Higgledy-piggledy Science'n'Philosophy


Science'n'Philosophy —

Feynman, the latter

Pronounced 'wugga-mugga';


How would he view modern,


Particle physics

The clever old so-and-so?


Double dactyl, or "Higgledy-piggledy" is a verse form. It is described in a nice Wikipedia entry which gives lots of examples, all of them biographical; and indeed, this seems to be a defining feature, as it is with the clerihew (and the limerick for that matter, at least as popularised by Lear and allowing for imaginary subjects). In its biographical guise the double dactyl was, apparently, 'invented' by the American poet Anthony Hecht in collaboration with Paul and Naomi Pascal, in 1951. Its basic structure is surely much older; consider:

Moses supposes his

Toeses are roses but

Moses supposes



For nobody's toeses

Are poses of roses as

Moses supposes his

Toeses to be

made famous by that duet in Singing in the Rain (1952) but presumably traditional.


The limerick is too hackneyed to be worth talking about, or writing except when some special effect is needed. The clerihew is less well-known and to my mind is very difficult: there is hardly room to do more than associate, in a deliberately inane or deadpan manner, the subject with something that he or she is famous for; it is a delicate balancing act. Here is a nice example by the group theorist John Dixon:

Camille Jordan

Camille Jordan

Was a remarkable man.

His famous Traité

Is still read today.


Only a Haiku says more with less. (By the way where does this come from:

I think the Haiku

As a verse form is best left

To the Japanese.

I wonder?) Anyway, Higgledy-piggledies, being slightly longer, should allow room to amplify a bit: the best amount to a mini-lecture on the person's life, character or work.

Martin Heidegger


Herr Rektor Heidegger

Said to his students:

"To Being Be True!

Lest you should fall into


This I believe

And the Führer does too!”

   Anonymous, apparently. I read it in this book review by Simon Blackburn


Werner Heisenberg


Herr Werner Heisenberg

Said "Now Your Honour

It just isn't fair,

That I was speeding is


Or if I was, then

I can't have been there!"

   Anonymous. I found it on Science Connection's jokes page


Those two seem perfect to me. They are a model for the solemn and weighty rules for a Higgledy-piggledy (c.f. this (paywalled) 1967 Time article and echoing more or less those given by Wikipedia for Higgledy-piggledy's close cousin, the double amphibrach):

  1. Lines 1-2: State subject's name, preceded by a nonsense double-dactyl. If you can sneak in some extra information, so much the better: Heidegger was Rektor of the University of Freiburg for one unsuccessful year (1933-34) and his inaugural address is a nationalistic rant.
  2. Lines 3-4: Introduce what it is you want to celebrate about them (perhaps as a teasing question or riddle)
       Said "Now your Honour/It just isn't fair"
  3. Lines 5-6: Resolve this introduction, with line 6 consisting of a single, six-syllable word which forms the poem's centre of gravity and captures the essence of its material.
       Inauthenticity, Unascertainable
  4. Lines 7-8: Conclude on a humorous counterpoint:
       This I believe/And the Führer does too!


I will now try and assemble a collection of double dactyls, double amphibrachs and muddled hybrids, one for each theorem posted at www.theoremoftheday.org. A waiver: Rule no. 3, humiliatingly disorientating my lexicographical manoeuvrability, is seldom obeyed!


If anyone would like to choose a theorem and contribute to this pointless endeavour that would be fun! Just email it to me at the address at the bottom of this page, or even write it in the visitors' book.


Pierre de Fermat

Higg-le-dy-pig, a dit

Pierre de Fermat:

"For two non-zero nth powers,

n more than 2,

To sum to a third requires


(Marginally harder

Was proving it true!)

   See Theorem no. 9


R.A. Bailey


R.A. Bailey,

Found what makes Latin Squares


A not inconsiderable,



Statistical feat.

   See Theorem no. 53


Johannes Kepler


Johannes Kepler,

Said spheres pack with density,

Pi over root

Eighteen; a propensity

For close proximity

Which, pending Flyspeck,

Is still a bit moot.

   See Theorem no. 101

(Since I wrote that last, the mootness of Kepler is banished, Flyspeck having successfully completed!)

Peter Cameron


Thus Peter Cameron,

(One might imagine)

Arriving in heaven:

"Take a random, sum-free set of

Positive integers..."

Thus God: "... oh ... gosh! ... about ...


Find out more here. Taking my eye off the ball — that wasn't a Theorem of the Day at all, or not yet anyway.


And having lost my thread, I will digress to mention a sort of triple amphibrach which I wrote a long time ago when I was coincidentally at Goldsmiths College with the much more illustrious Geoff Whitty. In fact I seem to remember I published it in the staff magazine Hallmark, under the pretence of providing a helpful aide-memoire. It was easy to write; much more difficult, as an exended version of "Which witch is which", to speak!

Which Whitty's Which?

"Which Whitty's which?" Goldsmiths College cried,

When faced with the two of them, side by side,

And it's true, it's a difficult thing to decide,

Unless you are very discerning.

Now Whitty's a witterer; Whitty's a whit

Less witty than Whitty is witty, to wit

The wit Whitty's writing concerning

Which Whitty's which Whitty and which is the wittier

Whitty and which is it wittily witters

And which is the Whitty that's written the wit

About which Whitty's which Whitty, which wit is which.

Of the two, it is true there's a weightier Whitty;

You'll find when you get down to the nitty-gritty,

This Whitty's a twit (but ... 'e's learning)


Anyway, enough of that — time to get back on track!

Neil Robertson and Paul Seymour



Made well-quasi-ordering

Trendy and cool:

Bulldozing out of the

Slums of topology

Chic mathematical

Urban renewal.

   See Theorem no. 52


Euclid of Alexandria


Euclid, like Bourbaki,

May not have actually

Existed as such;

With his/her/its proof

The primes form an infinitude,

I'm not so sure that it

Matters that much.

   See Theorem no. 4


Julia Robinson


Julia Robinson,

Spent her career,

Proving r.e. is D.

Her joy in acknowledging

Yuri Matiyasevich is

Why she's a personal

Hero of me.

   See Theorem no. 43


A.D. Forbes, M. Grannell, and T. Griggs



Coloured three points per quadruple

Blue, the fourth one red,

Constructing thereby the

Design of the Century:

Type B bipartite S(


   See Theorem no. 100


John D. Dixon


John D. Dixon,

Decided a question of

Eugene Netto:

Two random perms complete


\lim as n \rightarrow

\infty, bestow.

   See Theorem no. 49


\Pi \Mu


Peter M. Neumann:

Three cheers for his Maths Gene-

alogy stemma!

Three cheers for Omega's


As it obeys his Sep-

aration Lemma!

   See Theorem no. 64

Perhaps this is growing monotonous? Perhaps I am inserting a limerick or two just so I can reuse 'one I did earlier'? Or it's because Higgledy-piggledy doesn't really lend itself to playing fast and loose with form in the way that the limericks does:

Lowell Beineke

The mathematician Lowell Beineke,

Has characterised the graphs leineke

Thus: it is forbidden,

In G, to find hidden

A graph from his set of size neineke.

              See Theorem no. 48


R.L. Goodstein

From Louis Goodstein the logician

Comes hereditary base-k attrition:

Start his sequence at 4:

It's increased to three-score

In three steps, then some more: ..., 584, ..., 884, ...


(now imagine a long intermission)


..., 2, 1, 0 (done!)

                         See Theorem no. 73


Kazimierz Kuratowski

Who gave K5 and K3,3,
To those who thought planarity
Was nothing but topology.

       See Theorem no. 24

This last, by Frank Harary, which appears on Theorem of the Day courtesy of the Perseus Book Group, has lured me into the territory of the iambic quadrameter where can be found this, still only too relevant more than a hundred years after it was published:

The Microbe

The Microbe is so very small

You cannot make him out at all,

But many sanguine people hope

To see him through a microscope.

His jointed tongue that lies beneath

A hundred curious rows of teeth;

His seven tufted tails with lots

Of lovely pink and purple spots,

On each of which a pattern stands,

Composed of forty separate bands;

His eyebrows of a tender green;

All these have never yet been seen —

But Scientists, who ought to know,

Assure us that they must be so....

Oh! let us never, never doubt

What nobody is sure about!

     From More Beasts for Worse Children, Hilaire Belloc, 1897

The link to the excellent Baldwin Project will allow you to read The Microbe with Basil T. Blackwood's



illustrations from which it must always remain inseparable. Their absence on this page leaves me space to quote from Belloc's no less timeless tease directed at the academy (and even at constrained writing):


      Don dreadful, rasping Don and wearing,

      Repulsive Don — Don past all bearing,

      Don of the cold and doubtful breath,

      Don despicable, Don of death;

      Don nasty, skimpy, silent, level;

      Don evil, Don that serves the devil.

      Don ugly — that makes fifty lines.

      There is a Canon which confines

      A Rhymed Octosyllabic Curse

      If written in Iambic Verse

      To fifty lines. I never cut;

      I far prefer to end it — but

      Believe me I shall soon return.

      My fires are banked, but still they burn

      To write some more about the Don

      That dared attack my Chesterton.

           Lines to a Don, Hilaire Belloc, 1910


Alors, revenons à nos moutons!

François Viète

Hegel de Pigalle dit:

François Viète,

A fait l'impossible

Quadrature du cercle:

Faut juste reconstruire

Sa circonférence par

Des racines carrés pendant

... Deux, trois siècles.

   See Theorem no. 102

Cheryl Praeger


Cheryl E. Praeger,

With Cameron, Saxl and

Seitz, answered C.

Sims: Yes! Orbit size, but for


Does `bound' |G_x|


   See Theorem no. 65

Sophie Germain

Hegel de Pigalle dit:

Sophie Germain —

Vos premiers éponymes de quoi

S'agit-il donc?

"Ça dépend les cas! C'est


Vaut mieux que vous demandiez à

Monsieur LeBlanc!"

   See Theorem no. 59

What's it all about then, this Hegel-Pigalle thing? Hegel visited Paris in 1827 but at that time Montmartre was not even a part of the city and anyway he stayed in the 6th arrondissement on the other side of the river. So those first lines are complete and utter rubbish, which is as it should be in a double dactyl. (I had a little help from Emmanuel Amiot with those, by the way.)


Kate Okikiolu



Beginning her journey at

Jones in 2D,

Ended it solving the


Analyst's version of

The TSP.

   See Theorem no. 108

Kenneth Appel and Wolfgang Haken


Appel and Haken,

Announced to the world that "Four

Colours Suffice";

("Fail us not, in thine un-



Reducing Device!")

   See Theorem no. 1

Kenneth Arrow


Kenneth J. Arrow —

Invoked by the ballot box


"Combine IIA with

Pareto Efficiency —

You'll only end up with

A bloomin' dictator!"

   See Theorem no. 69

Emanuel Sperner


Emanuel Sperner

Coloured his triangles

red, blue and green;

Whereby bi-chromatic and


Coloured ones were not

The only ones seen.

   See Theorem no. 16


Isaac Barrow and Isaac Newton


Isaac and Isaac

Established duality

Twixt f(x),

And the area 'neath f, its


And 'tween this f and


   See Theorem no. 2


An ironic abuse of notation since I've used Leibniz's rather than Newton's!

J. Beardwood, J.H. Halton and J.M. Hammersley


Jillian Beardwood,

John H. Halton and

John Hammersley,

Routed their salesman


Through asymptopia


   See Theorem no. 109


The term 'asymptopia' was used by David L. Applegate in an email to me — it is perfect.

David Gale and Lloyd Shapley


Gale and Shapley,

Leant the estate that is

Not entered lightly,

Pre-emptive advice against

(Nudge, nudge) activities:
Choose Mr rightly!

   See Theorem no. 68


Actually I received from John Drost a very neat haiku on this same theorem which sums the whole thing up in just 8 words instead of 8 lines:


    unmarried couples

    not preferring each other

    makes stability

And having been again seduced from the double dactyl I will venture so far as the iambic heptameter or fourteener, because I cannot resist posting this gem, which my friend Helen Connies-Laing emailed me:

John Welsey Brown et al (and Dr Rutherford)

Today I turned my calendar of ‘Theorem of the Day’

And for once I felt an inkling of what the theorem had to say.

You see, I recall a discussion long ago with Dr Rutherford

When she tried quite hard to explain to me why Latin squares are good.

She told me about farmers and planting stuff in fields

Though there’s nothing on the calendar that with agriculture deals….

She didn’t mention Wesley Brown, Fred Cherry or the rest –

In the light of which, I feel that I really must protest.

Has she really got a PhD in Matroids/Combiniatorics?

Is that why our discussions have the same effect as Horlicks?

Because looking at the calendar, today on June’s first day,

Not a sausage corresponds to what Dr Ruther had to say.

I like the pretty colours – though the yellow’s rather loud

And I must admit when I saw the squares I felt a little proud.

You see, it’s very rare I open it and see upon the page

Something – however tiny – with which I can engage.

   See Theorem no. 131

An exercise in constrained writing:                                                    ...and some unconstrained inventiveness:


Stepan Banach

If M's a complete metric space,

And non-empty, we know it's the case

That if f's a contraction

Then under its action

Just one point remains in its place.

              See Theorem no. 145

      See Theorem no. 143

The inventiveness being that of Dilip Sequeira, whose clever verse sparked a scintillating rejoinder from Michael Fryers (in Eureka, nos. 52 and 53, respectively—I am grateful to the Archimedeans for permission to reproduce Sequeira's poem here and both of them in Theorem no. 145 itself).

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