Good numbers . . .

     My wish for the New Year 2012 is that you will have good numbers -- that your happiness will have high peaks, that your sadness and grief will weigh no more than you can bear.
     In the spirit of assessment and introspection that captures many of us at year-end, I offer a small poem, "Good Fortune" -- one that I wrote in late December ten years ago when I was, as I am now, taking stock. "Good Fortune" appeared in my 2006 chapbook, My Dance Is Mathematics (Paper Kite Press -- available online here). Another tiny poem, a more recent one, "14 Syllables" -- from Red Has No Reason (Plain View Press, 2010) -- continues the focus on assessment using numbers. 

A mathematical woman

As in an earlier posting (20 December 2011), today's feature includes verse by Lord Byron (1788-1824). This time the source is Byron's satiric poem Don Juan. In Canto I, the poet describes Don Juan's mother, Donna Inez, as learned and "mathematical." Here are several stanzas about her -- sagely seasoned with words like "theorem," "proof," and "calculation."

Counting on Christmas

 11

 one1

 2 two 21

 3 three 3 31

 4 4  four  4 41

 5 five 5 5 5 five 51

 6 six 6 6 six 6 6 six 61

 7 7 7 seven 7 seven 7 7 71

 8 eight 8 8 8 eight 8 8 8 eight 81

 9 nine 9 9 nine 9 9 9 nine 9 9 nine 91

 10 ten 10 10 10 10 ten 10 10 10 10 ten 101

 11 eleven 11 11 11 11 11 11 11 11 11 eleven 111

 12 twelve 12 12 12 12 12 12 12 12 12 12 twelve 121

 HAPPY1

  HOLI  -1

 DAYS !!1

Thoughts Suggested by a College Examination

Just when I was convinced that mathematical subject matter appears proportionately more in modern than in classical poetry, I turned again to work by Lord George Gordon Byron (1788-1824) and began to contradict myself. Here (from Byron's Complete Poetical Works) is "Thoughts Suggested by a College Examination."  As is common today in literature and verse, the mathematicians (and scientists) are found wanting (though we are not the only deficient ones).

Ruth Stone counts

It seemed as if she might write -- and write well -- forever.  But she did not.  Moreover, poems by award-winning poet Ruth Stone (1915-2011) are not celebrated for their use of mathematical imagery.  Still, she noticed numbers.  She counted.  As in "All in Time."  

A puzzle with a partial solution

     When we have experiences near to each other, we may try to connect them. We form superstitions. "Bad things come in threes" -- and something similar for good things. And we make poetry -- offering new associations that delight and surprise.
     Gertrude Stein is one of my favorite poets. She was, like me, born in Pennsylvania (though she, unlike me, left and became Parisian).   She creates almost-meaning from unlikely juxtapositions.  I find in her work the delight of a puzzle to which I can find a partial solution. And come back for more. Here are two stanzas from Stein's "Stanzas in Meditation" that play with some mathematical meanings.

Poetry captures math student

This sonnet retells a familiar story -- a teacher influences a student's choice of studies. Prior to reading, many in mathematics may wonder:  how can a student leave mathematics for poetry when mathematics is poetry?  Whatever your view, I think you will enjoy this poem.

Prof of Profs       by Geoffrey Brock

     For Allison Hogge, in memory of Brian Wilkie

I was a math major—fond of all things rational.
It was the first day of my first poetry class.
The prof, with the air of a priest at Latin mass,
told us that we could “make great poetry personal,”

Monsieur Probabilty

In recent months, I have encountered a variety of poems about mathematicians (Links to several of these are provided at the end of this post.) and one of the sources is Scottish poet Brian McCabe's  collection Zero (Polygon, 2009).    It is said that life imitates art -- and this is vividly demonstrated by the art of mathematics as lived by Abraham de Moivre (1667-1754).  Here is McCabe's poem. 

Poetic Pascal Triangle

First published in 2007 in Mathematics Magazine, Caleb Emmons' poem "Dearest Blaise" has the form of (Blaise) Pascal's Triangle.  That original publication offered also a challenge:  what is the next line of Emmons' poem?   What is your guess?  

Mathematics works with witchcraft

T. A. Noonan sometimes uses the languages of mathematics and computer science as tools in her experimental poetry, gathered in her collection The Bone Folders (Sundress Publications, 2011).  These poems examine -- at times with mathematical vocabularies and notations -- the complexities of love and loss in the regime change in a coven of Louisiana witches.  Here, for example, is Noonan's opening poem, "Difference Engine." 

Echoes of childhood rhymes

For those of us who live and breathe mathematics, there is much of it that affects us deeply.  Even those of us whose mathematics is mostly arithmetic have a literature of number that we hold close .  And does anything affect us more than the counting rhymes of our childhood?  Washington, DC poet Rosemary Winslow uses emotionally-charged repetition of nursery-rhyme numbers to help us know incest in "Four Five Six." 

How much for a digit of PI?

Scottish poet Brian McCabe writes playfully of numbers.  In the following poem he imagines an auction of the digits of π.

   Three Point One Four One Five Nine Two
   Six Five Three Five Eight Nine Seven Nine
   Three  Two Three Eight Four Six Two Six
       Four Three Three Eight Three Two
         Seven Nine Five Zero Two Eight             by Brian McCabe 

Open and Closed -- Tomas Transtromer

A background in mathematics gives my enchantment with words a special twist. Each time I see familiar math terms in a poem I layer their mathematical meanings amid their mainstream ones. Two such terms are "open" and "closed." (I'll supply brief mathematical explanation at the end of this post but, first, here is "Open and Closed Spaces" -- a poem by the winner of the 2011 Nobel prize  for Literature, Swedish poet Tomas Transtromer. )

Reading the Rubaiyat

Omar Khayyam (1048-1131) was a mathematician who wrote poetry.  Here are two quatrains from his Rubaiyat.

        XLVI

   For in and out, above, about, below,
   'Tis nothing but a Magic Shadow-show
        Play'd in a Box whose Candle is the Sun
   Round which we Phantom Figures come and go.  

Equivalence

In telling the time, we commonly refer to hours that differ by a multiple of 12 using the same number. Sixty hours after 3 o'clock it is again 3 o'clock. The clock relationship -- with its times that are named by the same number but are not, after all, exactly the same -- illustrates the mathematical notion of an "equivalence relation." In "Equivalencies," the insights of poet Judith McCombs stretch this mathematical concept.

Equivalencies     by Judith McCombs

The fear of not writing, of having no words,

Is the muscles not working, the pack top-heavy,
the hard slime on ledges where the ankle gives way

Portrait of Max Dehn

Today I offer a poem by Portuguese mathematician F. J. Craveiro de Carvalho -- its initial English publication was in Topology Atlas, 2005 -- about an outstanding mathematician, Max Dehn. Dehn inhabited Craveiro's office via a Springer-Verlag Poster.  Here is a portion of  Craveiro's introduction to the poem.

Portraits of a mathematician

Ideas for this posting began with my post on 30 October 2011 in which I selected 7 favorite lines of poetry as a sort of self-portrait.  That posting led to an exchange with blogger Peter Cameron -- which prompted me to write these abecedarian portraits of a mathematician.

   I know a mathematician . . .     by JoAnne Growney  

   always busy
   counting, doubting
   every figured guess,
   haply idling,
   juggling, knowing
   logic, measure, n-dimensions,
   originating
   playful quests,
   resolutely seeking theorems,
   unknowns vanish :
   wrong xs, ys -- zapped. 

Mathematics of desire

Last Monday evening, I listened with pleasure to Pennsylvania (Fogelsville) poet Barbara Crooker read at Cafe Muse (with Meredith Davies Hadaway and Erin Murphy). Barbara writes fine poems -- and reads them well. Although she offered no mathematical poems that evening, hearing her reminded me to hunt for her love poem "The Irrational Numbers of Longing . . " and to offer it to you here:

Mathematician-Poet Glaz

     Sarah Glaz, a professor-mathematician at the University of Connecticut -- and a poet -- is at the forefront of appreciation and advocacy of mathematics as an art and closely connected to other arts, particularly poetry.  Her webpage offers more than a hundred links to "Undergraduate Resources; Math Links for Information and Fun" and to scholarly articles that offer teachers and students math-poetry ideas to ponder carefully.  This link, for example goes to an article entitled "The Poetry of Prime Numbers" that Glaz presented at the Bridges 2011 Conference in Portugal.
     One of my favorites of Glaz' poems is this one whose structure relies on the Fundamental Theorem of Arithmetic (see note following the poem).  Here is "January 2009"  :

Four colors will do

     As I work with Gizem Karaali, an editor of the Journal of Humanistic Mathematics, to plan a reading of mathematical poetry at the JMM (Joint Mathematics Meetings) in Boston on 6 January 2012, my thoughts return to a poetry reading that I helped to organize at JMM in Baltimore in 1992. One of the participants was a friend and former colleague, Frank Bernhart, whose work is guided by the rhythm pattern of a well-known song.
     Bernhart is an expert on the Four-Color Theorem and his poem celebrates its history -- including consideration of its proof (in 1976) by Kenneth Appel and Wolfgang Haken. (The theorem asserts that any map drawn on a flat surface or on a sphere requires only 4 colors to ensure that no regions sharing a boundary segment have the same color.)

Division by zero

The November 2011 issue of the Scottish ezine, The Bottle Imp, is just out and it includes my review of poet Brian McCabe's Zero (Polygon, 2009). To stir your interest, I include a few lines from McCabe's title poem (which chronicles the irregular history of zero) -- and then offer a human interpretation of division by zero in a poem by Ann McNeal.

What can 7 objects say? Or 100?

     A friend, a high school art teacher, had one of her students paint a portrait of her -- not of her bodily self but a still life of the seven possessions that she felt best defined her.  Since that time, more than seven years ago, I have been trying to decide what my seven objects would be.  How might I portray me?    
     An article in today's NY Times, "Stuff that Defines Us," reminded me that I have neglected that project.  The article tells of the British Museum's ambitious and fascinating project to choose 100 objects from their collection to summarize the history of the world.

Music on the hypotenuse

Dr. Cai Tianxin is a professor of mathematics (specializing in number theory) at Zhejiang University, China. He also is an accomplished and  well-known poet.

   The Number and the Rose     by Cai Tianxin 

Submit math-science poetry

During the month of November, the online journal Talking Writing is seeking submission of poetry with connections to mathematics and the science.  Submit 4-6 poems to editor@talkingwriting.com.
  

          O                                T     T                 

          ON                                 E               
          ONE                           N     N                

These visual poems "One" and "Ten," above, are mine.

Chaos Over the Hors d'Oeuvres

Some systems of equations can produce vast changes in output with only small changes in input.  Or not.  This sensitivitiy to initial conditions is a key characteristic of chaos.  As happens not infrequently in mathematics, the term chaos also carries larger-world meanings additional to the correct ones -- indeed, the phenomena studied in chaos theory are not haphazardly disordered but are complex.  Very very complex.  Judy Neri's poem addresses this topic. 

Permutations and Centos

A Cento is a collage poem made of lines taken from other poems -- such as a sonnet composed of lines from fourteen of Millay's sonnets, or Shakespeare's -- or from newspaper articles or television advertisements or whatever. Here's a three-line sample from a Cento, "Patchwork," composed by Joanna Migdal to celebrate women poets.

   I dwell in Possibility.                                              (Emily Dickinson, #657)
   Yes, for that most of all.                                        (Denise Levertov, “The Secret”)
   It’s four in the afternoon. Time still for a poem.   
                                                                        (Phyllis McGinley, “Public Journal”) 

A whole and its parts

     Aristotle may have been the first to assert that a whole is more than the sum of its parts.  Mathematics textbooks are likely to say otherwise, postulating that a whole is equal to the sum of its parts. 

     Emily Dickinson also comments on the matter.

                (1341)         by Emily Dickinson
 
     Unto the Whole -- how add?
     Has "All" a further realm --
     Or Utmost an Ulterior?
     Oh, Subsidy of Balm! 

Things the fingers know

Blogger Peter Cameron sent me a link to an lively article, "Eveline Pye: Poetry in Numbers"  in the September 2011 issue of the statistics magazine, Significance.  Written by Julian Champkin, the article tells of Eveline Pye -- lively and interesting Glasgow statistician, teacher, and poet -- and includes a selection of her work. One of the poems offered therein is "Solving Problems."

A small Fib

My dilemma

   I've
   lost
   the art
   of careful
   thought, asea in floods
   of  trivial  information.               by JoAnne Growney

Hamilton -- mathematician, poet, Irishman

     October 15-22 is Maths Week in Ireland -- as I learned from this article in the Irish Times celebrating maths and the Irish mathematician Willam Rowan Hamilton (1805 - 1865).  Turns out that Hamilton's quaternions are useful in design of video games and 3D effects in the cinema.
     Hamilton -- a mathematician, astronomer, and physicist -- was also a poet; a contemporary and friend of Samuel Taylor Coleridge and William Wordsworth. His poems do not speak of mathematics -- but here is a sonnet he wrote to honor Jean Baptiste Joseph Fourier (1768 – 1830), a prominent French mathematician and physicist.

Like poetry, mathematics is beautiful

     Congratulations to Justin Southey who is completing his doctoral studies in mathematics at the University of Johannesburg under the direction of Michael Henning. Recently Justin contacted me to ask permission to include one of my poems in the introduction to his dissertation, "Domination Results:  Vertex Partitions and Edge Weight Functions."  Here is a portion of Justin's request: 

Numbers from the Piano

     Of all of the things we might try to say when we sit down to write a poem, which are the ones we should choose?  Sometimes we may say what first occurs to us -- begin to write and keep going until we are done.  This may suffice -- or it may seem to lack care.  To be more careful, we might seek a pattern to follow:  perhaps we might form lines whose syllable-counts follow the Fibonacci numbers.   Or construct a sonnet -- fourteen lines with five heart-beats per line and some rhyme.  Or devise a scheme of our own.

Counting the women

     The stimulus for this posting appeared a few weeks ago in the Washington Post -- in an article that considers the loneliness of women in STEM fields (science, technology, engineering, math). 
     For me, it was never a conscious thing -- the counting.  It simply happened.  The numbers are small and you know, if you are a woman and a mathematician in a room full of mathematicians, how many women are in the room.  Any room.  It is a small counting number.  Sometimes it is 1. 

How I won the raffle

Dannie Abse is a deservedly celebrated Welsh poet -- and before his retirement he was also  a physician.  I first saw "How I Won the Raffle" in Poetry  in 1992 -- now it also is included in his collection Be Seated Thou (Sheep Meadow Press, 2000).

   How I Won the Raffle     by Dannie Abse

   After I won the raffle with the number
   1079,
   the Master of Ceremonies asked me why,
   ‘Why did you select that particular number?’

Action at a distance

One of the great things about writing this blog is the people who have -- out of the blue and across the miles -- sent along a great poem or tidbit.  One of the valuable contributors is Tim Love, a British computer guy and poet -- and also a blogger (at LitRefs). The mysterious concept of "Action at a Distance" drives this Love poem:

The square root of Everest

Of the poets who frequently use mathematical ideas in their work, Howard Nemerov (1920-1991) is one of my favorites.  Recently, while browsing at The Writer's Almanac, I found this poem.

To David, About His Education       by Howard Nemerov

Math meets Dr Seuss

Blogger Sue VanHattum (MathMamaWrites) sent me a link to a posting on another blog, kGuac, on which she found a Dr Seussical expression of the quadratic formula -- written by blogger Katie Benedetto for extra credit in her college abstract algebra class.  Here are several stanzas of Katie's poem:  

Learning to count

The childhood of Romanian poet Nichita Stanescu (1933-1983) took place during World War II and his teen years during his country's adjustment to a new Communist system; his dark images are drawn from a culture largely unknown to the outside world.  Often, however, he utilized mathematical imagery or terminology; here is his "Learning to count." 

Mathematical theorems tornadoing

This poem is fun!

   Horse’s Adventure    by Jason Bredle 

   The horse discovered a gateway to another
   dimension, and with nothing else to do, moseyed
   into it just for grins, and man, you
   don’t even want to know what happened
   next—it was just, like, Horse at the French
   Revolution. Horse in Franco’s living room.

The wealth of ambiguity

When we read these lines by Robert Burns (1759-1796),

     Oh my luv is like a red, red rose,
     That's newly sprung in June . . .
    
we don't know whether he compares a woman he loves to a flower or whether it is his own emotion he describes.  And the multiplicity of meanings is a good and pleasing thing.  Similarly, when we read the problem,

     Solve the equation, x² + 4 = 0 

Poetry at JMM -- in Boston 6-Jan-2012

Call for Submissions:
     The Journal of Humanistic Mathematics will host a reading of poetry-with-mathematics on Friday, January 6, 5-7 PM in Boston’s Hynes Convention Center at the annual Joint Mathematics Meetings. Reading organizers include JHM editors, Gizem Karaali and Mark Huber, and poetry-math blogger, JoAnne Growney.  Although the reading is open to all, without pre-selected readers, we will prepare a written program of poets who submit their work by our December 1 deadline. Both mathematician-poets and others who use mathematics in their poems are invited to submit.

Baseball, math, and poetry

The end of summer approaches and, with it, the end of the baseball season.  This blog celebrated the triplet (baseball, mathematics, poetry) on 9 April 2010, featuring samples from and links to poems by Marianne Moore and Jerry Wemple. Today we herald the same trio, this time with "Night Game" by Jonathan Holden.

Best words in the best order

     Writers of mathematics strive for clear and careful wording, especially in the formulation of definitions. Well-specified definitions can enable theorems to be proved succinctly. For example, the relation "less than" (denoted <) for the positive integers {1,2,3,...} may be defined as follows:

     If  a  and  b  are integers, then 
               a < b  if  b - a  is a positive integer. 

     Although the simple definition of "less than" as "to the left of" in the list {1,2,3,...} is intuitively clear, the formal definition above is better suited for mathematical arguments. It defines "less than" in terms of the known term, "positive." This sort of sequencing of definitions is common in mathematics -- one may go on to define "greater than" in terms of "less than," and so on.
     Saying things in the best way is also a goal of poetry. Well known to many are these words of poet Samuel Taylor Coleridge (1772–1834): 

Analysis of a sacred site

Poet Allison Hedge Coke descends from moundbuilders and mixed ancestry from several Native American communities with several Europoean ones.  Her verse play, Blood Run, is dedicated to the original citizens of the former city now named Blood Run along the Big Sioux River and to all who work to preserve sacred sites. Moreover, the entire text is mathematically encoded.   Chadwick Allen, an English professor whose interests include American Indian and New Zealand Maori literatures and cultures, has written an article for American Literature that explores the sacred numbers and thematic geometry that connects Hedge Coke's verse with the sacred site; we will offer a sample of Allen's analysis following "Snake Mound"from Blood Run: 

A Piece of Coffee -- Stein with some math terms

I love the poetry of Gertrude Stein.  Perhaps this is so because I have never taken a class in which her work was taught and I have never read it with pressure to "understand."  I enjoy reading Stein's poems aloud.  Because they keep me alert -- both eye and tongue.  Because they puzzle me. And because I sometimes see something amazing, true and almost within reach.  Here, from Tender Buttons / Objects: is "A Piece of Coffee." 

Symmetric 4 x 4 square

Martin Gardner (1914-2010) studied philosophy and was interested in everything.  For 25 years he wrote the "Mathematical Games" feature for Scientific American.  At Magic Dragon Multimedia, Jonathan Vos Post has collected many of the poems Gardner featured in his column over the years.  Here is a symmetric square poem from February, 1964.

            C U B E
            U G L Y
            B L U E
            E Y E S

Applying statistics . . .

From Seattle poet Kathleen Flenniken, a sensitive application of the normal distribution to the population of participants in an elementary school recorder recital:

   The Beauty of the Curve     by Kathleen Flenniken

   The curtain lifts on Bryant Elementary School's
   Spring Recorder Recital.  Ninety third-graders
   fumble with their instruments, take a breath

   and blow.  Their parents, braced, breathe too
   as "Hot Crossed Buns" emerges, a little scattershot --
   the Normal Distribution brought to life.

Two ways to compute 1/3

Here, from Betsy Devine and Joel E Cohen, is a "mathematical" limerick:  
     

An Integral Limerick

This plane of earthly love

Poet Joan Mazza celebrates qualities mathematical: 

   To a Mathematician Lover     by Joan Mazza

   As we embark on this plane
   of earthly love, I should explain,
   my experiences with men
   have doubled my troubles
   and halved my pleasures,
   divided my time into fractions

Earthquake and Hurricane

It would not be easy to argue that a poem whose numbers merely identify its stanzas is "mathematical" but "Curriculum Vitae," found at poets.org and written by Pullitzer Prize winning poet Lisel Mueller, also contains the words "earthquake" and "hurricane" and thereby is significant on this Saturday in Silver Spring -- five days after a 5.8-magnitude earthquake damaged both the Washington Monument and the National Cathedral and on the very day that millions of us are watching the progress of Hurricane Irene as it storms north along the eastern coast of the US. In acknowledgment of these days, I invite you to read this fine poem:

350: Science --> Poetry --> Music

350 parts per million is the "safe upper limit" for CO₂ in our atmosphere presented by NASA scientist Jim Hansen in December 2007 and widely agreed upon.  From that number 350.org .was born. On October 24, 2009, 350 Poems celebrated an international day of climate action with a posting, from poets all around the world, of 350 poems of 3.5 lines each --  each responding to concern for man-made climate change. 

A thousand and fifty-one waves

Twenty-five years ago I had an enormous appetite for poems by Stevie Smith (1902-1971).  I loved the way that they seemed so unstudied -- playful and yet spot on and profound.    Smith did not use much mathematics in her poetry, but she wrote this poem, "Numbers." 

Half-twist and link -- in a Sestina

     Mobius strip       by Heidi Willamson

     A simple science trick to try at home.
     Half-twist a slip of paper. Link the ends
     to make an ‘O’. Take a pencil, trace a line that loops
     the shape formed by the surface. See
     how the in and out sides merge. The join
     tangles dimensions. There’s no front or back.

Lieber's INFINITY -- poetic prose

It has surprised me to discover that some of my best-remembered learning took place at the hands of teachers I did not particularly like.  One of these was a professor who introduced me, via outside reading assignments, to books by Lillian R. Lieber (1886-1986).  Her free-verse-style lines in Infinity:  Beyond the Beyond the Beyond gave me insights into the calculus I had recently completed as well as the set theory of my current course. (Lieber wrote not just as a mathematician but also as a human being, as a wonderfully informed and openly opinionated person.  For this, too, I treasure her work.)

Some cat!

My title is a borrowing from E. B. White's Charlotte's Web -- which I saw recently with grandchildren at Glen Echo Park's Adventure Theater. It (the title above) refers to my wonderful Himlayan, Noah, who lived to 15 years and 3 months;  this posting is done in his memory.  Herein we connect cats with mathematics.

The hypotenuse of an isosceles triangle

Detroit poet, Philip Levine, has been selected as the new Poet Laureate of the United States. Selected by the librarian of Congress (James Billington), Levine follows poet W. S. Merwin in the honored position.  A Poet Laureate is responsible merely for giving readings in October and May but some laureates also use the position to proselytize for poetry.   Here, from Levine's early collection, What Work Is (Knopf, 1992), is a poem that looks back on a math-art moment in a middle-school classroom.

Can a mathematician see red?

Held late in July, this year's 2011 Bridges (Math-Arts) Conference in Coimbra, Portugal included a poetry reading for which I'd been invited to read but was, at the last minute, unable to attend. (See also 26 July 2011). Poets Sarah Glaz and Emily Grosholz each, however, read favorite selections from my work.  Glaz read one of my square poems, "The Bear Cave" (see 19 June 2011) and Grosholz read the poem shown below, "Can a Mathematician See Red?"

Banach's Match Box Problem

A poetry collection by Susan Case (see also 5 July 2011 posting)  -- The Scottish Cafe (Slapering Hole Press, 2002) -- celebrates the lives and minds of a group of mathematicians in Poland during World War II. Its observations and insights add a new dimension to the important story of the Scottish Book to which it refers -- a book in which the mathematicians reorded their problems and solutions. First published in a mimeographed edition in 1957 by Stanislaw Ulam, The Scottish book: mathematics from the Scottish Café (Birkhäuser, 1981) may now be seen and searched at GoogleBooks.  Case's collection includes statements of two of the Scottish Book's problems:  here, below, is "problem 193" -- which I offer as a "found poem."  A photo of its Scottish Book solution follows.

Cantor Ternary Set

The second issue of the Journal of Humanistic Mathematics has recently been posted -- with more new poems.  The first issue contained a poem by Philip Holmes about one of the most amazing collections of numbers in all of mathematics, the  Cantor Ternary Set.  This set, discovered by Henry John Stephen Smith (1826-1883) but popularized by Georg Cantor (1845-1918) consists of all the real numbers whose base 3 or ternary representations involve only the digits 0 and 2. Like a fishing net, the Cantor Ternary Set is mostly holes. "Gaps" by Philip Holmes spreads it out before us -- and reflects on what else it may represent:

Puzzle play

In volume 4 of The World of Mathematics (James R Newman, Editor; Dover 2003), in a section entitled "Amusements, Puzzles, and Fancies," is an essay by Edward Kasner and James R. Newman entitled "Pastimes of Past and Present Times." This piece is prefaced by a quote from Mark Twain: "Work consists of whatever a body is obliged to do, and play consists of whatever a body is not obliged to do." One of the characteristics that mathematicians and poets have in common  is that both enjoy mind-play -- mental adventures with ideas or numbers or words, dancing and shaping into some new thing.

Mathematical Induction -- principle, perhaps poem

One of my teachers -- I think it was Mr Smith in "College Algebra" during my freshman year at Westminster -- gave me these words to remember:

     When confronted
     with a statement
     that seems true
     for all positive integers
     the wise student
     uses mathematical induction
     as her proof technique. 

Bridges in Coimbra

     Newton's binomial is as beautiful as Venus de Milo.
     What happens is that few people notice it.

                -- Fernando Pessoa (as Álvaro de Campos) (1888-1935)
                    translated from the Portuguese by Francisco Craveiro

Little Infinite Poem

   Little Infinite Poem       by Federico Garcia Lorca

               For Luis Cardoza y Aragón

      To take the wrong road
   is to arrive at the snow,
   and to arrive at the snow
   is to get down on all fours for twenty centuries and eat
         the grasses of the cemeteries.

The wind, counting

     Who can ever forget
     listening to the wind go by
     counting its money
     and throwing it away?

Finding a square root

Here is an old poem (1849) by George Van Waters that offers instruction on finding a square root. This process was part of my junior high learning at the Keith School in Indiana, PA lots of years ago but I suppose the algorithm is seldom taught in 21st century classrooms.  (In case the poem's directions are unclear, additional instruction is offered here.)

I have dreamed geometry

   Descartes     by Jorge Luis Borges

   I am the only man on earth, but perhaps there is neither earth nor man.
   Perhaps a god is deceiving me.
   Perhaps a god has sentenced me to time, that lasting illusion.
   I dream the moon and I dream my eyes perceiving the moon.
   I have dreamed the morning and evening of the first day.

Seeking a universal language

Is mathematics a universal language?  Not only is this universality often postulated but also it was said  -- some decades back -- that devices were broadcasting into space the intial decimal digits of pi, expecting that other intelligent beings would surely recognize the sequence of digits.  Robert Gethner examines this arrogance in a poem.

Ancestry -- what counts

Etheridge Knight began writing poetry while an inmate at the Indiana State Prison and published his first collection, Poems from Prison, in 1968.  His poem "The Idea of Ancestry" shows us what a man in prison finds time to count:

   The Idea of Ancestry   by Etheridge Knight

          1
  
   Taped to the wall of my cell are 47 pictures: 47 black
   faces: my father, mother, grandmothers (1 dead), grand-
   fathers (both dead), brothers, sisters, uncles, aunts,
   cousins (1st and 2nd), nieces, and nephews. They stare
   across the space at me sprawling on my bunk. I know
   their dark eyes, they know mine. I know their style,
   they know mine. I am all of them, they are all of me;
   they are farmers, I am a thief, I am me, they are thee.

Mathematicians at work

     About her collecton, The Scottish Café (Slapering Hol Press, 2002), Susan Case offers this note:
     This series of poems is loosely based upon the experiences of the mathematicians of the Scottish Café, who lived and worked in Lvov, Poland (now L'viv, Ukraine), a center of Eastern European intellectual life before World War II, close to the area from which my own ancestors emigrated to the United States.  A book, known as the Scottish Book, was kept in the Café and used to write down some of their problems and solutions.  Whoever offered a proof might be awarded a prize.
     Here is "Fixed Points," the opening poem from Case's collection:

Mathematicians divide

One of my fine graduate courses at Hunter College was a "World Poetry" course taught by William Pitt Root.  One of our texts was Against Forgetting:  Twentieth-Century Poetry of Witness (W W Norton, 1993), edited by Carolyn Forché.  In this collection is found "To Myself," a poem that confronts fear, by Abba Kovner (1818-1987), a hero of anti-Nazi resistance. Kovner dares to open the poem with the word "Mathematicians."

5 x 5 and 6 x 6

Many poets have found the sonnet to be an ideal poetic form -- its iambic pentameter lines are like five heartbeats assembled in a single breath;  its fourteen lines are a good number for considering a matter carefully. My own frequent form is different -- not a sonnet but a square of some or another dimension.   Here are two of my recent syllable-squares.

     I squint with tension,
     puzzle over this:         
     dissatisfaction's
     itchy appetites
     are my happiness.

The Joys of Mathematics

   The Joys of Mathematics     by Peter Boyle

   At fifty I will begin my count towards the infinite numbers.

   At negative ninety nine I will start my walk towards the
      infinitesimally small.

Creation Myth on a Mobius Band

On the  website of Bert-Jaap Koops, I found this small poem by a poet I admire greatly, Howard Nemerov (1920-1991).

     Creation Myth on a Moebius Band   by Howard Nemerov

     This world’s just mad enough to have been made
     by the Being His beings into Being prayed.

Something for nothing

     Among my favorite mathematical ideas are the seeming-paradoxes -- notions that require a twist and a turn and a leap before one can say "aha."  Using a symbol for "nothing" is one of those leap-requiring ideas.  I don't remember when I first understood zero, but I have enjoyed watching my children -- and now grandchildren -- grapple with ideas of things that are absent rather than present. 
     Here, from Hailey Leithauser, is a poem  that celebrates the cipher. 

Circling -- with Rilke

Ranier Maria Rilke (1875-1926) was born in Prague but emigrated to Germany and is one of the great modern lyric poets.   The following Rilke poems draw on images of circles.

Found in Flatland

Over the years I have shared with friends and students my copy of Edwin Abbott's Flatland (first published in England in 1884) and, alas, not all of these other readers have matched my level of excitement with the small volume.  Even though the book's Victorian attitudes are mostly at odds with my own views, still the tiny book opened me to possibilities of new ways of seeing. Since observing the Flatlanders stuck in two dimensions from my advantageous three-dimensional position, I have wondered how I can now make the leap from three to four or more dimensions.

Stanescu - poetic mathematics

Today I found a link to a recent article, "Matematica şi poezia," that considers commonalities among the arts and mathematics and, therein, mentions a poem by Nichita Stanescu (1933-1984) which Gabriel Prajitura and I have translated.  The poem, "Poetic Mathematics," is dedicated to Romanian mathematician Solomon Marcus.  Here is Gabi's and my translation: 

Lagrange points

The Italian-French mathematician Josef Lagrange discovered the existence of five special "Lagrange points" (aka Lagrangian points) in the vicinity of two orbiting bodies where a third, smaller body can orbit at a fixed distance from the larger ones. More precisely, Lagrange Points mark positions where the gravitational pull of the two large bodies precisely cancels the centripetal acceleration required to rotate with them. Poet Catherine Daly considers these points in a poem:  

Counting on things -- a prose poem

Russell Edson is one of the contemporary masters of the prose poem (a poem whose words are organized into paragraphs rather than stanzas). A selection from May Swenson's prose poem (and short novel) "Giraffe" is available in the October 19 blog posting. Here is Edson's poem "One Two Three, One Two Three" -- which considers the secrets hidden inside one's head.  Another mind, even that of one of our children, is a mystery incompletely known to any of us.

Right Triangle

The shape of a poem influences our reading of it -- short lines cause reading with lots of pauses whereas we read long lines quickly to get the entire line completed in a single breath. Moreover, some poetry is intended to be primarily visual -- to be taken in as a seen-image rather than read.  UBU Web offers several example of early visual poetry and one may also explore the  UBU Web site for modern examples.  Visual poetry may also be termed "concrete" poetry; consider, for example, "Concrete Block" by Michael J. Garofalo:

Math lyrics -- Lehrer et al

Mathematicians with poetic tendency often use their word-talents to write song-lyrics rather than poems; a master of the song-writing art was/is Tom Lehrer.  As an undergraduate at Harvard in the 1940s,  Lehrer majored in mathematics; he is best known for songs he recorded in the 1950s and 1960s.  Here are Lehrer's lyrics for "The Derivative Song" -- written to be sung to the tune of "There'll Be Some Changes Made" (by Benton Overstreet, with original lyrics by Billy Higgins).

A square poem of Romania

When I'm working on a poem that resists my efforts to express what I must say, sometimes I turn to the square for a rescue -- that is, I attempt to find the best words by re-forming the poem as a square (same number of lines as syllables per line).  That is how I came to the following poem, "The Bear Cave,"  (a 9 x 9 square). 

Fear of math

California poet Carol Dorf is a high school math teacher (and has taught in a science museum) -- and images from math and science permeate her work.  An article on math anxiety (and its connections to the brain) in today's Washington Post brought to my mind this poem of hers: 

Once a student of Euclid

The Chair     by Charles Simic

The chair was once a student of Euclid.

The Bridges of Konigsberg

From the August 1997 issue of The Mathematical Intelligencer, we have this poem by Judith Saunders about a long-standing puzzle solved solved by the mathematical giant, Leonhard Euler (1707-1783).