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.