| Tabular / categorised version |
| Tabular / categorised version |
Aah, Cambridge lectures, don't we just love 'em? Whether sanctimonious, stimulating or soporific, lectures can often be described by words beginning with 'S'. But occasionally a gem of a quote will slip from a lecturer's lips and rouse me from my stupor / distract me from mathematical ponderings. Here are a few of the ones that I managed to remember. (Or copy down on my lecture notes, or type into my organiser's memory, or got sent by friends...)
This section is just the quotes from Part II lecturers, in my
third year.
(Earlier lecturer quotes may be found here...
featuring Dr Körner, Prof Grimmett, and many more!
Or look here for quotes from my Part III lecturers in my fourth year: Imre Leader, Oliver Johnson, and more from Ian Grojnowski and Thomas Forster!)
)
NB: I am not making fun of these lecturers in any way! I publicise
these quotes in order to show how cool my various lecturers are. I'm a
big fan of all of the men quoted here! In fact, there usually
tends to be a positive correlation between the number of amusing quotes
a lecturer makes, and the general quality of their lecturing and how well
we learn. So cease thy paranoia, o lecturers!
Maths Part II |
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 Prof
Grojnowski
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(Representation Theory, Lent 2000) |
Favourite quotes: "How are we going to prove this: Well it's obvious.
We're going to follow our nose - er, my nose, chalk-covered though it may
be"
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| Dr Thomason | (Combinatorics, Lent 2000) |
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"Theorem 3: Every non-trivial tree has at least 2 leaves"
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| Prof Coates | (Algebraic Curves, Lent 2000) |
| "If you meet an elliptic curve on the street and I ask you to add two points on it... " | |
| Dr Forster | (Logic, Computation and Set Theory, Mich. '99) |
| [arriving shortly] | |
The math of our century. - Er - I mean - the century we're still really part of - or something
I get silly when I get woken up too early
Ignore this if it doesn't make complete sense
"Proof is an exercise" - which means that I'm not going to use it and you're not going to use it
Riemann surfaces, algebraic curves... what'd you call them?...Donuts with many holes!
I'm going to keep asking you if this makes sense, and it's a lot easier if you're not... no! no! I don't mean it like that!
"Example 5" - are there 5 examples? "Yet another example"
"Hint - just think". Yeah - thinking is good
Thinking is good but I'm also meant to do a lot of the thinking for you
That makes that obvious, doesn't it? - Just stare at it for a while
I'll give you enough examples in the next 20 seconds
that you won't have to stare at it, you'll pick it up by osmosis!
I'm getting so old, dammit, that I can't remember not knowing this! It's a weird feeling...
The group of 2 elements acts on me. Well it doesn't really act on me, it acts on my silly little picture...
Oh dear. Never wear black when teaching...
This idea looks pretty simple. And is pretty simple. But I still don't understand it
What does G do? - it permutes these bunnies around
And this thing is just... [bingles thoughtfully]... sitting there
Do some parts of groups just die, do they just get knocked off never to be seen again? The answer is no - isn't that reassuring!
This lecture has been brought to you by Functions on Something
Doesn't this kind of thing make you think that mathematicians are so weird!?
Isn't it boring? I just repeat things. Isn't it boring? I just repeat things.
And anyway, as I seem to enjoy repeating myself - and anyway, as I seem to enjoy... no, done that one already
Doing the problem sheet is more important than listening to me. It's very nice if you want to listen to me...
I don't want you to start thinking you have to visualise a 4-dimensional space, cause that would just be silly
student: Is that a 9 or a 1?
- dr groj: It's a 4!
It's my handwriting that's ridiculous - thank you for tolerating!
This is an early-in-the-morning exercise, meaning we already know the answer
a a a a. - No! It's a a - a a ...
If
you were thinking this early in the morning, you'd be throwing chalk at
me for giving you such a boring example... but I'm the one with the chalk
If you're as out of it as I am most minutes of the week...
[At 9:15] On the one hand, this is obvious to most of us, right? ...On the other hand, it's about 20 minutes after most of us got up...
You're supposed to start grinning at this stage! Shame on those of you who aren't grinning!
At
this point it would be a good idea to revise what we've learnt... "We have
learnt that it is very hard to get up this early in the morning"...
This is what I'm saying when I say the character table is square - but it's squarer than that! ...But it's not really really square.
Notation is baaad. But bad notation is worse!
I know this is vague, but it's reelly important!
The first 2 million 12 thousand and 3 times you do this, you get the order wrong
Have I said something stupid? No? Just incomprehensible
I'm normal today! This is me as I usually am! Previously you've had a sleep-deprived me, but this is the normal me!
Shall I explain why these are obviously equal?
If you were that much of an optimist, you'd be wrong. But if you were a slightly more relaxed optimist...
It doesn't have a hope in hell of being irreducible!
I'd forgotten the thing about not wearing black while teaching... I've been sparing myself my black jeans for weeks for this very reason, chalk marks and things but I forgot about the [brushes arms in distaste]... Anyway...
It's clear that, um... What is it clear that? It's clear that I should start again on this next lecture...
It makes sense to check that it makes sense
The nice thing about be a mathematician is that you can be paranoid and a conspiracy theorist. You know if you're a paranoid conspiracy theorist, you believe that everything coheres and everything fits together? Well in maths, it all really does fit together!
If it isn't obvious, it's confusing
[on a lovely snow-covered morning] At the moment to me "fields" are fields covered in snow, not fields as algebraic objects
Ah! So you have seen it before, but nobody knew what I was talking about!
It's
not easy being ludicrous... Some are born to it, others aspire to it, and
others don't have a hope in hell!
How are we going to prove this: Well it's obvious. We're going to follow our nose - er, my nose, chalk-covered though it may be
"Proof: Follow my nose"...
No thinking is required here... but thinking is a good thing, so maybe we'll do a bit of thinking about it in a minute and we'll realise it's obvious
What does that say? Well, let's stare at that for a moment... In fact, let's stare at it for the next five minutes
In general addition is not commutative, especially before breakfast!
If you don't know this, you're bad! I did teach you this! Bad bad bad...
It's kinda obvious... by which I mean it's a fair summary of all we learnt
My fault, bad me...
The answer is called Frobenius reciprocity. [apologetically] Hey, it's just a name!
When's our next lecture? Thursday? Thankyou. So today must be Tuesday.
If you're doing research, trying to understand the world, and something like this comes up, what do you do? Other than run away screaming...
It's a stupid thing to do. Why is it stupid thing to do? Well, it just is, isn't it
It has a corollary which is even stupider
The conclusion is: this is garbage!
Continuous - which I can't spell which is why I'm abbreviating it to "cts"
G is a compact group if it's also compact
I can add, right? And let's ignore the fact that I can't subtract
I don't know what I was doing last night! -[students snigger; responds with] No, no, nothing interesting!
Exercise: Check that I haven't lied to you
I'm just stating the obvious, in more ways than I care to mention
Do you feel that you can now go to cocktail parties and when you tell people you study how symmetries occur in nature, though they look at you strangely they'll... no, they'll just look at you strangely...
Cocktail parties? Do people still do those any more? No, they go clubbing! But you can't talk to people when you're out clubbing...
Mathematics has room for lots of weirdos in it
I think this is a natural question if you're weird... maybe even if you're not
It's a wonderful book, but it's so Cambridge - it's so weird!
Before you try to analyze how a group acts in nature, it's kinda polite to meet the group first
Am I weirder than normal today? From the way you guys are laughing... I feel normal...
Shame on whoever taught it to you - I hope it wasn't me!
I'm sparing you from the working because 2x2 matrix computations are no fun for anyone... but you can't spare yourself from them
An example, just to remind me if no-one else
Everyone's looking very blank. Do I have to do all the work?
We prove this just by proving it!
It's got some strange features, this place [Cambridge], but that's one of the good bits, right!?
This should confuse you for about 1/10 of a second, and then you should go "Uh, of course". But somehow you need the 1/10 of a second, just to see there's a point
There is no way they're getting me to teach at 9am next year
If you attend a course on Lie algebras and they don't teach you how to solve this by drawing pictures, then throw chalk at them!
Tell them it's by this person called Pashmanawara, and it's in a paper called... Structures of Crystals? Or something? And then they'll throw chalk back at you!
This letter is a Gothic G. It's one of these fascist G's that are marching through the years...
I'm being serious. There's a point to this. But I see why it seems ludicrous.
I'm just teaching you to differentiate [taught in secondary school] without using the words. But I think you know how to differentiate.
And now I want to burble for 3 seconds: "Why the hell do you do this?" Oh, yes, that was a good burble...
The course just changes completely in flavour, doesn't it? It goes psshhhhhhh... bler!
This has the property that if we get to the top and hit it, you fall off the edge and die, right? You get zero. This is a good thing. So we need a lemma, um, a lemma to say this is a good thing to have...
[His highest compliment:] Lie algebras you can do in the morning
It's faster to compute another example and then try to figure out what the hell's going on
All sets are finite. Well actually that's a lie...
The book "Graph theory": There's an updated version, called "Modern graph theory". It's not any more modern, but it covers twice the material for half the price, so that seems fairly good value
Theorem
3: Every non-trivial tree has at least 2 leaves
Let's think about a tree for a moment
What we have to do is write that down without waving our hands
You
call the thing a matroid - sounds like something you should be rubbing
cream on, to me, but never mind
There is a proof - and it was discovered by a man named Prüfer!
What were we doing last time? We were matching men with women, as I recall
Introduce d gregarious women, knowing all the men... "gregarious" is perhaps the wrong word, but I'll let you insert your own adjective
Then remove the d men. Some of the women may have been married to these men, so they... well, I was going to say "lose out", but whether this would be a loss or not is unclear
Replace each woman by d clones of herself.
This is H dashed in that potato, I'm sorry
No-one realised it was there until many years later people went back and found it
But now we start fooling about above the waist. [Waist of the n-cube, that is...]
Even though the proof we have is entirely trivial, this proof is even more trivial...
How do you make your shadow as small as possible, is what we're interested in
We may assume this component is the smallest. - [thoughtfully] Oh! May we? - Look, there's 2 minutes left so we're going to have to assume this component is the smallest...
Among these 6 friends there are either 3 mutual friends or 3 mutual enemies, which would be more likely in parties that I go to...
Imagine everybody's attached to everybody else by a piece of coloured string
Pull
somebody out of the party and look at them: they've got five coloured strings
coming out of them
What number shall I give this theorem? [turns to audience] [student calls out "29!"] Right. Theorem 29, then...
I don't want to suggest Ramsey was a bit dim - on the contrary, he was a Cambridge undergrad... [audience laugh] Well, OK, that doesn't prove anything as you well know...
There was a little competition to prove this between these two [mathematicians]: they were trying to impress a girl at the time
It says something about Hungary, I guess, that one can impress women by proving theorems
[after explaining in words why a proof works] Right. Somebody has to write this down, and I think it's me
The algebraic ideals are just the ones we'd like to meet on the street
I define, you define, mankind defines...
There's no God-given class group - well, there's zero, but somehow that's not God-given, it's just... mankind's aberration
If you were slightly more mature... Sorry! That's in no way meant as an attack on your maturity. But if you were slightly more mature as mathematicians...
Let me remind you that there's no God-given local parameter. You can find them in the street.
These constants are never wrong when you get them right
If you meet an elliptic curve on the street and I ask you to add two points on it...
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