Coleridge: A Mathematical Problem

 "A Mathematical Problem" by Samuel Taylor Coleridge (1772-1834) -- found online at Elite Skills Classics -- uses verse to describe construction of an equilateral triangle; Coleridge introduces the poem with a letter to his brother telling of his admiration of mathematics, a view rather rare among poets.   

The Nightmare of an Unsolved Problem

Back in the 1980s when I first met the Collatz conjecture in a number theory textbook it was stated this way:
     Start with any whole number  n :
          If  n  is even, reduce it by half, obtaining  n/2.
          If n is odd, increase it by half and round up to the nearest whole number, obtaining  3n/2 + 1/2 = (3n+1)/2.   Collatz' conjecture asserts that, no matter what the starting number, iteration of this increase-decrease process will each time reach the number 1.   

Numbers are more than numbers

Today, a poem in three parts, "Trouble with Numbers" -- from the collection Mathematics and Other Poems by William Wall. 

Celebrating Newman's "World of Mathematics"

Lionel Deimel is a database and Web site designer, a steam locomotive enthusiast, a cat lover, an essayist and a poet who maintains an eclectic website entitled Lionel Deimel’s Farrago.  There I found a small poem about one of my most-valued literary treasures, The World of Mathematics, a four-volume collection compiled with commentaries and notes by James R Newman, first printed in 1956. The range of topics is vast and the primary requirement for reading is not calculus but curiosity.  Sections of Volume 4 include "Mathematics in Literature," "Mathematics as a Culture Clue," and "A Mathematical Theory of Art." (You should not be without this fine collection.)    Here is Deimel's poem: 

Counting: 1, 2, 3, 4, 5, . . .

At Peter Cameron's Blog, "Counting the things that need to be counted," the July 14, 2010 entry contains a reflective poem entitled "Millenium" which meditates on the ten digits in stanzas whose lengths count them.  Here are the opening stanzas: 

Who are our prophets?

Here is the opening sentence of an article, "Mathematicians and Poets," by Cai Tianxin, a mathematics professor at Zhejiang University -- it appears in the April 2011 issue of Notices of the AMS:

     "Mathematicans and poets exist in our world as uncanny prophets."  

9 9-square stanzas

In the current (March 21, 2011) issue of The New Yorker (pages 46-47) may be found the poem "Green Farmhouse Chairs" by Donald Hall.  Hall's fine nostalgic poem consists of 9 stanzas; each stanza is "square" -- and has 9 lines with 9 syllables per line.   Enjoy!

Remembering Pi-day, a day late

Yesterday (3-14) was Pi-day, but my recent thoughts have been focused on my math-teacher son Eric (who has acute pancreatitis) and his family -- and I forgot to post this poem on the proper day.  Thanks to Lana Hechtman Ayers for these opening lines of  "Circumference:  A love poem." 

Teaching Math

When I was a new professor in the 1970s at Bloomsburg University (then Bloomsburg State College) my colleague PH and I discussed our teaching efforts and compared them with the ways we had been taught. We agreed that our university teachers seemed simply to dump mathematics on us in any manner whatever -- believing, it seemed, that those who were "smart enough" would pick it up.  (And other students should study sociology or communications  or the like.)  We and all around us worked to improve our teaching techniques and yet many years later it seems to continue that the privileged -- whether of wealth or education or gender or birthplace or whatever -- seldom see their advantages over those who are different.  And sometimes those of us who try the hardest fail our students because we do too much.  This latter idea led me to write this poem.

Numerology

On her website Deanna Rubin describes herself this way, "I have a degree in Technical Writing and Computer Science from Carnegie Mellon University, and my head is full of random numbers."  Illustrating this latter claim is her poem, "Numerology":    

Journal of Humanistic Mathematics -- V1, Issue 1

A new door has opened for those of us interested in the humanistic aspects of mathematics.  Under the able leadership of editors Mark Huber (Claremont McKenna College) and Gizem Karaali (Pomona College), the idea of the former Humanistic Mathematics Network Journal has been revived and Volume 1 Issue 1 of the Journal of Humanistic Mathematics is now available online.  The inaugural issue contains several poems, including the following one by Caleb Emmons, "Seeing Pine Trees,"  in which Emmons characterizes the views of a poet and a mathematician as two halves of one whole. 

Perfect as soap bubbles

An alert to today's poem came from Greg Coxson, a University of Wisconsin-educated, Silver Spring-based, radar engineer who loves mathematics and poetry.  The poem is by Howard Nemerov  (1920-1991) and it builds to a presentation of its perfect mathematical image near its end.  

Immense polygons of evening

Sometimes one wonderful line makes me fall in love with a poem. I offer the following -- in which the title first draws me in and then "immense polygons of evening" delights me even more.  Here, by Paula Closson Buck, is "A Betrayal of Integers," which uses mathematical terminology as the perfect mix of seasonings for a gourmet dish. 

Counting rhymes -- Catalan, Bell numbers

     In mathematics, the Catalan numbers (named for Belgian mathematician Eugène Charles Catalan, 1814–1894, and beginning with 1, 1, 2, 5, 14, 42, 132, 429, . . . ) and the Bell numbers (named for the Scottish mathematician Eric Temple Bell, 1883-1960, and beginning with 1, 1, 2, 5, 15, 52, 203, 877,  . . . ),  provide answers to a variety of mathematical counting-problems, including counting the number of rhyme schemes for stanzas of poetry.  In English, earliest classification of rhyme schemes dates back to George Puttenham and his treatise, The Arte of English Poesie (published around 1590). 

Poems of set paradox and spatial dimension

Universal Paradox     by Sandra DeLozier Coleman

     One gigantic set made of all that there is
     Boggles the mind with paradoxes.
     For it is greater than all, but smaller than this —
     The set which consists of the subsets of it.

Black History Month -- celebrate Haynes and Hughes

Living on the border of Washington DC I am exposed to items of local history for our nation's capital.  One such item involves the "discovery" of Langston Hughes (1902-1967) by poet Vachel Lindsay (1879 - 1931) at the Marriott Wardman Park Hotel, a leading conference hotel in the city.   A second story is a mathematical one.  Martha Euphnemia Lofton Haynes (1890-1980), a fourth-generation Washingtonian, was the first black woman to earn a PhD in mathematics -- conferred in 1943 by Catholic University. 

Srinivasa Ramanujan

One of the most intriguing tales in the modern history of mathematics involves Indian-born mathematician and genius Srinivasa Ramanujan (1887-1920) who traveled to England to work with G H Hardy (1877-1947).  Poet Jonathan Holden, who writes often of matters mathematical, offers this portrait of the Indian prodigy: 

Thinking about Thinking

The question of what it means to think is never far from my focus -- and is particularly on my mind during these days that the computer Watson is competing on the TV game show, Jeopardy.   Here is a poem I like a lot -- "New Math" by Cole Swensen  -- in which the poet (writing more than 20 years ago) considers the limits of computation (and whether it could aid persons unable to recognize faces). 

Puzzles, puzzlers, and parody

     For lots of fun, go to plus online magazine at this link to find a poem that requires a knight's tour of a chess board for you to unscramble its words and read its eight lines.

Loving a mathematician (Valentine's Day and . . . )

A perfect way to celebrate Valentine's Day -- especially for you who enjoy mathematics --  read (aloud and to each other) some "poems of love and mathematics." Such is easily possible, for the anthology, Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008), edited by Sarah Glaz and me, contains words on the topic by more than 150 poetic voices.  

Dividing by Zero

Fairy godmothers have their magic wands and mathematician have division by zero as a way to make the impossible happen -- for example, we can show that 2 equals 3:

How much math does a math-poem need?

Poems offered in this blog vary in the levels of mathematics they contain.  One mathematical reader commented privately that in some of the poems the use of mathematical terms is "purely decorative."  Indeed, some people have particular expectations for poetry that relates to mathematics -- they want the content to use mathematical notation or to present a mathematical truth. Such as, perhaps, this abbreviated statement of the four-color theorem (formulated as a 4x4 square): 

Electronic poetry -- Stephanie Strickland

     Computers offer new opportunities for poetry -- permitting new types of poems.  Animated perhaps, or hypertext, or vast manuscripts of which we can see at most a fragment -- the possibilities are many.  Stephanie Strickland is one of the pioneers of electronic literature -- and this post was sparked by my experiences at her presentations at Georgetown University on February 1.  

AWP avoids mathematics

I am currently attending the 2011 AWP* Conference and am disappointed that none of the sessions involves connections of writing with mathematics -- this disappointment has prodded me to write the Fib that I include below. (Recall that a Fib is a poem whose successive line-syllable counts follow the **Fibonacci seqence -- the numbers that count the petals on a flower, the spirals of seedheads on a pine cone or pineapple, and many other natural things.) 

Painting tragedy with numbers

Although words such as "massacre" and "victim" and "buried" help us to understand the effects of disaster and injustice, sometimes the most vivid descriptions of horrific events are painted with numbers -- 6 million slain, 4-year-old girl raped, 11 days without food.   One of the strong poetic voices of the twentieth century was June Jordan (1936-2002).  Works in her collection, Kissing God Goodbye  (Anchor Books, 1997), speak out for all victims, in Baghdad or Belfast, in Lebanon or Algeria.  In the following poem from that 1997 collection, Jordan uses numbers to heighten her portrayal of tragedy in Bosnia. 

Romanian poets -- Cassian and Barbu

Born in 1924, in Galati, Romania, Nina Cassian has published over fifty books -- besides poetry, she has works of fiction and books for children. Since 1985 she has lived in exile in the United States. Among those Cassian credits with strong influences on her poetry is mathematician / poet Dan Barbilian / Ion Barbu (1895-1961).  This poem by Cassian illustrates those mathematical influences:

Sonnet for a geometry teacher

Wisconsin poet Ronald Wallace has fun with math-words in the following sonnet that celebrates a teacher of plane geometry. 

Poems starring mathematicians - 8

Even though Johnny Depp played a mathematician in his recent film, The Tourist, we don't learn much about what mathematicians think or do from that story. Poetry offers more insight. Mathematician and writer Sherman Stein gives us this portrayal:

Self-portrait with numbers

Visual poet Geof Huth  lives and blogs in Schenectady, NY.  In 2010 he turned 50 and early in 2011 he sent me (via snail mail, on smooth white paper) a letter.  The letter is a poem; the poem is a celebration of life, a sort of self-portrait, using numbers.  Geof gave me permission to post it here.

Poem and parody -- isomorphic?

In mathematics, algebraic systems that have different objects but the same structure are described as isomorphic.  The parody in poetry illustrates the same idea -- a new poem is created that matches the form of a chosen poem, but uses different words.  For example, here are the opening stanzas of a poem published in 1799 by Robert Southey (1777-1843) that was later parodied by Lewis Carroll (1832-1898) in Alice's Adventures in Wonderland.

Integrals -- a poem

Integrals    by Jonathan Holden

     Erect, arched in disdain,
the integrals drift from left
across white windless pages
to the right,
serene as swans. 

Hyperbolic effects

Last month I went to the Hyperbolic Crochet Coral Reef Exhibit at the Smithsonian Museum of Natural History -- for a photo scroll down to the end of this post -- and that visit provoked me to begin searching for the term "hyperbolic" in poems.   I came close when I found "hyperbola" in a poem by Jonathan Holden and hyperbole in a sonnet by Elizabeth Barrett Browning: 

Poetry inspired by Chaos

Poet Robin Chapman studies the language learning of children -- and has collaborated with physics professor Julien Sprott on a lovely and fascinating collection The Art and Poetry of Chaos:  Images from a Complex World (World Scientific, 2005).  In the following poem Chapman offers (as she does throughout the poetry of the collection) a human interpretation of technical terminology.  

Dr King's dream and Black math students

Today is our public celebration of the January 15 birthday of Martin Luther King, Jr (1929-1968) who was both preacher and poet in the "I have a dream" speech he delivered on the steps at the Lincoln Memorial in Washington D.C. on August 28, 1963. 

Rather like an elephant

What is mathematics?
          These days I am outside of mathematics looking in and my views of the subject are more complex than during the days when I was a professor and mathematician. Back in my math-prof days -- when I moaned about those who held the view that mathematics is merely computation -- I tried to explain to uncompreheding friends the role of calculation within mathematics with this analogy:  computation is to mathematics as spelling is to poetry.  But those for whom computation is all of their mathematics do not accept this argument.  Indeed, I myself now have the notion that one can navigate life competently without algebra -- much as I get along without Spanish or Chinese. But I regret not knowing them -- they are, like algebra, among the world's important languages.

Geometry and autism

We do not easily describe what goes on inside our own heads and have still greater difficulty seeing into the minds of others.  Pennsylvania poet Barbara Crooker uses images from geometry to help us to see into autism. 

Tribute to four teachers

Many people offer advice about education--and, in particular, about mathematics education.  I'm skeptical of general pronouncements because my encounters with learning (as student or teacher or parent) have been singular:  one mind meeting another mind for a period of exchange.  Here's a poem that recalls four of my teachers, three of them teachers of mathematics. 

Which are "real" numbers?

The adjective "real" in the term "real number" causes confusion for many whose mathematics is casual rather than intense.  I like the mathematical definition of a number as real iff it corresponds to a point on the number line -- for this gives the abstract number a geometric counterpart (an attachment to reality) -- but there are others for whom the reality of a number depends on its emotional connections, perhaps used in ways that poet Ginger Andrews uses numbers in the following poem.  

Mathematics and race

Sherman Alexie is a Spokane / Coeur d’Alene Indian from Wellpinit, Washington. Besides several collections of poetry, Alexie has published novels and short-stories; he wrote the screen-play for the 1998 film, Smoke Signals. Here, in verse, he deals with the mathematics of racial identity:

New poems from old -- by permutation

     One of the founding members of the Oulipo, Jean Lescure (1912-2005), devised categories of permutations of selected words of a poem to form a new poem; three of these rearrangements are illustrated below using the opening stanza of "Mathematics or the Gift of Tongues" by Anna Hempstead Branch (1875-1937). Here is the original stanza from Branch's poem:  

From 2010 -- titles and dates of posts

List of postings  March 23 - December 31, 2010
A scroll through the 12 months of titles below may lead you to topics and poets/poems of interest. Also helpful may be the SEARCH box at the top of the right-hand column; there you may enter names or terms that you would like to find herein.
    Dec 31  The year ends -- and we go on . . .
    Dec 30  Mathematicians are NOT entitled to arrogance
    Dec 28  Teaching Numbers
    Dec 26  Where are the Women?
    Dec 21  A Square for the Season
    Dec 20  "M" is for Mathematics and . . .  

The year ends -- and we go on . . .

Immortal Helix     by Archibald MacLeish  (1892-1982)

HEREUNDER Jacob Schmidt who, man and bones,
Has been his hundred times around the sun. 

Mathematicians are NOT entitled to arrogance

Godfrey Harold “G. H.” Hardy (1877 – 1947) was an English mathematician known for his achievements in number theory and mathematical analysis. One of Hardy's lasting contributions is his 1940 essay, ;A Mathematician's Apology, which offers his self-portrait of the mind of a working mathematician. Here, written in lines and stanzas -- as a found poem -- is the opening paragraph of Hardy's essay:

Teaching Numbers

Californian Gary Soto  writes for both children and adults and much of his work suits both groups.  Here from A Fire in My Hands (Houghton Mifflin, 2006) is "Teaching Numbers":

Where are the Women?

Here is a small square poem about a paradox that's been on my mind recently.

               Little Women

               In school, many
               gifted math girls. 
               Later, so few
               famed math women!

A Square for the Season

          Now,  near the Solstice,
          we turn on  bright lights
          and  give gifts.  Oh, Sun,
          please shorten our nights
          with  your  quick  return.

Season's Greetings
     to mathematicians, to poets, and to all who inspire them-- 
          from JoAnne Growney.

"M" is for Mathematics and . . .

Today's poem by Miroslav Holub (1923-98) is square, having 5 lines of 5 letters each; it describes the letter M by using what is "not M" -- a style of reasoning often used to good effect in both poetry and mathematics.        

An Elegy from Argentina

Mathematicians are mourning the too-soon death of Cora Sadosky (1940-2010) on December 3.  Born in Argentina, Sadosky earned her doctoral degree at the University of Chicago in 1965 and published more than fifty papers in harmonic analysis and operator theory. A strong advocate for women in mathematics (1993-95 president of AWM) and active in promoting greater participation of African-Americans in mathematics, Sadosky was a long-time faculty member at Howard University.
     Here, in recognition of the contributions of Cora Sadosky, is "An Elegy" by Argentinian poet Mirta Rosenberg.  Using Rosenberg's words for her mother, we celebrate a foremother in mathematics:

Can we trust numbers?

Poet Lucia Perillo was honored Monday evening, December 13 at the Library of Congress -- as her collection Inseminating the Elephant won the 2010 Bobbit National Prize for Poetry.  It was my good fortune to be there to hear her read.  She is direct and upretentious, tough and witty.  An evening of good poetry read well.  Perillo has an undergraduate degree in wildlife management and her deep understandings of the natural world are evident in her poems.  In  an earlier collection, we find "In Light of the Absent Constant," a Perillo poem of science and number: 

New poems from old -- by substitution

Poet Lee Ann Brown was the featured poet at the November, 2010 Conference on Constrained Poetry at UNC Ashville; this conference celebrated the 50th anniversary of the founding of Oulipo.  In a poetry sampler archived from the Boston Review, we find "Pledge" (see below) and other samples of Brown's work.  Recordings are available at Penn Sound. 

Satire Against Reason . . .

     John Wilmot (1647-1680), 2nd Earl of Rochester, was a friend of King Charles II, and author of much satirical and bawdy poetry. Even though logical reasoning is central in mathematics, reason has not lead us to a utopian society -- and Wilmot's poem, "Satire Against Reason and Mankind," reminds us of the many ways that we can be wrong. 

Cryptography -- an MAA lecture and a poem

     Living near the Silver Spring metro station, on the border of Washington, DC, makes travel to the offices of the Mathematical Association of America (MAA)  an easy trip for me, and I am able to enjoy occasional lectures at MAA's Carriage House Conference Center.  On December 9 I was fortunate to attend an entertaining and informative lecture on  "Cryptography:  How to Keep a Secret," by UC Irvine math-computer-science professor (and Numb3rs consultant), Alice Silverberg. (Podcasts of lectures are available at the MAA site.) 

8 January 2011 -- Math-Poetry at JMM

Here's an invitation for math-poets -- at 5 PM on Saturday, January 8 at the 2011 Joint Mathematics Meetings in New Orleans there will be an open reading of poetry related to mathematics.  All are invited.  Interested persons are invited to contact Gizem Karaali of Pomona College for more information. 

Poems starring mathematicians -- 7

Activist mathematician Chandler Davis -- an editor of The Mathematical Intelligencer, career mathematician at the University of Toronto, and author of It Walks in Beauty (Aqueduct Press, 2010) -- has written of his friendship with Norberto Salinas (1940-2005), a mathematician originally from Argentina who was a long-time faculty member at the University of Kansas: 

Are all mathematicians equal?

My first posting for this blog (on March 23, 2010) featured one of my earliest poems, a tribute to mathematician Emmy Noether (1882 -1935) entitled "My Dance Is Mathematics."  Even as it praised Noether's achievements, the poem protested the secondary status of math-women, not only in Noether's day but also today.  It ends with the stanza :

     Today, history books proclaim that Noether 
     is the greatest mathematician
     her sex has produced. They say she was good
     for a woman.

Horizon line

Poet James Galvin often uses mathematical imagery in his poems.

   Art Class      by James Galvin
  
   Let us begin with a simple line,
   Drawn as a child would draw it,
   To indicate the horizon,  

Will I really NEED algebra after school?

For those of us who create and teach mathematics, algebra is one of our much-used language skills.  We cannot imagine lives in which we do not write equations easily.  Thus inclined, we insist on the worth of algebra for students.   Taking an opposite view, here from Hanging Loose Press editor Robert Hershon  is an algebra-protest poem.  

Minimal poem from Saroyan

This poem appears in Complete Minimal Poems by Aram Saroyan (Ugly Duckling Presse, 2007).  Another of Saroyan's minimal poems was posted on November 9.

Poetry with base 10

In his collection, Rational Numbers (Truman State, 2000) Harvey Hix presents "Orders of Magnitude" -- a collection of 100 stanzas in which each stanza has ten lines and each line has ten syllables.  Beyond this numeric structure is frequent use of mathematical imagery; here are samples (stanzas 42 and 100):

A square riddle -- by Sylvia Plath

Metaphors     by Sylvia Plath (1932-1963)

I'm a riddle in nine syllables,
An elephant, a ponderous house,
A melon strolling on two tendrils.
O red fruit, ivory, fine timbers!
This loaf's big with its yeasty rising.
Money's new minted in this fat purse.
I'm a means, a stage, a cow in calf.
I've eaten a bag of green apples,
Boarded the train there's no getting off.

This 9 x 9 square first appeared in Crossing the Water (Faber and Faber, 1971).  

Butterfly Effects

An equation or system of equations is said to be "ill-conditioned" if a small change in input data can produce a very large change in the output.  This inverse relationship between input and output has become popularly known by the phrase "butterfly effect."  Two poets from Eastern Pennsylvania, Gary Fincke and Harry Humes, have written poems about this phenomenon. 

More from Guillevic

     My October 13 post presented three small poems by the French poet Guillevic (1909-97).  Strongly drawn to his work, I have purchased the collection Geometries (translated by Richard Sieburth, Ugly Duckling Presse, 2010);  Guillevic has found in each geometric figure a personality and a voice.  Buy the book and enjoy!
     Here are three additional samples from Geometries:

Syllable-Sestina -- a square permutation poem

Some poetry is "free verse" but many poems are crafted by following some sort of form or constraint--they might be sonnets or ballads or pantoums or squares, or possibly even a newly invented form.  From poet Tiel Aisha Ansari I learned of a "syllable sestina challenge" from Wag's Revue. The desired poem contains six lines and only six syllables, which are repeated using the following permutation-pattern (the same pattern followed by the end-words in the stanzas of a sestina):

Celebrate Constraints -- Happy Birthday, OULIPO

Patrick Bahls and Richard Chess of the University of North Carolina at Ashville have organized a "Conference on Constrained Poetry" to be held on November 19-20 in celebration of the 50th Anniversary of OULIPO (short for French: OUvroir de LIttérature POtentielle), founded in 1960 by Raymond Queneau and François Le Lionnais. The group defines the term littérature potentielle as (rough translation): "the seeking of new structures and patterns that may be used by writers in any way they enjoy." Constraints are used to trigger new ideas and the Oulipo group is an ongoing source of novel techniques, often based on mathematical ideas -- such as counting letters and syllables, substitution algorithms,  permutations, palindromes, and even chess problems.

Special square stanzas

My recent posting (November 14)  of a symmetric stanza by Lewis Carroll illustrates one variety of  "square" poem -- in which the number of words per line is the same as the number of lines.  My own square poems (for examples, see October 7 or June 9) are syllable-squares; that is, each stanza has the same number of syllables per line as there are lines. Lisa McCool's poem below is, like Carroll's, a word-square; in McCool's poem --  in addition to the 6x6 shape -- the first words of each line, when read down, match the first line of the poem, and the last words of each line, when read down, match the last line of the poem.

Symmetric stanza

Although the following stanza by mathematician-author Lewis Carroll first appears to be a merely melodramatic example of Victorian verse, a bit of scrutiny reveals its special symmetry.

     I often wondered when I cursed,
     Often feared where I would be—
     Wondered where she’d yield her love
     When I yield, so will she,
     I would her will be pitied!
     Cursed be love! She pitied me…

This 6 line stanza by Carroll (well-known for for his nonsense verse) reads the same both horizontally and vertically. 

Theorem-proof / Cut-up / poems

     For mathematicians, reading a well-crafted proof that turns toward its conclusion with elegance and perhaps surprise -- this mirrors an encounter with poetry.  But can one have that poetry-math experience without being fluent in the language of mathematics?  Below I offer a proof (a version of Euclid's proof of the infinitude of primes) and a "cut-up" produced from that proof-- and I invite readers (both mathematical and non-mathematical) to consider them as poems.

Minimal Poem

This poem appears in Complete Minimal Poems by Aram Saroyan (Ugly Duckling Presse, 2007).

One type of "mathematical" poetry

When I began (in the 1980s) collecting examples of "mathematical poetry," I sought lines of verse that included some mathematical terminology.  More recently, my view has expanded to include structual, visual, and algorithmic influcences from mathematics; however, the two samples from the work of William Blake (1757-1827), presented below, fit into that initial category -- selected as "mathematical" because of their vocabulary -- one speaks of "infinity," the other of "symmetry."  (Blake was an artist as well as poet and his volumes of poetry were illustrated with his prints.)  The following stanza is the opening quatrain for Blake's poem "Auguries of Innocence." 

Troubles with math, expressed poetically

     Should I admit that I sometimes feel a bit of resentment toward people who are insistently articulate about their difficulties with mathematics?  As if that good energy might be turned toward learning the subject they decry.
On the whole, though, it seems better to face the fact that we folks who speak the language of mathematics are the odd ones.  Here are perceptive trouble-with-math poems by John Stone (1936-2008), who wrote as a parent trying to help with homework, and Elizabeth Savage, who compares a pair of differently-able friends. 

Creation from "nothing"

     Christian Otto Josef Wolfgang Morgenstern (1871-1914) was a German writer whose poetry often involved paradox or nonsense and whose witticisms are oft-quoted by his German admirers;  for example, the following line from "The Impossible Fact" ("Die unmögliche Tatsache", 1910): "Weil, so schließt er messerscharf / Nicht sein kann, was nicht sein darf." which may be translated as  "For, he reasons pointedly / That which must not, can not be."  

The Fib -- a form that gathers strength

The "Fib" is a poetry form in which the numbers of syllables per line follow the pattern of the Fibonacci numbers.  (See also April 19 and April 29 postings.)   The sequence of Fibonacci numbers starts with 0 and 1 and then each successive Fibonacci number is the sum of the two preceding.  Thus, the non-zero members of the sequence are:
          1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
Poet Athena Kildegaard's collection Red Momentum (Red Dragonfly Press, 2006 ) consists entirely of Fibonacci poems.  The following samples from Kildegaard's collection illustrate the way that increasing line lengths can build to dramatic effect. From a simple start, complexity grows.

Ghost stories in algebra -- Happy Halloween!

Born in Yugoslavia, Charles Simic emigrated at age 15 to Chicago; widely known and respected as a poet and teacher (at the University of New Hampshire), Simic served as US Poet Laureate during 2007-08.    This little poem is from The World Doesn't End (Mariner Books, 1989).

               Ghost Stories Written          by Charles Simic

Continuing Climate Concerns

     Split This Rock, an activist confederation of poets concerned with vital human issues, has directed attention to environmental concerns by publishing my "Mitigation of Toxins" as their poem of the week for this final week in October; please follow the link and enjoy this poem and others their archive offers.  ("Mitigation of Toxins" first appeared in Innisfree and also is included in my new collection, Red Has No Reason .)
     In continued support of climate concerns--which seem to me often to fit a square-poem format -- here is "Arctic," a 5x5 square by poet Linda Benninghoff, author of six chapbook collections. 

A Lemma by Constance Reid

Constance Reid (1918-2010), died on October 14.  Sister of a mathematician (Julia Robinson), Reid wrote first about life in World War II factories that supported the war effort and then, later, several biographies (including one of her sister) and other books about mathematics.  Kenneth Rexroth's poem "A Lemma by Constance Reid" (offered below) is based on material appearing in Reid's popular book From Zero to Infinity:  What Makes Numbers Interesting (Thomas Y Crowell, 1955).  Reid is known for the enthusiasm and clarity with which she presented mathematical ideas--seeking to attract and to satisfy non-mathematical readers. 

Writing poetry like mathematics

In an article about the Chilean mathematician and poet Nicanor Parra, Paul M Pearson says, :  "Parra almost wrote poetry like he would a mathematical theorem using an extreme 'economy of language' with 'no metaphors, no literary figures.' "  Today I present work by Nicanor Parra and Richard Aston, both of whom write their poetry with the same economy and care that are used when writing mathematics.

"The Equation" by Owen Sheers

This posting is brief to encourage you to have time to read Owen Sheers' fine poem several times and let it settle in and be part of you.  Thanks to F J Craveiro de Carvalho, University of Coimbra, Portugal, who brought the poem to my attention. 

I miss you, Martin Gardner

Martin Gardner (1914-2010), featured also in my June 6 posting, would have been 96 years old today--October 21, 2010.  All over the world lovers of mathematical puzzles have taken time today to celebrate Gardner's puzzling--and the ways it stimulated their own.  Although Gardner disclaimed poetic gifts, he popularized puzzle poems written by others -- and he introduced the poetry strategies of the OULIPO (see March 25, August 5, and August 23 postings) to American readers.  Here is a puzzle poem, by an unknown author, included in Gardner's Puzzles from Other Worlds (Vintage, 1984) and in Strange Attractors (A K Peters, 2008). 

Giraffe -- novel (& prose poem) by May Swenson

Poet and playright May Swenson (1913-89) was born in Utah to Mormon parents and grew up in a home in which Swedish was the primary language. Swenson wrote of the experience of poetry as "based in a craving to get through the curtains of things as they appear, to things as they are, and then into the larger, wilder space of things as they are becoming." Here are the opening stanzas of Swenson's prose poem, "GIRAFFE:  A Novel," from In Other Words:  New Poems (Knopf, 1987).  I think this is FUN -- and hope you also enjoy it.

The Length of a Coastline

In the nineties, fifteen or so years ago, when I began posting mathematical poems on the Internet, two of my earliest connections were Ken Stange, a poet and polymath and professor of psychology at Ontario's Nipissing University, and his daughter Kate, then a teen.  Kate publicized her love of mathematics and poetry by creating an online collection,"Mathematical Poetry:  A Small Anthology" which she has continued to maintain for many years--during which she has completed undergraduate and graduate studies in mathematics. 

Voices in a Geometry Classroom

I have been invited to return next week (October 20 at 7 PM) to Bloomsburg University, where I taught mathematics for lots of years, for a poetry reading.  Preparation for the reading (which celebrates my new book, Red Has No Reason) drew my thinking back to my teaching days at Bloom and to "Geometry Demonstration," a poem about the arguments in my head as I faced a particularly challenging class of geometry students.  Here it is.

Varieties of triangles -- by Guillevic

My introduction to French poet Guillevic (1909-97) came from UK poet Tim Love who found three of his triangle poems translated into Italian.  Jacqueline Lapidus translated them for me from French into English, after which I also found Guillevic's collection Geometries (Englished by Richard Sieburth, Ugly Duckling Presse, 2010) -- with its circles, ellipses, parallels, and so on.  And so, beyond these three, there will be more to enjoy later.  

Varieties of palindromes in poetry

My posting for October 6 mentioned palindromes. Today we continue with the topic, including illustrations of the various ways they may influence poems.  A number such as 12345654321, which reads the same if its digits are reversed, is the sort of palindrome one encounters in arithmetic.  Palindromic poetry includes more variety.  These sentences, taken from a list compiled by Ralph Griswold, are samples of palindromes in which the unit is a single letter.

"The Seventh" by Attila Jozsef

Attila József (1905-1937)  is one of the most important Hungarian poets of the 20th century. 

     The Seventh   by Attila József

     If you set foot on this earth,
     you must go through seven births.
     Once, in a house that's burning,
     once, among ice floes churning,
     once, amidst madmen raving,
     once, in a field of wheat swaying,
     once, in a cloister, bells ringing,
     once, in a pigsty a-squealing.
     Six babes crying, not enough, son.
     Let yourself be the seventh one.

Squares of Climate Concern

The square (with as many lines as syllables per line) is a poetry-form that has existed  for centuries and is now enjoying a revival.  Here are three small squares that come from my concerns for the precarious imbalances we humans have created within our natural environment. 

      There is no                           
      place to throw                     
      that's away.                          

"Poetry, in other words, is mathematics"

From Tim Love, British poet and member of the Computer Systems Group in the Engineering Department at Cambridge University, I received this link -- National Poetry Day: unlock the mathematical secrets of verse -- to an article announcing the October 7 holiday in the UK.  The article's author, Steve Jones (a professor of genetics at University College), goes so far as to begin his third paragraph with the sentence quoted as title to this posting.  Follow the link and form your own view.  Is mathematics truly important to poetry? 

"The Reckoning" by M. Sorescu (Romania,1936-96)

Works by poet and playwright  Marin Sorescu (1936-1996) continue to be popular with Romanian readers--and he is one of the most-frequently translated of Romanian poets.  In "The Reckoning" we see and hear his irony twisting among images chosen from mathematics.

Art, poetry, and mathematics -- and Rafael Alberti

On September 23 I was privileged to hear Annalisa Crannell, mathematics professor at Lancaster's Franklin and Marshall College, speak on "Math and Art:  the Good, the Bad, and the Pretty."  This informative presentation, sponsored by the Mathematical Association of America (MAA) and pitched toward undergraduates, showed ways that artists use mathematics. 

Nursing--and other vital applications of counting

     Although counting is one of the basic activities of mathematics, its importance also extends to the highest mathematical levels.  We count the solutions to systems of equations, the crossings in a diagram of a knot, the intersections of surfaces in multi-dimensional space, the necessary repititions in a circuit covering the edges of a graph. Counting likewise imposes order on some of life's difficult and non-mathematical tasks.  In Veneta Masson's poem, "Arithmetic of Nurses," we have a vivid picture of the careful alertness required of those who cares for ill patients.
     Following Masson's poem, is "Things to Count On," one of my own poems of counting--a prose poem describing the way that numbers order the life of a frugal farmer and his family, working to make ends meet in Pennsylvania in the middle of the 20th century. 

Is mathematics discovered -- or invented?

The issue of whether mathematics is invented or discovered is posed often.  Less frequently, queries as to where poetry falls in these categories. Perhaps individual answers to these questions depend on how each of us, from the inside, views the workings of the mind.   Here we have, from poet (and math teacher) Amy Uyematsu,"The Invention of Mathematics."  

Ideal Geometry -- complex politics

Christopher Morley (1890-1957) was an American poet, novelist, and publisher who was the son of a poet and musician (Lilian Janet Bird) and a mathematics professor (Frank Morley) at Haverford College. His "Sonnet by a Geometer," below, is written in the voice of a circle and compares mathematical perfection with human imperfection.  For us who read the poem 90 years after its writing, Morley's phrase in line 13 -- "They talk of 14 points" -- is puzzling at first.

Reflections on the Transfinite

     Georg Cantor (1845-1918), a German mathematician, first dared to think the counter-intuitive notion that not all infinite sets have the same size--and then he proved it:  The set of all real numbers (including all of the decimal numbers representable on the number line) cannot be matched in a one-to-one pairing with the set of counting (or natural) numbers -- 1,2,3,4, . . . .   Sets whose elements can be matched one-to-one with the counting numbers are termed "countable" -- and Cantor's result showed that the set of all real numbers is uncountable.
     Cantor developed an extensive theory of transfinite numbers -- and poet (as well as philosopher and professor) Emily Grosholz reflects on these in a poem:

Goldbach's conjecture -- easily stated but unsolved

This blog's July 20 posting featured work from poets who have spouses or siblings who are mathematicians.  Today, introducing the work of  Michele Battiste (who considers Goldbach's conjecture), we again honor that theme.  Goldbach's conjecture asserts that every even integer greater than 2 can be expressed as a sum of two prime integers.   For example, 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 7 + 3 or 5 + 5, and so on.  The conjecture was first proposed in 1742 by German mathematican Christian Goldbach in a letter to Swiss mathematician Leonhard Euler -- and in 2010--though it has been verified for many, many, many even integers--it still remains unproved. 

The Magic of Numbers -- Kenneth Koch

I first became acquainted with Kenneth Koch (1925-2002)  through his small and hugely valuable paperback of teaching strategies, Wishes, Lies, and Dreams:  Teaching Children to Write Poetry.  Later, searching for poems about trains, I stumbled upon  "One Train May Hide Another" -- which I return to again and again for its wise beauty.  Today I present, for our reflection, Koch's poem, "The Magic of Numbers."  Enjoy.