Discovering Patterns in Mathematics and Poetry

There was a young man from Trinity
Who solved the square root of infinity.
While counting the digits,
He was seized by the fidgets,
Dropped science, and took up divinity.¹ 

Are you surprised that this MAA Review begins with a poem? Perhaps not! The poem aptly describes the feeling many mathematicians have suffered while fiddling too much with infinity. Then let us ask the question, which would surely surprise you and catch your attention, what is common between the above poem and the sequence {(2n+1)/4}? If still not surprised and the answer is not apparent, then let us try one more example: compare the sequence 1/(–1), 2/2, 3/5, 4/8? with the nursery poem, "One, Two, Buckle my shoe; three, four shut the door."

Apart from the natural numbers present in both the sequence and the poem, what each of them has are countable patterns: we all know the patterns that are present in the above sequence. The patterns in the poem lie in the form of rhythm and rhyme. It is an example of accentual verse where four stressed beats are present in each line.

Discovering Patterns in Mathematics and Poetry, by Marcia Birken and Anne C. Coon, shows the readers the commonality between mathematics and poetry. Both mathematics and poetry have regular structure and patterns. Many poems have particular shapes, sizes and form much like the geometrical figures of mathematics. Just like numbers can be counted, beats, stresses, syllables, rhythm, feats can be counted in poems. Particular patterns in mathematics give us Pascal's Triangle or Fibonacci sequence; similarly, certain types of patterns give us sestina, sonnet and villanelle in poetry. Also many poems have symmetry much like mathematics..

Poetry is also influenced by mathematics as evident in the following poem Fractals, by Diana Der-Hovanessian.

Euclid measured order and left the knot
of chaos to be unraveled by Mandelbrot
who found truth in the course of blood and air.
Euclid looked on beauty stark and bare,
But Mandelbrot appraised her everywhere.

Another example of mathematical influence on poems can be found in Nautilus, in which Denis Garrison created the poem based on Fibonacci sequence. The number of syllables in the first seven lines of the poem follows the Fibonacci sequence: 1-1-2-3-5-8-13. The last seven lines of the poem have the sequence in the reverse order: 13-8-5-3-2-1-1.

Not surprisingly, mathematicians also often dabble in writing poems. Mathematicians celebrated the proof of Fermat's Theorem by Andrew Wiles through a poetic competition. Fermat's Last Theorem Proven, by Marion Cohen, was one of the poems in the competition:

Fermat said the proof was too large
To fit in the right or left marg-.
True, back of the paper
Or proof made to taper
Might help, but he said, "I'm in charge".

Iamb, trochee, dactyl, anapest, spondee; true, slant, masculine, feminine, eye and internal rhymes, virelay — many such intriguing terms are explained in the book as are explained, sonnets, ballads, limericks, sequences, fractals, hyperbolic geometry and cyclic numbers. The book gives interesting historical snippets: Al-Karaji of Baghdad referred to arrangements of numbers in a tenth century work. Who knew poems could also be experienced as visual art? Sometimes they even need to be solved (so that they can be read and enjoyed) like puzzles:

The above is an example of a pattern poem in which five Latin words, sator, arepo, tenet, opera and rotas, can be read top to bottom, bottom to top, left to right and right to left. If one is interested in all this information, one should read this book.

The book is written in a straightforward way that anyone without any deep knowledge in mathematics and poetry would be able to follow and understand. It is a book that can be read easily and appreciated by both young and mature readers. Mathematicians would find this book useful as a tool to pique students' interest in mathematics. Poem-lovers would come to know a great deal about poetry. As the authors have said, "We hope to translate their languages [the language of mathematics and poetry] for a general audience." The reviewer feels that they have succeeded.

The book should be available in public, school and college libraries. The book can and should be used as a text book in schools and colleges to intellectually challenge students and introduce them to the various deep and profound concepts in mathematics and poetry. Perhaps that would lead many students to appreciate mathematics (the reviewer sincerely hopes so, since she is very biased towards the subject) and to experience the feelings expressed by Walt Whitman in When I Heard the Learned Astronomer:

When I heard the learn'd astronomer,
When the proofs, the figures, were ranged in
Columns before me,
When I was shown the charts and diagrams, to add, divide,
And measure them,
When I sitting heard the astronomer where he lectured
With much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander'd off by myself,
In the mystical moist night-air, and from time to time,
Look'd up in perfect silence at the stars. 

[1] All the poems, examples and facts in this review are taken from the book. While giving some of the examples, I did not mention the name of the poet or the poem. Everything is in the book and anyone interested should refer to the book.

Srabasti Dutta received her PhD from SUNY–Stony Brook and is currently an Assistant Professor in the College of Saint Elizabeth. She is also the public relations officer for MAA-NJ. She can be reached at srabastidutta@gmail.com.