Saturday, 28 March 2015


David Hilbert
Was often mistaken for Gilbert.
"I did NOT write Trial by Jury!"
He would say, in fury.
Fleischmann and Pons
Confounded their fellow dons
By demonstrating fusion in a football stadium
And later at the London Palladium.
Alan Turing
Needed reassuring
That a Turing machine made of papyrus
Was immune to almost every virus.
Professor John Coates
Mistyped his lecture notes;
But "Useful for Bankers" had more takers
Than the intended: "Useful for Bakers".
W.H. Auden
Never lived in Morden:
In his poems the central line
Is usually very fine.
Andrey Nikolaevich Kolmogorov
Had a headache, but it wore off.
He didn't find the test that statisticians learn of
Until he discovered Smirnoff.
G.H. Hardy
Was rather tardy
At patching up his quarrel
With Stan Laurel.
I find Maclaurin
Very borin'
And Taylor's series
Also wearies.
Bertrand Russell
Once choked on a mussel
Which is why he says nothing exciting
about shellfish in his writing.
 Donald Knuth
Thought it very uncouth
Of people to rhyme TeX
With Sex.
George N. Kayatta
Had some novel views on matter.
When your velocity is high,
You find pi in the sky.
E.C. Bentley
Taxes me mentally.
But Edward Lear
Is crystal clear.
Stephen Hawking
Is always talking
Of that stitch in Time
Which saves nine.

The Right Honourable Anthony Wedgewood Benn
Is as common as other men.
"I'm NOT a Viscount," says he.
"I'm a teapot, you see."
Is not easy to parody.
He would take legal action
If you said "Proof by induction".

The poems of Trad
Are not so bad,
But Anon's verse
Gets steadily worse.

Not wearing pyjamas.
He feels more mighty
In a white nightie.

Joseph of Arimathea
Wore trousers of barathea.
The same applies to Mr Michie's*

* A character in Lucky Jim, and this bit is true.

What mathematicians write about

As far as I could tell, these are the most commonly occurring words in titles of papers listed in MathSciNet, excluding the likes of "and", "of", "the", etc.:

equation (169,596), problem (152,343), system (123,957), function (112,503), space (102,400), solution (98,857), theory (97,817), method (82,817), group (73,474), linear (66,798), theorem (65,826), differential (65,421), model (60,637), operator (56,991), class (51,260), two (48,300), order (48,261), application (46,494), boundary (44,574), finite (44,135), field (43,788), type (41,569), integral (41,114), property (39,699), time (38,130), set (37,639), point (36,067), analysis (35,658), value (34,789), matrix (34,774), approximation (34,520), certain (34,010), control (32,073), number (31,463), algorithm (31,164), distribution (30,665), polynomial (29,614), stability (29,257), graph (29,178), asymptotic (28,532), condition (28,100), note (28,062), representation (27,766), random (26,742), quantum (25,396), wave (24,922), optimal (24,741), series (24,704), variable (24,351), ring (22,547), stochastic (21,701), flow (21,365), dynamic (21,362), inequality (21,050), form (20,680), existence (20,414), invariant (20,334);

with words such as algebraic, behavio(u)r, bounded, characteristic, coefficient, complex, construction, continuous, curve, data, decomposition, difference, elliptic, extension, first, fixed, fluid, free, fuzzy, global, hyperbolic, infinite, inverse, large, limit, local, map, mapping, mean, mechanics, metric, module, motion, normal, numerical, one, parabolic, partial, periodic, positive, potential, principle, product, real, regular, relation, remark, second, sequence, simple, singular, spectral, sum, symmetric, three, transformation, vector and zero following on their heels.

A few more surprising words also appear, and not all in papers by statisticians performing unlikely analyses:

sandwich (224), bandit (206), monster (116), sex (116), secretary (110), god (56), sausage (53), devil (50), cake (42), egg (39), demon (38), football (31), snark (29), worm (25), tadpole (24), spider (23), frog (21), hairy (20), ham (19), mouse/mice (18), sober (16), sponge (13), apple (12), banana (11), baseball (11), cheese (11), tortoise (10), dirty (9), slug (8), cricket (7), coffee (6), lobster (6), blotto (4), murder (4), snail (4), penguin (3), tea (3), vampire (3), boojum (2), drunkard (2), merry-go-round (2), mole (2), butter (1), grebe (1), jazz (1), molehill (1), python (1), silly (1), sloth (1), spam (1), whelk (1), ...

(Recall that there are concepts known as the Ham Sandwich theorem, the Monster group, the Wiener sausage, the Devil's staircase, the science of cake cutting, egg domains, Maxwell's demon, snarks (graph theory and, independently, topology), dilaton tadpoles (mathematical physics), leap-frog algorithms, the Hairy Ball theorem, mice (set theory), sober spaces, Swiss cheeses, the Achilles and tortoise paradox, dirty black holes, slug flow, lobster trees, Colonel Blotto's game, the drunkard's walk, and the problem of logical sloth.)

Here are a few words which do not yet occur in titles of mathematical papers, and are thus a challenge to future mathematicians:

albatross, custard, disgusting, elk, foolish, jackdaw, lumberjack, puffin, raving, weasel, wombat.

Last updated January 23rd 2003. Thanks due to various contributors (you know who you are).

Tuesday, 24 March 2015

Jeeves and the slippery paradox

A recently discovered manuscript containing an unpublished P.G. Wodehouse story has led some scholars to the theory that the "Bertie Wooster" stories were in fact based on the career of Bertrand Russell, and that the Drones club was none other than Trinity College, Cambridge. Here is the story so that readers can decide for themselves.

"Professor Whitehead to see you, sir," said Jeeves, as he shimmered in with my morning coffee.

Pieface Whitehead is one of my oldest friends and we had been out on the town together only the previous night, celebrating the Boat-race. Indeed two pals of ours, Stinker Hardy and Bingo Littlewood, had been caught throwing a porter's bowler hat into the fountain and it was only thanks to Jeeves' persuading the Senior Tutor that they were washing it for a friend that the Dean had let them off the hook.

"What-ho, Pieface!" I said brightly.

"What-ho, Bertie!" my friend replied. "Dashed off any more of the jolly old Principia lately?"

At this time Pieface and I were collaborating on a little venture which we had given the snappy title of "Principia Mathematica" not realising that it had been used before. My aunt Dahlia (the nice one, not to be confused with Aunt Agatha who is the one who eats broken bottles) had said that she had long known that her nephew Bertrand Rooster had the mind of a shrimp, but that hitherto they had managed to keep it in the family.

"No, I'm still having a spot of bother with the jolly old plot," I confessed. "I'm trying to sort out the proof that 2 plus 2 is 4, but the bally sum doesn't seem to be coming out."

"Well stick at it, old man," said Pieface. "By the way, ever heard of an old boy named Frege? He's sent me this book about set theory. Can't make out what the old buzzard's getting at."

"Foreign johnny, isn't he?" I replied. "One of Jumbo Hilbert's cronies? Man with a strange glint in his eye? Met him once or twice."

At that moment Jeeves shimmered in with a telegram and stood respectfully waiting while I read it.


"I fancy that Professor Frege is in a logical dilemma, sir." replied Jeeves after some thought. "It might help if he were to go to a lady barber, on logical if not sartorial grounds. Naturally one would not expect him to grow a beard. As the poet Wordsworth puts it..."

"This is no time for the poet Wordsworth, Jeeves." I snapped. "Matters of philosophy are at stake."

"Very good, sir. If I may make a suggestion, sir..."

"Oh, fire away, Jeeves. Now is the time for all good men to come to the aid of the party."

"Well, sir, it occurred to me that Professor Frege's logical dilemmas merely constituted a new form of the Epiminedes paradox. Possibly if you were to devise a theory of "types" for him, then he would be able to prove the existence of his shave."

"Er, really, Jeeves?" I asked, somewhat impressed.

"Yes, sir. Indeed it might well lead you to a new proof that 2 and 2 make 4, if I may venture the observation."

The rest is history.

How to be a good lecturer

Well hello and welcome to the first lecture of the course er look I said hello look I'd like to start now will you shut up SHUT UP PLEASE oh thank you I don't mind you talking if you do so quietly I didn't ask to do this course you know I wanted to do algebra I told them I didn't know any analysis

now this course is all about complex numbers and I've got a list of recommended books here er well no in fact I seem to have left it behind never mind they're all out of print anyway now let me write up a definition where's the chalk gone ah here it is SNAP ah let me take another piece THUD not very big these platforms are they I keep falling off them

now definition 1.1. is ah um of course I haven't said what this section's called yet oh it doesn't seem to have a name anyway it's all about convergence of power series you did something like it in real analysis didn't you don't you remember well he should have done it in his lectures I don't have time to go into it now

now definition 1.1. scribble scribble can you read that at the back no oh well sit further forward then can you read it at the front ah come to think of it I can't read it either perhaps if I turn on this light ah no not that one another one oh well the cord was a bit frayed I suppose well look that symbol is a capital sigma yes what's the problem yes well green seems to be the only colour they have left in the box probably because nobody in his right mind uses it so they leave it for me

well look perhaps if I explain it in words it's all in the textbooks anyway I can't help it if they're missing from the library people eat them or something well now I'll draw a diagram you don't have to copy this exactly because it's slightly wrong anyway this is diagram 2 good question I think I forgot to draw diagram 1 anyway as I say it doesn't help much phew let me take my jacket off a bit rip oh well I sewed that button on myself you can tell can't you

now let me digress a minute about the history of the subject here it was discovered by Cauchy or do I mean Gauss one of those people and he sent a copy of his paper to someone else who well anyway it's very important and has a lot of applications such as er such as well anyway you will see applications in your other courses I expect of course they don't use the same notation but then they don't have the same ideas of rigour as we do and now let's write down the first result lemma 1.2

lemma 1.2 oh I haven't actually defined radius of convergence yet have I still let me write it up and we can decide what it means later well I still seem to have a few minutes left so I'd better start the proof let n be this and r be this and v be that and n be that no on second thoughts I'm already using n now so I'll call it nu pardon no it's a nu a greek letter you must have seen it before you know greek letters alpha etcetera no this one is nu all right call it v if you like but we're already using v still it won't cause confusion

now multiply this out and obviously what we get is er clearly um oh that can't be right what have I done wrong here can you see the mistake maybe I lost a minus sign somewhere search me oh dear it's time to finish isn't it well give me just 5 more minutes and I'll finish this off and oh maybe I should do this bit again more carefully next time ah that should have been a nu maybe no it should be a v oh it's an r is it oh well look I'll finish this next time I'm sure I've got most of the details right it's really very elementary after all I haven't done anything nontrivial yet...

How to be a good member of a lecture audience

Aaaachoooo! Cough. Splutter. Wheeze. Yes I've got a cold. There's a lot if it about. No I don't use a handkerchief. Sniff. Sniff. Cough. Oh thanks, now I've sneezed on your notes I might as well blow my nose on them. Zurrrrrkkk! Hoooossssh! Now what lecture is this?

Do you think he's got this bit wrong? Well I'm sure you can prove it quickly using matrices. Shall I ask him whether you can? No. Something wrong? No, nothing wrong. I was just wondering if you could prove it more quickly with matrices. Oh I see. Stick my head in a bucket of WHAT? Oh right. Yes.

God this is so boringly obvious. I think I'll do the crossword instead. Mixed-up caterpillar in tribal religion, we hear? Hmm. Can you think of an anagram of caterpillar? Oh I'm SORRY. I didn't realise you were listening to the lecturer. Oh I thought he was proving a different theorem. Excuse me, how do you get x-squared there? You just explained that. Sorry, I didn't realise.

Can I borrow a bit of paper? Have I really borrowed one every day this week? Ah thanks. I don't suppose you have a pen I could use? Yes I'll take care of it. Ooops, it's on the floor. SCRUNCH. Ah well at least we know where it is now.

Eeeek, I've lost my contact lens. It must be down there somewhere. Sorry, yes I'll try and look for it quietly I know you've got a lot to cover today. Could you tell me if there's a contact lens down there? How about the row behind? Yes it is important I can't see without it. Oh it's all right I am wearing it. Just got a bit of dust in my eye. You can stop looking now. Help I'm two blackboards behind now. What can I do?

And how to be a good exam invigilator

O.K. you can start writing as soon as you get to your places. Look would you mind sitting down? What do you mean there isn't a desk for you? You must be in the wrong room. What's your name? Oh. Well there don't seem to be enough desks. Perhaps you could sit on the floor this time. Come on, let's get started.

Ha ha ha ha ha! Oh sorry. I've just seen the joke in question 5. I don't know how they think of them. What a laugh exams are, eh? Anyway don't let me disturb you. Sorry about that.

What do you want? Well why didn't you go beforehand? Honestly, the incontinents you get round here. Well why didn't you bring a pottie with you? Oh all right I'll find someone to escort you. Can't have you stinking the place out, can we? Though maybe you should have a doctor's certificate (rustle rustle). No, it doesn't mention that. O.K. get a move on.

Creak, creak, creak, crash! Bloody hell, they don't make chairs like they used to, do they. I bet Chippendale's chairs never gave way when you leant back on them. Oh well, now I've nowhere to sit down. Tramp, tramp, tramp. (God what a useless answer that chap's writing. Even I know that 2+2 is 4 not 5. Must be nerves, poor chap.) Oh sorry, am I putting you off? I'll go and breathe down somebody else's neck.

Ah, this one looks calm -- he's writing away nineteen to the dozen. A-a-a-a-a-SHOOOO!!! Oh sorry. Yes we can pick up all the sheets of paper. And I'll try and find you a clean question paper. What was that sheet that went through the window? Question 2? Oh well, maybe somebody will pick it up and hand it in to us. You wouldn't have got many marks on it anyway, it's quite tricky.

Right, all writing must cease now. In fact if you knew your stuff it would have ceased 20 minutes ago. Look I told you to stop writing. Well you'll have to hand it in anonymously then, won't you? I don't suppose it'll make much difference to your result.

The first million digits of pi

"The first million digits of pi" is a truly original book. The authors have clearly perceived the breakdown of language as a medium of communication, and have bravely and successfully fallen back on mathematics as a medium for imparting deep truths. Were James Joyce alive today, he would be enraptured by the portentous start to this novel. "3.14159..." is the sonorous opening, and the pace never falters.

The allusions in this novel are many and subtle. For example, the phrase "666" occurs several times, bringing up suggestions of the Beast of the Revelation. Whether it was Nero, or maybe Euclid, the authors do not need to say. Another ringing passage begins "1 1 1 ..." clearly symbolising the feelings of isolation and loneliness that the authors suffer. So far the literary establishment has ignored this novel almost entirely -- no nominations for Nobel prizes or Booker prizes, not even a Fatwah from fundamentalist Muslims who might be expected to see this as a parody of the book of Numbers.

I cannot resist quoting a passage which is so rich in allusions that one could study it for a lifetime and still be able to find new insights.

"5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 ..." it runs. Note the rhythm of the passage, the rippling of the nines and the rugged tension implicit in the sevens. Despair is writ in every syllable. Like a Gothic cathedral it towers above mere prose.

What is unique about "pi" -- as it will be known to future generations -- is that it is independent of language. For those who want sex, there is plenty (if they read it in Latin). German devotees of Tolkien will find the 'elf' motif cropping up every so often. French critics have already noticed the references to 'huit' -- it would be rash to rule out the theory that this novel contains the real truth about crop circles.

This is the novel which Archimedes longed to write. As Rousseau put it, Man is born Three. So indeed is Pi, and what follows is the greatest novel on the human condition ever penned.

The private life of Tolkien

Many people have noticed that Tolkien's novel "The Lord of the Rings" bears an uncanny resemblance to the game of Dungeons and Dragons, in that it contains elves, dwarves, orcs and so forth. Clearly Tolkien was much influenced by D&D, and a recently unearthed recording, probably made by MI5, shows him playing Dungeons and Dragons on the floor of his rooms in Merton College, Oxford one evening with C.S. Lewis, Charles Williams, and various other luminaries.

Here is part of the transcript of the recording, which all will agree is of great historical interest.

C.S. Lewis: Well, Tom, it's really good of you to come along and act as Dungeon Master for the evening. Haven't enjoyed myself so much since I played in G.K. Chesterton's dungeon and slew Father Brown.

T.S. Eliot (for it is he): Thanks. Anyway, is Father Aslan going to go and explore the Waste Land further yet, or will he have another drink?

Lewis: That depends on the rest of the party. Radagast?

Tolkien: Yes, I want to go and see Madame Sosostris the clairvoyante and see what she has to say.

(Murmurs of assent from Dorothy L. Sayers, Charles Williams, Bertrand Russell (visiting), etc. etc.)

Eliot: O.K. Radagast I want you to roll a D20 at this stage to see what happens as you walk across the Waste Land.


Tolkien: Who is it?

Voice outside: Iss only me, Professor Tolkien. Juss poor Smeagol. He's brought his essay for the nice Mr Professor.

[Tolkien goes over to open the door, doing his best to block the view of the dice, counters and miniature monsters on the floor. Meanwhile the rest of the party hurriedly leap into chairs and pretend to be having a deep discussion.]

Lewis: Yes but we all remember what St Paul says about the Numinous in his Epistle to the Confusions...

Tolkien: Well, Smeagol, where's this essay? Can't you see I'm busy discussing the Numinous?

Smeagol: Don't be hard on poor Smeagol, he couldn't find his precious elvish dictionary. That nasty Baggins had borrowed it. Oooh, what's that on the floor?

Tolkien: Er, nothing. My son must have left his toys there.

Smeagol: Can Smeagol be an orc?

Bertrand Russell: Certainly not. We don't want any orcs. I've come over specially to play White Head the dwarf.

Lewis: You mean, 'to argue the non-existence of God,' don't you?

Russell: Er, yes. Sorry.

Tolkien: Off you go boy and hand your essay in on time in future. [Door slams]. Now, my character Radagast threw a 12. What happens to him?

Philosophy class

O.K. I'll take the roll call. Archimedes? Wittgenstein? Hobbes? Buddha? No, just say "Yes," not "Om", boy. Locke? Hume? Descartes? What do you mean you don't know, boy? Think. That's better. Yes, of course you're here. Kant? Heidegger? ... oh all right I think everyone else is here.

Now today we're going to... Socrates. What are you drinking in class? Hemlock, boy? Put it away? I don't care if you are going to die, you're not doing it in class. And stop egging him on, Plato.

Who said "Om" just then? Was that you, Buddha? If you're going to be enlightened, do it later. Now be quiet. Yes, meditate if you wish.

You're being very rowdy today. And you, Nietzsche, shouldn't be wearing that Superman tee-shirt in class. I don't care if it is going to supersede mankind. It's not doing it today.

Archimedes! Come back boy. You can't run around shouting "Eureka" every time you have a bright idea. It disturbs the others. And you ought to be wearing more than a bath towel anyway.

Descartes, are you still with us? Wake up, child. Now your work is due in today. Russell, I want you to get the work from just those people who don't hand it in themselves, and hand it in. What do you mean, that's a logical contradiction? Yes, of course you have to hand in your own work. No, that doesn't mean that you don't hand it in yourself.

Zeno. Why didn't you do the work? You did half of it, yes. Then what? You had to do half of what was left? Yes, right. Then what? You still had to do half of what was left? ... Well everyone else manages. You ought to organize yourself better, boy...

About this blog

I'm gradually transferring files from my private home page at Leeds. These were mostly written 20 years ago, but there may occasionally be the new post as well.