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). 

Celebrate Martin Gardner (1914-2010)

Martin Gardner described his relationship to poetry as that of "occasional versifier" -- he is the author, for example, of:

     π goes on and on
     And e is just as cursed
     I wonder, how does π begin
     When its digits are reversed?

Discovering the Secret

In this Robert Frost couplet, “The Secret Sits,”  the poet may not have intended to speak of mathematics but his lines sing true for mathematical discovery.

We dance round in a ring and suppose,
But the Secret sits in the middle and knows.

from The Witness Tree.

Glances at Infinity

Counter-intuitive notions are among my favorite parts of mathematics and, in considerations of infinity, these are numerous.  Recalling Zeno's paradox, we capture the infinite finitely in this summation:

     1 + 1/2 + 1/4 + 1/2³ + . . . + 1/2ⁿ +   . . .    =  1

Sense and Nonsense

     Nonsense verse has a prominent place in the poetry that mathematicians enjoy. Perhaps this is so because mathematical discovery itself has a playful aspect--playing, as it were, with non-sense in an effort to tease the sense out of it.      Lewis Carroll, author of  both mathematics and literature, often has his characters offer speeches that are a clever mix of sense and nonsense. For example, we have these two stanzas from "Fit the Fifth" of The Hunting of the Snark, the words of the Butcher, explaining to the Beaver why 2 + 1 = 3.

Poems starring mathematicians - 6 (Mandelbrot)

More familiar than the name Benoit Mandelbrot are images, like the one to the left, of the fractal that bears his name.  Born in Poland (1924) and educated in France, Mandelbrot moved to the US in 1958 to join the research staff at IBM. A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole, a property called self-similarity. 

The epitome -- Euler's Identity

Mathematics is a visual language.  As with poetry, placement on the page is a key ingredient of meaning.  Here is one of my favorite visual poems, "The Transcendence of Euler's Formula," by Neil Hennessy, a Canadian poet and computer scientist.  For additional math-poetry from Neil, follow the link.

          epitome
          epitome
          epitome
          epi+ome
          epItome
          _____________
          epit0me

Margaret Cavendish (1623-73) -- The Circle of the Brain cannot be Squared

Margaret Cavendish (1623-73) was a writer who published under her own name at a time when most women published anonymously.  Her writing addressed a number of topics, including gender equity and scientific method.

Mathematical 'grooks' from Piet Hein

Piet Hein (Denmark, 1905-1996) was many-faceted--by times a philosopher, mathematician, designer, scientist, inventor of games and poet. He also created a new poetic form that he called 'grook' ("gruk" in Danish). Hein wrote over 10,000 grooks, most in Danish or English, published in more than 60 books. Some say that the name is short for 'GRin & sUK' ("laugh & sigh", in Danish).  Here are samples, with links to more:

Poems starring mathematicians - 5

In my own library this next poem is found (untitled) in Collected Sonnets by Edna St Vincent Millay (1892-1950),  but it also is found online at various sites. The first line of the sonnet, which announces Euclid as its subject, is well-known to most mathematicians; enjoy here all fourteeen lines.

A Numerical Poem (Fibonacci)

Consider the following poem involving the Fibonacci numbers:
 

        1/89 = .0        +

                  .01        +

                  .001        +

                  .0002        +

                  .00003        +             

                  .000005        +

                  .0000008        +

                  .00000013        +

                  .000000021        +

                  .0000000034        +

                  .00000000055        +

                  .000000000089        +

                  .0000000000144        +

                  .  ...

Poems starring mathematicians - 4

Each of today's poems is in the voice of a student who looks back.  First, from Carol Dorf, a poem to the author of a book--written as a fan-letter, "Dear Ivar."   And then, for his hero (a special Grammar School teacher) by Czech poet and scientist Miroslav Holub (1923-98), "The Fraction Line."

       Dear Ivar,

       I read your book on the unexpected.

       Like most poets, I opposed mathematics

       when I was young, seeing it as the converse

       to feeling. The previous statement is false.

Poems starring mathematicians - 3

Today's poems illustrate the satirical humor and rhyme that frequently inhabit poems by mathematicians. (Previous postings of poems about mathematicians include March 23, April 14, and April 15.)

I Even Know of a Mathematician      by John L Drost

        “I even know of a mathematician who slept with his wife only
                   on prime-numbered days…” Graham said.
                            ―Paul Hoffman, The Man Who Loved Only Numbers

Poems of Calculus

In her thoughtful poem "Calculus" mathematician-poet Sarah Glaz writes of sharing with her students some of their subject's history--a drama enacted by two different sorts of mathematician.  Here are Glaz' opening lines:

A Square for Earth Day

Greetings on EARTH DAY.  Earth's inhabitants today pay a price not only for our own careless habits but also for earlier ignorance about the fragility of our world. (As Garrett Hardin has said, "There is no away to throw to.")  The April 20 edition of  the Washington Post had an AP article about the risks of trash to wildlife in the Atlantic that provoked me to write the following square poem.

April -- Poetry, Math, and Boxing

April continues—both as National Poetry Month and as Mathematics Awareness Month (with theme math and sports).  As in the April 9 posting on baseball, in this post I also blend these interests with a math-and-sports poem--this one celebrates boxer Sugar Ray Robinson.

Poems with Fibonacci number patterns

In 21st century poetry, there are a variety of non-rhyming forms--and several of them have derived from the Fibonacci numbers.*  The Danish poet, Inger Christensen (1935-2009), wrote a book-length poem, alphabet (New Directions, 2000) in which the numbers of lines in stanzas followed the sequence of Fibonacci numbers.  "Fibonacci," shown below, by Judith Baumel is a shorter example of this form.

Poems starring mathematicians - 2

Published a century later than William Benjamin Smith's "The Merman and the Seraph" (see April 14 posting) we have Crossing the Equal Sign (Plain View Press, 2007)--a poetry collection by Marion Deutsche Cohen.  Cohen lives in Philadelphia and teaches mathematics at Arcadia University where she has used her literary interests to develop a new course, "Truth and Beauty: Mathematics in Literature."  I have chosen several excerpts from Cohen's collection that offer internal snapshots of  her sort of mathematician:

Poems starring mathematicians - 1

This is the first in a series of postings involving poems in which the principal subject is a mathematician.

     In “The Ideal Mathematician,” an essay in The Mathematical Experience, authors Philip Davis, Reuben Hersh, and Elena Marchisotto endeavor to describe the most mathematician-like mathematician:  He rests his faith on rigorous proof ...  He is labeled by his field, by how much he publishes . . .   He finds it difficult to establish meaningful conversation with that large portion of humanity that has never heard of [his research topic] ...  His writing follows an unbreakable convention:  to conceal any sign that the author or the intended reader is a human being ....

Poetry and Mathematics -- Similarities

HOW are mathematics and poetry similar?

Often-quoted in mathematical circles are words from mathematician Karl Weierstrass (1815-97): “It is true that a mathematician, who is not somewhat of a poet, will never be a perfect mathematician.”    And from physicist Albert Einstein (1879-1955):  "Pure mathematics is, in its way, the poetry of logical ideas." More recently, from Lipman Bers (1914-1993): “  . . . mathematics is very much like poetry . . . what makes a good poem—a great poem—is that there is a large amount of thought expressed in very few words."

April: along with baseball we celebrate poetry and mathematics

Is it coincidence or design that

     April  is  National Poetry Month
            
           and

   April  is  Mathematics Awareness Month
          (This year's theme is  "mathematics and sports")

In my own reading, baseball is the sport for which I have found the most poetry.

Braided lines form a PANTOUM

The pantoum is derived from a Malaysian form of interlocking four-line stanzas in which lines 2 and 4 of one stanza are used as lines 1 and 3 of the next. The lines may be of any length, and the poem can go on for an indefinite number of stanzas; it may be completed with a final stanza that uses lines 1 and 3 of the first stanza as lines 4 and 2 of the last, closing the circle of the poem.  As with recursion, each stanza provides an impetus for the next.