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.

Visual Poetry -- from Karl Kempton

Poet Karl Kempton offers readers a great variety of visual poetry -- often including elements of mathematics. Kaz Maslanka's MathematicalBlogspot , Geof Huth's Visualizing Poetics blog, and Dan Waber's Logolalia offer introductions to the work of Kempton and other visual poets.  Here are three samples from Karl's collection,  3 Cubed: Mathematical Poems, 1976 - 2003  (Runaway Spoon Press, 2003). 

Prisoner's Dilemma -- and permutations

In game theory's original, single-play, Prisoner's Dilemma problem, two prisoners each are given the choice between silence and betrayal of the other. The optimal choice is betrayal -- and therein lies a paradox.  Volume 1.3 of the online journal Unsplendid includes the following poem by Isaac Cates that reveals the nature of this classic decision dilemma.

Ghosts of Departed Quantities

     Years ago in calculus class I excitedly learned that an infinite number of terms may have a finite sum.  Manipulation of infinities seems somewhat routine to me now but my early ideas of calculus enlarged me a thousand-fold.  Algebra was a language, geometry was a world-view, and calculus was a big idea.  Like any big idea, even though it had been hundreds of years in formation, it met with resistance.  In 1764 Bishop George Berkeley attacked the logical foundations of the calculus that Isaac Newton had unified.  Here, from the online mathematics magazine plus,  is a description of the attack.

Word Play with the Hypotenuse

Here we have a playful treatment of the language of the Pythagorean Theorem in "Talking Big" by John Bricuth. 

Grasping at TIME

Different persons experience time differently -- as illustrated by the few lines included below (part II of  "Time" from my new collection, Red Has No Reason).  This musing is followed by the beautifully precise "Four Quartz Crystal Clocks" by  Marianne Moore (1887-1972).

Against Intuition

One of my favorite poets (mentioned previously for her poem, "Pi" in my September 6 posting) is the Polish Nobelist (1996) Wislawa Szymborska.  Her language is apt and spare, her thoughts are wise, and her gentle humor is frequent. 

More of Pi in Poetry

Recording artist Kate Bush has written a song entitled “Pi” which includes some of π's digits in the lyrics. Likewise, Polish Nobelist (1996) Wislawa Szymborska also features its digits in her poem, “Pi,” which begins:

Rhymes help to remember the digits of Pi

Calculated at the website, WolframAlpha, here are the first fifty-nine digits of the irrational number π (ratio of a circle's circumference to its diameter):

     π = 3.1415926535897932384626433832795028841971693993751058209749...

Before computers became available  to calculate π to lots of decimal places in an instant, people who did scientific calculations could keep the number easily available by memorizing some of the digits.  The website fun-with-words offers several mnemonics for  π , the most common type being a word-length mnemonic in which the number of letters in each word corresponds to a digit. For example the sentence, "How I wish I could calculate pi," gives us the first seven digits.

What is the point? -- consider Euclid

A two-line poem by Chilean poet, Pablo Neruda (1904-73), found in my bilingual edition of Extravagaria, reminded me of the poetic nature of several of the opening expressions of Euclid's geometry.  Both of these follow:

"Two Pair" by Howard Nemerov

This poem by Howard Nemrov (1920-1991) uses scientific terminology in ways that seem especially deft:

   Two Pair

   More money's lost, old gamblers understand
   On two pair than on any other hand;

The Irrational Sonnet -- An Oulipian form

An irrational sonnet has 14 lines, just as the traditional sonnet, but differs in its stanza-division and rhyme:  there are five stanzas--containing 3, 1, 4, 1 and 5 lines, respectively (these being the first five digits of the irrational number pi), and a rhyme scheme of   AAB  C  BAAB  C  CDCCD.  This form was devised by Oulipo member Jacques Bens (1931-2001) in 1963.   (Previous postings concerning the Oulipo occurred on March 25 and August 5.) 

From Miroslav Holub -- a reflection on accuracy

In applications of mathematics, as in other scientific research, it is important to distinguish between the precision of measurements (how closely they agree with each other) and their accuracy (how closely measured values agree with the correct value).  One of my favorite poets, Miroslav Holub (1923-98), also a research scientist (immunologist), has captured this dilemma with irony in his "Brief Reflection on Accuracy," translated from Czech by Ewald Osers.

From "Red Has No Reason" -- a poem about the nature of mathematics

My new poetry book, Red Has No Reason, is now available (from Plain View Press or amazon.com).  Several of the poems mention math--and one of them comments on the nature of mathematics.  Ideas for "A Taste of Mathematics" (below) came from a mathematics conference in San Antonio, TX (January 1993) where it was announced that the billionth digit in the decimal expansion of  π  is 9.  Recently an amazing  new calculation record of 5 trillion digits (claimed by Alexander J. Yee and Shigeru Kondo) has been announced.

Poetry and applied mathematics

Back in the 1980's when I began taking examples of poetry into my mathematics classrooms at Bloomsburg University, I think that I justified doing so by considering poetry as an application of mathematics.  For example, Linda Pastan applies algebra to give meaning to her poem of the same title.  Here are the opening lines.

Zero-sum game -- in a poem by Okigbo

Game theory (with origins in the 1930s) was initially developed to analyze competitive decisions in which one individual does better at another's expense--"zero sum" games--and this term has become a part of everyday vocabulary; here we find it in a poem by Christopher Okigbo (1932-1967), a Nigerian poet. 

Excitement in mathematics classrooms

Poems from three women illustrate a range of emotional content in the mathematics classroom: Rita Dove's "Geometry" captures the excitement of a new mathematical discovery.  Sue VanHattum's "Desire in a Math Class" tells of undercurrents of emotion beneath the surface in a formal classroom setting.  Marion Deutsche Cohen's untitled poem [I stand up there and dance] offers a glimpse of what may go on in a teacher's mind as she performs for her class. 

A poem of calculus (of ants on a worm)

Philip Wexler plays with the terminology of calculus in this poem:

     The Calculus of Ants on a Worm

     Swarming tiny
     bodies nibble
     away, no limits,

Snowballs -- growing/shrinking lines

Today's post explores poetic structures called snowballs developed by the Oulipo (see also March 25 posting) and known to many through the writings of Scientific American columnist Martin Gardner (1914-2010).  TIME Magazine's issue for January 10, 1977 had an article entitled "Science:  Perverbs and Snowballs" that celebrated both Gardner and the inventive structures of the Oulipo. Oulipian Harry Mathews' "Liminal Poem" (to the right) is a snowball (growing and then melting) dedicated to Gardner.  The lines in Mathew's poem increase or decrease by one letter from line to line.   Below left, a poem by John Newman illustrates the growth-only snowball.

What nobody else has thought

     Albert Szent-Gyorgyi (1893-1986) was a Hungarian Biochemist who discovered Vitamin C and won the 1937 Nobel Prize for Medicine.  Szent-Gyorgi offered this summary of the research process:  discovery is seeing what everyone has seen and thinking what noone else has thought. Mathematicians and poets join research scientists in that quest to see and say something new.     I was reminded of Szent-Gyorgyi's view when I read this little poem, "The Roasted Swan Sings," by Mark Baechtel in the anthology, Cabin Fever (WordWorks, 2003):

A wedding song -- shaped by mathematics

This posting includes a stanza from of "A Wedding on Earth" by Annie Finch.  In the poet's words: the poem has 11 stanzas with 11 lines for a total of 121 lines, this number symbolizing the two single members of a pair joining into a 2, which is the prevailing theme of the poem; and each stanza combining [averaging] the stanza of Spenser's epithalamion (18 lines)  with Sappho's stanza (4 lines).

Poets who Count

For some poets, counting is part of the language of the poem. For others, counting determines the structure. Here are two poems of the former sort -- "Counting" by British poet Philip Larkin (1922-1985) and "Adding It Up" by New England poet Philip Booth (1925-2007) -- followed by opening stanzas of a poem for which counting is part of both content and structure:  "Millennium" by mathematician Peter Cameron .

Trouble with Math in School

     Sad and lonely experiences seem to produce more poems than joyful ones.  And so it is easier to find a poem about a trouble in a math class than success there.  Jane Kenyon (1947-1995) was a poet and translator whose work I admire.  Here is her math-class poem:

The infinitude of ecstacy -- a la Israel Lewis

Israel Lewis is the pen name of a polymath who earned his living as a scientist and is a writer in his retirement.  His webpage offers a variety of his creations--many of them permeated with mathematics.

Mathematics in poetry by Nichita Stanescu

     Though formerly a math professor, my recent teaching has involved poetry--and I have been fortunate to spend several summer months at Scoala Andrei Muresanu in Deva, Romania, teaching poetry and conversational English.       

In the same family -- a poet and a mathematician

When a poet and a mathematician are members of the same family, understandings result.  Ohio poet Cathryn Essinger is a twin of a mathematician and writes about this relationship.  Here are opening stanzas of two of her poems.

David Blackwell (1919 - 2010) -- and Game Theory

     David Blackwell, the first black scholar to be admitted to the National Academy of Sciences, a probabilist and statistician, died early this month. His NY Times and Washington Post obituaries tell of his many contributions. Blackwell's career connects to poetry through his interest in the Theory of Games.  He was co-author with Meyer Girshick of Theory of Games and Statistical Decisions, 1954, one of the early treatises on game theory.  

Ray Bobo's mathematical poem

Ray Bobo, a retired Georgetown mathematics professor, has written a love poem with mathematical symbols.  And, for those of us who might be unsure how to interpret the mathematics, Bobo has provided a parallel column with an English-language  interpretation of his mathematics.  Enjoy! 

Poetry-application of The Fundamental Theorem of Arithmetic

Destructive effects of human greed and neglect on the earth's natural environment are echoed hauntingly in the repetitions within "We Are the Final Ones" -- a dirge-like poem I've constructed using the Fundamental Theorem of Arithmetic.  (For those unfamiliar with the theorem, brief explanation is included in paragraphs that follow the poem):

Jordie Albiston -- structure behind the writing

       I love sonnets and the one below by Jordie Albiston is a favorite of mine.
     Albiston is an Australian poet with a sense of orchestration learned from music.  Her collection, The Sonnet According to 'M' recently won the New South Wales literary award.  In her words: 

Poetry-and-Math -- Interdisciplinary Courses

     On July 1 my posting considered math-poetry anthologies and began with a reference to Against Infinity, the discovery of which was a catalyst for my own inclusion of poetry in my mathematics classrooms.  Other mathematicians and writers have gone further and developed interdisciplinary courses--such courses are the topic for this posting. 
     I begin with a small item from Against Infinity, this one a "Found Poem" by Elaine Romaine (found in the math textbook Calclulus on Manifolds by Michael Spivak):

Digital poetry -- Stephanie Strickland et al

Stephanie Strickland writes with mastery of numbers, as we see in her poem below.  But numbers are only the beginning of her work.  A director of the Electronic Poetry Association and author of "Born Digital," Strickland is one of the leaders in the development of new types of poems that are constructed using animation and rearrangements and other visual and aural communications made possible by computers and the internet.

Poetry with Mathematics -- Anthologies

More than thirty years ago at a mathematics conference book exhibit I stumbled upon Against Infinity:  An Anthology of Contemporary Mathematical Poetry, edited by Ernest Robson and Jet Wimp.  This collection, now out of print, became a resource for my mathematics courses--an opportunity for students to see the links between mathematics and the surrounding world.   One of my early loves was "Arithmetic Lesson:  Infinity" by Linda Pastan.  Found also in Carnival Evening, the poem opens with these these lines:

Mathematics, like poetry, is ART

Doing mathematics is often misunderstood as primarily computation--an error that seems equivalent to seeing poetry writing as primarily a spelling exercise. 

Poetry with mathematical symbols

On the internet and elsewhere a variety of viewpoints are expressed about the criteria poetry should satisfy to be "mathematical." Today I want to introduce samples and links for three writers:   Bob Grumman (Florida), Gregory Vincent St Thomasino (New York), and Kaz Maslanka (California).  Grumman and Maslanka write poems with a strong visual element and, as the blogs and comments for all three testify, they differ in their views of what may be properly called "mathematical" poetry..

Three poems with the word "axiom"

Poems that contain  "number" are numerous; those with "axiom" are less easily found.  Here are 3 of them -- by 19th century American poet, Emily Dickinson (1830-1886), by Canadian poet and fiction writer, Margaret Atwood (b 1939), and by a poet from Virginia, Lesley Wheeler, whose work I recently have come to know.  I particularly enjoy Lesley's poems about parenthood--because they ring true and also because when I was a parent of young children I was not finding time to write.

Send your math-poems to QUARC

Canadian journal seeks submissions from poets or fiction writers whose work makes use of metaphors from the sciences or engages scientific themes.  Deadline: September 1, 2010.

Girls and Mathematics

In Indiana, Pennsylvania, my senior high school advanced math teacher was Laura Church--a Barnard College graduate and a flamboyant silver-haired woman who never let any of us suppose that girls could not do mathematics. In college my science scholarship kept me from fleeing mathematics to study literature when I was the only girl in my classes.

Square comment on shoe styles

     Recently I have returned to Silver Spring from a trip to Latvia, traveling with a friend who was born there.  My effort to find poetry with mathematics there was stymied by the fact that little Latvian literature has been translated into English.   
     The Latvian capital, Riga, is a charming city--and its cobblestone streets do not deter women from wearing elegant tall-heeled shoes.  The sight of them reminded me of a little poem I wrote a few years ago--a square poem--which comments on this stylish sort of shoe (in which I've never been able to walk).