proof."

"The world is not quite as simple as we think because we are very stupid."

"Yes, there is a Father Christmas - you just have to change the question a bit, and then you've got your logarithm."

"Accept my word as a scholar and a gentleman."

"You have your dissection - which is futile, and with which I disagree entirely."

"The next remark is both trivial and vital."

"...like people who travel by aeroplanes to conferences on the dreadful effects of modern technology."

"We don't cross our fingers, because we're trying to write at the same time."

"...at least as half as..."

"We have a blister in our shoe." (discontinuous Riemann integrable functions)

"...whereas I can simply say, 'Look, it's true!'" (on proof)

"That is the proof that we have rigorised."

"It's a bit like tieing your shoelaces while chewing gum and walking at the same time."

"There is the definition. God bless her and all who sail in her."

"This result is illustrated by this famous diagram, which you should dream about."

"I'm going to write down this picture algebraically."


"It's just like going into a shop and buying a small yellow sheep"

"You would still be epsiloning away"

"Don't worry about this thing, which is written by a trained ant"

"What is mathematics for but to baffle the non-mathematicians?"

"If one extra strawberry gives me one smile of pleasure..."

"We still have this bloody error - I'm the King of Siam except for an error"

"Obviously applied mathematics is nothing to do with pure mathematics - I apologise for mentioning it"

"I can't cross the purple line because it isn't there" (defining the complex logarithm)

"The set of complex differentiable functions is like Little Red Riding Hood." Audience: "Do you mean Goldilocks?"

"Functions are always slipping out of your grasp"

"There is a lot to be said for that, including truth"

"Feel free to throw things at the lecturer" (on making a mistake)

"Like Romeo and Juliet, only more spiky" (On the upper and lower sums of a particularly nasty integral failing to approach each other)

"I did not use insidious propaganda or get you to do 200 questions on Taylor's theorem" (on having proved the said theorem)

"But this is going to infinity like a bat out of hell"

"I can do it, because I'm equipped for axe warfare"

"Of course, mathematicians occasionally find they have defined a man-eating duck, but they don't mind" (on defining things without proving they exist)

"Formula only has 1 r. That's a useful thing to know" (on misspelling it)

"Every single white hair is a student's mistake" (on not having an ordering)

"A mathematician is someone who knows it's worth flogging a dead horse. You don't come across a dead horse very often."

Research seminar, Michaelmas 2002

"It's a very, very profound triviality." [Baire's category theorem]

"You need only juggle one point at a time."

"Whatever it is, you're agreed that it's very easy to do it" 1