|[||Parts IA & IB
(1st & 2nd year)
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 calculator's memory, or got sent by friends...)
First, a couple of collections of classic quotes...
http://www.cs.stir.ac.uk/~scu/Humour/Education/cambr_mat.html - The ultimate repository of Science and Maths quotes, from the last 12 years of Cambridge silliness. All else is but shadows thereof. (It is from Cambridge, despite being stored on a server in *xf*rd.)
...and http://www-i3.informatik.rwth-aachen.de/en/funny/prove.html - a collection of the styles of proof occasionally used by our lecturers on bad days.
Check my CompSci quotes pages for more links.
And now my own quote collection. This is very incomplete, but serves to illustrate the joys of Cambridge...
|Dr Korner||(Analysis, Michaelmas '98)||Arthur Norman||(Java, Lent '98)|
|"A theorem is just a friend you have not met yet, ...and only when it bites you on the hand do you adopt a more cautious approach"||"I frequently send myself encrypted messages, but I can never decode them so I don't know what I'm talking about"|
|Dr Shellard||(Maths Methods, Mich. '98)||John Bates||(Op. Sys., Easter '98)|
|"Legendre invented Legendre polynomials. I know very little about him, except that he looks like a parrot."||"I'm a bit like an operating system really... 'multitasking' between these two OHPs, 'interrupting' you, ... 'sending you to sleep'... "|
|Prof Gowers||(Quadratic Maths, Mich. '98)|
|"I beg your pardon... No, I don't beg your pardon. A double change of mind there, sort of cancelled itself out."||
Operating Systems printed notes
|Prof Grimmett||(Markov Chains, Mich. '98)|
|"I'm sure this is a mistake, if only because I make one mistake each lecture and there's only ten minutes left"|
|Dr Brookes||(Linear Maths, Mich. '98)|
|"You should get out your whip and make sure your supervisor performs properly"|
|Dr Hudson, Dr Saxl||(Algebra+Geometry, Mich. '97)|
|"Even an interesting tetrahedron is not the most interesting thing ever..."|
|Assorted lecturers||(Lent '98)|
|"It's somewhat difficult to explain the difference between a left hand and a right hand to someone who doesn't have hands"|
|Dr Sheppard-Barron||(Geometry, Easter '98)|
|"To say that the sphere is curved and the plane is flat becomes more and more profound the more you understand the meaning of the word 'curved'."|
|Assorted Supervisors||(from Robinson College)|
|"I've now done the first two halves of the three halves of the course..."|
|Elizabeth Ayer||(Group theory supervisor, Lent '99)|
|So, we remember the Isomorphism Theorem! - tarantaraa!
- jsn23: ...Does he have a cape?
- liz: Yes, he does! <draws cape on the words 'Isomorphism Theorem'>
|Miscellaneous Other Lecturers|
|"...And this is finite, where 'finite' is infinitely large."|
Many of these quotes were originally recorded by Vivien Easson and later
donated to this site, so credit due to her!
DR KORNER (Analysis, Michaelmas
See Korner's own homepage!
|That's for the pedants in the audience: a pedant is anyone who disagrees with me.||If it is Monday and I am the King of Siam, then it is Monday||This is the clever bit. You may say it's not very clever - well of course it's not very clever, but the rest is even less clever|
|This makes no sense, but mathematicians can make sense of this||Every point in the empty set is the King of Siam, but it's obvious that not every point in the empty set is the King of Siam.||One of the problems with this formula is actually working out what the hell anything is|
|A real theorem is one that if you had been around in 1880 and proved it they would have given you a professorship||I think I'm being punished for an earlier life, where I did something stupid like leave a bike on top of the Master's Lodge||Just as every one of you has a mother, so every bit of this formula means something|
|The human brain is not equipped to do what we're going to do next||No brain cells have been killed in the making of these proofs||A theorem is just a friend you have not met yet...|
|This doesn't mean anything to us... BUT IT SHOULD!||So the function f must lie entirely within this green snake||...and only when it bites you on the hand do you adopt a more cautious approach|
|Human beings are very poor mathematicians||This theorem is also known as the GPUC by those who do not object to theorems which sound as though they were a branch of the secret police||I suspect there are people walking the streets today who don't know that int(f+g,a,b) = int(f,a,b) + int(g,a,b)|
|If we were more awake - if we weren't fresh from the trees - we'd immediately say "Mean Value Theorem!"||To anyone with experience (and you haven't got experience, since experience is what comes with getting experience) ...||Would we be happy if we just had "sigma x(r) minus x(r-1) times sup mod f(t) - inf mod f(t)"? Yes, deliriously so!|
|For the 12th time this course I'm going to turn to the audience and say "Can you see any method of estimating this?", and for the 12th time there's going to be dead silence||Example: 10-60* tan-1 x ... the 10 to the minus 60 is just end-of-term feeling|
|The open ball is open.||To the question "how did you think of something this clever?" the answer is of course "I didn't"||Mathematics has the curious property that the world rests on an elephant, which rests on a turtle, which rests on another turtle, which rests on another turtle...|
|The interval from j to infinity is VERY VERY BIG!||Second Noteworthy Proof: ... and in fact it's so noteworthy that I seem to have printed it out twice||Of course, the correct answer is it's turtles all the way down|
|Open is not the opposite of closed.||[on having a writing mistake pointed out] Epsilon is just an infinity that's turned round and split in two... if you don't watch them carefully they tend to do that||"The Royal School of Needlework, and drive like hell!"|
|This is all pretty easy.||You may feel you can't do these. This feeling is purely illusion and in fact you can do them...||New regulations for the safety of New York populace mean the speed of the taxi-cab has to be continuous|
|You can prove this lots of ways, all exactly the same, but this is a unique way||This course is marginally advanced over what we did in 1920
Back when I was an undergraduate, before the Flood...
|It is of course possible to go to sleep with a loaded hand grenade by your pillow and survive, but it's better to just keep your hand-grenades away from your pillow|
|The proof is trivial, but it's only trivial because we've done a fair amount of work||[after 2 boards of lecture notes] This is merely an extended hint||We seem to have spent all morning swimming through treacle, I'm sorry|
|This argument is rigorous - it may not look rigorous, but it is|
OTHERS IN MICHAELMAS '98
Dr Shellard (Methods):
|If I wave my hands enough, maybe you'll see what I'm trying to say||Legendre invented Legendre polynomials. I know very little about him, except that he looks like a parrot.|
|So let's switch on gravity - abracadabra||Cambridge University is planning to increase their intake from London Zoo... though I think 15% is really enough|
|This equation shouldn't pose too much of a problem to most of you with a constant on the right-hand side. [But what if I don't have a constant on my right-hand side...?]||It may surprise you that the shortest sailing time from Bristol to New York is not a straight line; that's because Ireland is in the way|
|Some of you might be finding this a bit dry... maybe even a little... ...boring?... ...and you'd be right, actually.||Maths and alcohol don't mix: ... don't drink and derive.
[Old, very old, but still one of the classics]
|Brainpower at work||Jelly!|
|10^-35 metres is quite short||There's a very exciting demonstration coming up with some blobs|
|This is an attempt to show you how this is useful, so if you're easily confused think about something else||Changing the reference frame in which we look at our jelly won't change the elasticity tensor|
|So we want a method that minimizes the amount of work we have to do to minimize a function||So we're predicting that when we press down on our jelly... it'll get squashed!|
Prof Gowers (Quadratic Mathematics):
|If that's your view, then... ahm... you're wrong||I've written it as infinite, but that's not meant to preclude the possibilty that it might stop at some point||Your rough mental picture of this should be you fiddle around with it until you've proved it|
|I beg your pardon... No, I don't beg your pardon. A double change of mind there, sort of cancelled itself out...||Something's different about the chalk today. I don't normally break chalk with quite the frequency I am today. That's your choice really, chalk that looks disgusting but doesn't break so much, or chalk that actually looks quite nice but does break... Aanyway...||There's a nice simple test to see if 4 works: the answer is it always does...|
|Poor old orthogonal matrices are probably feeling left out, so we'll have a result to do with them next time|
Prof Grimmett (Markov Chains):
|This is not examinable... Well, it's not very examinable||And that's the bit of mathematics that makes this stuff truly correct. (If you want to make it truly correct.)||There's a slight problem here, but the problem goes away once you realise it's there.|
|We've all got dirty little tricks for changing the order of summations; if you haven't got a dirty little trick, go and find one||But this [theorem] is not true -- oh -- <stares into space> umm, is it true?||I'm not sure I could justify it myself... but it is justifiable|
|The hardest thing about queueing theory is spelling "queueing"||There are only about 2 processes like this. Well I'm exaggerating, there are really an infinity of them...||...modulo a little bit of rigour...|
|We used to study this at A-level, back when A-level counted for something
<cue audience "ooooooo" of disapproval...>
|The problem with infinity is it's awfully big||Let's pretend the j is on a previous incarnation of the blackboard|
|It's not the purpose of an undergraduate course to study weirdness, though there's plenty of it around anyway||If it's true, this is why it's true... If it's false, you got it wrong
I'm not quite sure what's going to happen next... in fact the theorem is false.
|[But he proved himself a true mathematician in the next-to-last
lecture of term, with this:]
The equations are perfectly interpretable in a non-ambiguous way, it's only when you try to put them in words it can get a bit misleading
|I'm sure this is a mistake, if only because I make one mistake each lecture and there's only ten minutes left||Faced with a differential equation you can't solve, you move to another space: jump in your spaceship and move to another universe||I'm an individual. I may divide into 2|
|The ability of lecturers to give good notes is different from the ability to give good oral presentations... as you know from the quality of your notes and of your lecturers||In our mathematical abstraction, we need to know what a mountain looks like: we assume it's a regular grid.||People who are big can say that. People say "Oh, he's right because he's big"|
|Some of you have heard the word Laplace, and some of you have heard the word transform; a few of you may have even heard them both together||This is a difference equation with a difference! [groan...]||The world is perfect, almost by definition|
|This is a peculiar way of looking at this, but that's just how I'm feeling at the moment||I've got n bullets here, each of which represents a telephone call||What is the coincidence? I mean, there is a coincidence, but whether it's a coincidence I don't know|
|I'll have to come back and do my ritual dance over this in a moment||If you go to a masked ball, it's a good idea to recognise a few people, otherwise you may get in terrible trouble|
|If we sum -- [stops dead. Silence for 10-20 seconds, then he says:] ...Do lecturers normally stop in the middle of sentences?|
Dr Brookes (Linear Maths):
|I want to multiply by my favourite matrix... [suddenly, to himself] I can multiply, can't I?||You should get out your whip and make sure your supervisor performs properly||We have to convince ourselves we're not talking nonsense|
|You should be getting excited by all these big matrices... or at least, the paper firms should be getting excited||It frequently happens on Saturdays, that we talk nonsense, but on this occasion we're not talking nonsense|
Pure mathematicians don't squiggle
Whenever something is trying to be a triangle, it really is a triangle
Even an interesting tetrahedron is not the most interesting thing ever...
Well to prove this theorem... umm... you'll have to believe ME. It's called "proof by intimidation".
These are things that you might want to get up to in the privacy of your own home... If you get them wrong like I did last night, they can get very messy
It's somewhat difficult to explain the difference between a left hand and a right hand to someone who doesn't have hands.
No real excuse for the lateness of the sheets, other than me going mad.
We can define all sorts of things, but they don't necessarily exist.
If you go stand in a shopping centre, you don't get a random sample - you tend to get people who go to shopping centres.
I'm not going to tell you how to explain this, because I don't know how myself.
DR SHEPPARD-BARRON (Geometry, Easter '98)
To say that the sphere is curved and the plane is flat becomes more and more profound the more you understand the meaning of the word "curved".
It's not a point. That's the point.
Up to a finite degree of ambiguity, a rotation is specified by a point on the unit sphere and an angle.
[On saying that a proof in Geometry had a cunning bit in it]: The cunningness consists of getting rid of the geometry.
The point of all this is... we get a picture where this is very very parallel, if you don't mind me saying that, to the unit sphere in R3.
There are a priori 24 ways of defining a cross-ratio, but actually only six, so if you don't like this definition, choose another.
[Seriously, at the last lecture of the course] I'm going to cheat, because I've been cheating all along.
|I've now done the first two halves of the three halves of the course
[And this from a mathematician?? :) ]
|Now we use l'Hôpital's rule... lovely old Loppy...|
|(student): [dismissively] Oh yeah, I've
done that question
(thomas): Oh, really? How did you manage that?
(student): [taken by surprise, frantically] Um, well, I, ah... I looked at the, um... well, I didn't.
|(student): [to drummond, in Beavis-&-Butthead-style
voice] You're like a God...
(drummond): [shrugging it off] Well, I am, as a matter of fact, but...
Actually I'm a devil
|The even Legendre polynomials are actually even!|
Elizabeth Ayer (Groups, Rings
|So, we remember the Isomorphism Theorem! - tarantaraa!||60 divided by 12 is four... <hysterically> no! five! five! five!!||It's not the most useful comment without some words to go with it|
| jsn23: ...Does
he have a cape?
- liz: Yes, he does! <draws cape on the words "Isomorphism Theorem">
|There are two definitions of this. (Well there are three, but only two good ones...)|
I'm not going to do this calculation because it's got logs in it.
And this is finite, where finite is infinitely large.
This doesn't work for d+1=6, well I suppose that's d=5, but 6 is more intuitive
The constant turns out to be constant actually
|people have laughed(?) at the Pre-1999 Lecturer Quotes since 14 March 2000|
|Back to the homepage!|