Mathematics and poetry

The essence of poetry is ambiguity. A good poem can be read many times; each time you read it, some new facet or shade of meaning presents itself to you.

By contrast, the essence of written mathematics is clarity. The writing must say exactly what the author means, and explain it clearly.

So probably there is no deep connection between these two subjects. (And yet I can’t help thinking that there must be more to it…)

In fact there is one place where mathematics and poetry meet. Consider cryptic crosswords: a good clue certainly should have poetry about it, but the answer should be completely precise. There is nothing more irritating to a crossword solver than an inexact clue or one with superfluous words.

More generally, the kind of poetry with very strict rules often appeals to mathematicians. The sonnets, triolets, villanelles, and so on of yesteryear are not as popular as they were, but mathematicians are attracted to forms like the limerick, the haiku,…

And the higgledy-piggledy. Here is a brief description from Robin Whitty’s Web page, which gives many examples of higgledy-piggledies associated with Theorem of the Day:

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 …

I was able to make use of the result of his creativity on one occasion. Here is a picture of me leading the audience in a recitation of a higgledy-piggledy on the Sims conjecture, at a conference for Cheryl Praeger’s birthday (she was one of the team who proved it).

Higgledy-Piggledy Higgledy-Piggledy

But I want to talk about an experiment I did a few years ago on an older form, the sonnet. I had been given the Wordsworth Book of Sonnets as a present. Contrary to what you might think, this is not a book of sonnets by the Lake poet; but a book of sonnets by many hands, published by a company called Wordsworth, who specialise in cheap editions of out-of-copyright material. The book was edited by Linda Marsh and published in 1995.

There are rules for sonnets, but all the great poets who have used the form break these rules. Roughly speaking,

  • there are fourteen lines, each an iambic pentameter;
  • the lines split as 8+6, with a development of subject-matter or tone from the 8 to the 6;
  • the rhyme scheme is ABBA ABBA CDEDEC (though the scheme for the last six lines is quite variable).

Hopkins wrote many sonnets, and used the rules very creatively; his sonnets may be shorter (one famous one is 10 1/2 lines, split as 6+4 1/2) or longer; extra feet are often added to a line.

Anyway, I decided I could regard the entries in the Index of First Lines in the book as an acceptable selection of sonnet lines (that is, breaking the rules to the degree that great poets thought appropriate). Now it was a case of dividing them up according to rhyme, and selecting lines with an eye to the sense. As you might expect, I had to watch the rhyme very consciously, and meanwhile something unconscious happened with the meaning; I think the overall effect is not too bad. Here it is.


Earth has not anything to show more fair!
Now sleeps the crimson petal, now the white;
In the long, sleepless watches of the night,
All Nature seems at work. Slugs leave their lair,
Keen fitful gusts are whispering here and there,
The azured vault, the crystal circles bright.
O soft embalmer of the still midnight,
What has this bugbear Death that’s worth our care?

Beauty, sweet Love, is like the morning dew.
There is a silence where hath been no sound;
It is the season of the sweet wild rose.
Lord, With what care has thou begirt us round!
When I consider every thing that grows,
I seek but one thing – to make sure of You.

Somehow there is a progression, from night to morning, and from a rather material view of nature to one which is more spiritual (I think).

For the record, the lines are the first lines of sonnets by Wordsworth, Tennyson, Longfellow, Coleridge, Keats, King James I, Keats, Walsh, Daniel, Hood, Meredith, Herbert, Shakespeare, and Mary Queen of Scots. Poetry was clearly a right royal occupation once!

P.S. It occurs to me that, as Martin Gardner once advocated, I have reversed Lewis Carroll’s maxim “Take care of the sense, and the sounds will take care of themselves”.

P.P.S. Ivar Ekeland, in The Broken Dice, and other Mathematical Tales of Chance, (University of Chicago Press, Chicago, 1993), says:

The formalism and rigor of skaldic poetry is in no way inferior to that of modern mathematics, and anyone who is able to weave kjenninger while respecting the rules of alliteration will also be able to derive theorems from one another following the rules of logic. In both cases, creativity is a bonus; it adds meaning and beauty and distinguishes the artist from the laborer.

About Peter Cameron

I count all the things that need to be counted.
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6 Responses to Mathematics and poetry

  1. JoAnne says:

    Thanks for the tribute to Martin Gardner on an earlier day — and for this thought-provoking entry as well. I agree to the reversal of the Lewis Carroll maxim but I disagree with a bit with your opening use of the term “ambiguity”–for I think that good poetry and good mathematics BOTH are rich from from the multiple meanings that cling to each symbol. I have tended to think of this not as ambiguity but as clustering or “chunking” of much meaning around few symbols.
    When time allows you can find some of my thoughts concerning math-poetry connections at

    • I admit I said that to be provocative. But I think both opinions have some truth in them. A piece of mathematics must have a single meaning which is clear. If it has more, that is a bonus!

      Thanks for your link.

  2. Pingback: Ambiguity « Peter Cameron's Blog

  3. Perhaps these comments got a bit hijacked by the discussion of ambiguity. There are other issues too.

    I am currently reading Sasha Borovik’s book Mathematics under the Microscope, and came upon this: “. . . we should not be disappointed that everyday language does not work any longer at the apex of our little theory. It is natural; like poetry, the very reason for the existence of mathematics is that it expresses thoughts and feelings which we cannot express in mundane everyday language. “

  4. The majority of men meet with failure mainly because of their absence of persistence in building innovative plans to take the place of those which fail

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