String Theory

     String Theory is a theoretical framework that attempts to explain, among other things, quantum gravity.  Its basic elements are open and closed strings -- rather than point-like particles.  The poem "String Theory" by Ronald Wallace offers imaginative and thoughtful interplay between these strings of theoretical physics and the strings of musical instruments -- I found the poem at the VerseDaily website and Wallace has given me permission to use it here.

      String Theory     by Ronald Wallace

      I have to believe a Beethoven
      string quartet is not unlike
      the elliptical music of gossip:
      one violin excited
      to pass its small story along  

Continue to celebrate Szymborska

If you are a frequent visitor to this blog, you know that Polish Nobelist (1996) Wislawa Szymborska (1923-2012) is one of my favorite poets.  My Romanian friend Doru Radu, who now lives in Poland, visited New York recently and during my visit with him there he surprised me with a gift -- a posthumous bilingual Szymborska collection, Enough (Wydawnictwo a5, translated by Clare Cavanagh).  Here is the English version of a small poem with numbers from that collection:

          Hand     

          Twenty seven bones,
          thirty five muscles,
          around two thousand nerve cells
          in every tip of all five fingers.
          It's more than enough
          to write "Mein Kampf"
          or "Pooh Corner."

Links to additional postings of Szymborska's work may be found here.
Remember also to visit the wonderful Spring 2016 issue of TalkingWriting -- with its smorgasbord of mathy poems.

Remembering Reza Sarhangi

     In 1998 at Southwestern College in Winfield, KS an Iranian mathematician, Reza Sarhangi, organized the first of a series of annual Bridges conferences that celebrate the intersection of mathematics and the arts.  On July 1, 2016, this vital mathematician-artist passed away.  Many will celebrate the life of this warm and generous and talented man.

     Here is a link to Bridges history and here is a link to the Bridges website 

where you can learn a bit about Reza Sarhangi and about this year's conference in Finland. 

 Here is a link to an article by Sarhangi on Persian art -- indeed, it includes a poem. 

 Here is a link to samples of Sarhangi's art.  

Sarhangi was at the time of his death, a professor at Towson University. 

 Here is a link to his informative Towson webpage which I hope the university will keep alive.

What Math Teachers Do

     They ignore me.  I
     raise my hand -- wave it
     to ask questions, to
     offer answers -- but
     they call on the boys.

A 5x5 syllable-square of protest, from JoAnne Growney

Revolutions and singularities

     Early in June it was my privilege to hear poet Lesley Wheeler read as part of the Joaquin Miller Poetry Series on summer Sundays in Washington, DC's Rock Creek Park.  Lesley read from her wonderful 2015 collection, Radioland, in which I found this mathy sonnet, a poem of twists and singularities and rich with double meanings:

       Concentric Grooves, 1983     by Lesley Wheeler

       Every whorl in the floorboard spins clockwise,
       the grain widening round the stain, a stream
       of years circling a burn-brown knot.  Strum
       and crackly gap.  Music drowns a wheeze 

Important online sources for mathy poems

Every issue of the Journal of Humanistic Mathematics contains poetry.

The Spring 2016 issue of TalkingWriting has more than a score of mathy poems.

This blog has offered math-linked poetry online since 2010, now with over 800 posts.  Scroll down to browse OR use the SEARCH box to look for poems with a particular mathematical image. The lower right-hand-column offers key-words that can be useful search terms.

Exponential power

From this week's New Yorker (June 27, 2016) from a poem by Maya Ribault entitled "Society of Butterflies" this mathy statement:

                                . . .                 I save  
            for retirement—to my bohemian eyes, 
            a fortune—though they say you need more
            than a million. Immerse yourself in the exponential
            power of dividends.      . . . 

Read the entire poem here.

A sonnet with numbers

     Sonnet: Now I see them    by Michael Palmer

          Now I see them sitting me before a mirror.
          There’s noise and laughter. Somebody
          mentions that hearing is silver
          before we move on to Table One
          with the random numbers. I look down
          a long street containing numbers.

Wanting things proportional . . .

Here is a reflective poem by San Diego poet Ben Doller (found also at Poets.org and included here with permission of the poet).

       Proportion    by Ben Doller

       Just want things
       proportional.

       Just things,
       not all.

       Not kings, kings
       should be below:    

Women occupy mathematics

     Poems thrive on imagery created from specific (rather than vague) details -- and numbers and other math terms are very specific!  Below I present several samples of mathematical imagery in poems from an excellent and important recent anthology Raising Lilly Ledbetter:  Women Poets Occupy the Workspace.

Here are the opening lines of "Circle of Silence" by Stacey K. Vargas:

     Like an electron trapped in an unstable orbit, I am seated 
                           in a circle of powerful men.
     In an awkward moment small talk ends 
                           and the meeting abruptly begins.
     The superintendent turns to me and says, 
                           "This was not sexual harassment."

And the opening lines of "The Typist" by Barbara Drake:

     I made 87 1/2 cents an hour typing,
     when I was a college student. 

When parallel lines meet, that is LOVE

Bernadette Turner teaches mathematics at Lincoln University in Missouri. And, via a long-ago email (lost for a while, and then found) she has offered this love poem enlivened by the terminology of geometry.

Parallel Lines Joined Forever    by Bernadette Turner

       We started out as just two parallel lines
       in the plane of life.
       I noticed your good points from afar,
       but always kept same distance.
       I assumed that you had not noticed me at all.  

Symbols shape our thoughts

     In mathematics -- as in spoken languages -- we have learned to use symbols to shape our thoughts.  Pioneering artist Marcel Duchamp (1887-1968) carefully expresses this important idea in terms of chess. 
  
     “The chess pieces are the block alphabet
     which shapes thoughts; and these thoughts, although
     making a visual design on the chess-board,
     express their beauty abstractly, like a poem...

     I have come to the personal conclusion
     that while all artists are not chess players,
     all chess players are artists.”

―Marcel Duchamp

This and other stimulating statements from Duchamp are available here.

During these days of celebration of the life of Muhammad Ali (1942-2016) I have refreshed my memory of his notable quotes (many of which are found here).  Here is one with some numbers:

     A man who views the world 

the same at 50 

     as he did at 20 

has wasted 30 years of his life.

A poem, a contradiction . . .

     One strategy for proving a mathematical theorem is a "proof by contradiction."  In such a proof one begins by supposing the opposite of what is to be proved -- and then reasons logically to obtain a statement that contradicts a known truth. This contradiction verifies that our opposite-assumption was wrong and that our original statement-to-be-proved is indeed correct.   (An easily-read introduction to "proof-by-contradiction" is given here.)
       Peggy Shumaker is an Alaskan poet whom I had the pleasure of meeting at a reading at Bloomsburg University where I was a math professor a few years ago.  Her poem, "What to Count On," below, has a beautiful surprise after a sequence of negations -- and reminds me of the structure of a proof-by-contradiction.

What to Count On     by Peggy Shumaker

Not one star, not even the half moon       
       on the night you were born
Not the flash of salmon
       nor ridges on blue snow 
Not the flicker of raven’s
       never-still eye 

Aesop's fables in verse ... the price of greed ...

     The farmhouse* in which I grew up had a room we called "The Library" because of its small bookshelf with my father's books -- including selections from Kipling and Twain and Aesop's Fables.  I liked to read.  And a lot of the morals are now stored in my head.  Recently I have found and enjoyed poetry versions of some of these in Jean de La Fontaine's Selected Fables (Dover, 2000) -- see also Project Gutenberg.  Here is one about the mathematics of greed ... .

The Hen with the Golden Eggs    by Jean de La Fontaine (1621-1695)

                                   translated by Walter Thornbury

My little story will explain
An olden maxim, which expresses
How Avarice, in search of gain,
May lose the hoard that it possesses.

Mathy poems OUT LOUD

     Here is a link to "Applied Mathematics" written and recited by London poet Dan Simpson.   This link leads to several math-arts samples (including two poems -- the first is by Gizem Karaali and you may scroll down to hear my poem, "A Taste of Mathematics") recorded by Samuel Hansen. (The complete text of "A Taste of Mathematics" is available here.)  This link connects to information about a 2014 YouTube video featuring a varied list of mathy poets.

The Man Who Knew Infinity

     A few days ago I followed a broken link on the Poetry Foundation website and the site offered me this cryptic quatrain by American poet J. V. Cunningham (1911-1985) -- it is the final stanza of a poem I have posted here.

       Error is boundless.
       Nor hope nor doubt,
       Though both be groundless,
       Will average out.
               – J.V. Cunningham, from “Meditation on Statistical Method”

     Often on my mind these recent days has been the film I saw last week -- "The Man Who Knew Infinity" -- and I invite you to follow these links to poetry concerning its central characters, mathematicians Srinivasa Ramanujan (1887-1920) and G. H. Hardy (1877-1947).

In Wyalusing, counting pelicans

     The number in the title of Robin Chapman's poem first attracted me to it and the mention of Wyalusing in the first line drew me further in -- for Wyalusing is the name of a small town in northeastern Pennsylvania (a region in which I lived and taught -- at Bloomsburg University -- for many years).  But, of course, Google was able to tell me of another Wyalusing, a park in Wisconsin, home state of the poet, and a place advertised as having plentiful bird-watching.  Enjoy:

       One Hundred White Pelicans     by Robin Chapman

       Over Wyalusing, riding thermals, they shine
       and disappear, vanish like thought,
       re-emerge stacked, stretched, 
       a drifting fireworks' burst.   

A math problem or a word problem?

     One of my recent poetry-finds has been the anthology Regreen:  New Canadian Ecological Poetry, edited by Madhur Anand and Adam Dickinson (Scrivener Press, 2009) and in it some small mentions of mathematics.  The following poem by artist and poet Erin Robinsong considers things big and small -- and observes some paradoxes. Is math the puzzle or the explanation or . . .?

SEED : CEDE   by Erin Robinsong  

Looking into the peach-pit, we find a vast spaciousness, as if actually looking into a pit –

A math problem:
A peach pit is weighed against
the year’s yield plus the tree: 
30 g, 900 kg.
Which weighs more? 

Squaring the Circle -- from the POETRY App

     One of my smart-phone delights is the App (available from PoetryFoundation.org) that gives me a selection of poems on the go. (My posting for 15 October 2015 gives a description of how the App works.)  A few days ago, spinning its dials -- matching the categories "Humor," "& Arts and Sciences"-- I found the exceptional poem "Squaring the Circle" in which poet Philip Fried has some fun with the impossible problem.   ("Squaring the Circle" first appeared in the July /August 2014 issue of Poetry and Fried has given me permission to include it here.)

Squaring the Circle      by Philip Fried

It’s a little-known fact that God’s headgear — 
A magician’s collapsible silk top hat,
When viewed from Earth, from the bottom up — 
Is, sub specie aeternitatis,   

A 6 x 6 syllable-square -- and links to more . . .

          Last Sunday's paper had
          an essay by a clown
          who said as long as I
          play dumb people let me
          do what I want.  And I
          cannot stop wondering.

 6, a perfect number    

Find lots of mathy poems here at TalkingWriting.com; this week featuring Sarah Glaz.

At this link find poems, etc. by Spelman College math students working with Colm Mulcahy.

Poems that count: Eight Buffalo

     In mid-April at the Split This Rock Poetry Festival, one of the sessions I attended and valued had the title " "Eco-Feminist Poetry, Intersectionality, & the End of the Earth."  In the midst of my concern about ecology and women is my addiction to mathematics -- and a poem by Cecilia Llompart started me counting.  See if you, too, count the word "buffalo" eight times during this poem; and shudder when you read the final word.

       Eight Buffalo      by Cecilia Llompart

       An obstinacy of buffalo 
       is not to say that the buffalo 
       are stubborn. No, not like 
       a grass stain. More that 
       the very bulk of one— 

Can you multiply with Roman numerals?

     Canadian writer Siobhan Roberts (whom I know from BIRS workshops) has a recent New Yorker article that celebrates the 100th birthday and achievements of Claude Shannon (1916 -2001) -- often referred to as "the father of the information age." Most of the important information in that article I leave for you to read for yourself, but I call to your attention to one of Shannon's accomplishments featured therein -- Claude Shannon built a machine for doing arithmetic with Roman numerals.  This connects to poetry via a poem by Ron Padgett, below.

The Roman numeral system has largely been abandoned 

because arithmetic is less cumbersome with a place-value system.

 Here is a link to a site that exhibits procedures for Roman numeral arithmetic.

 The Roman Numerals     by Ron Padgett

       It must have been hard
       for the Romans to multiply
       —I don’t mean reproduce,
       but to do that computation.

Talking-Writing offers Math Poems

     In recent weeks, the online journal Talking-Writing has been featuring math poems and last Monday they posted my "Skagway Study" -- which follows a style explored in one of my favorite poems by Wislawa Szymborska.
      Carol Dorf, poetry editor of Talking-Writing, is a math teacher as well as a poet and her work as well as those of others with math interest are explored in "Wild Equations," the Spring 2016 Issue of Talking-Writing.   Here are some links:

By Giavanna Munafo    "Twenty-Four Hours"

By JoAnne Growney    "Skagway Study" 

By Alice Major     "Euclid's Iron Hand" and "Bird Singularities"

By Amy Uyematsu   "Three Quick Studies of Math-Art"

By Carol Dorf   "Action Potential" and "e"

By Eveline Pye   "Celestial Navigation," "Three," and "The Law of Statistics"

By Larry Lesser    "Margins" 

By Katie Manning   "28, 065 Nights" and "Week by Week" (Fibonacci poem)

By Stephanie Strickland   "Doomed calculations which God acknowledged

                                                Islands (Invaginated by Saltwater
                                           Bays with a Stream and Another Both Flowing
                                              All Through Them along Enfolded Paths)" 

Earlier this week in an American Mathematical Society blog posting entitled "Math and Verbal Gymnastics," Duquesne University mathematician Anna Haensch also celebrated the join of mathematics and poetry.

"The Mathematician"

     Here is a selection from "The Mathematician," a long poem -- found in its entirety in The Rumpus -- by Oregon poet Carl Adamshick and recommended to me by poet R Joyce Heon  --  for a sample of her ekphrastic poems, follow this link and go to pages 37-42.  And this link leads to more poems (in this blog) starring mathematicians --- and a few of them are women!!

from   The Mathematician     by Carl Adamshick

What I do is calculate.
I’ve always seen the world as numbers,
buildings and trees factors,
math as a language better suited for explaining
how things work
than the formula of grammar.

Women in Mathematics Count!

     The theme for 2016 Mathematics Awareness Month is "The Future of Prediction."  And today I am wondering what date can be predicted for when the achievements of women in mathematics will be recognized with the same awareness as those of men.

How many female mathematicians can you name? 

Here are links to two articles to to help you lengthen your list of math-women:  "12 Brilliant Female Mathematicians You Should Know" -- an article by Olivia Harrison whose list starts with Hypatia (who lived around 400 AD) and continues to the 21st century, featuring Maryam Mirzakhani, an Iranian mathematician at Stanford who in 2014 won the prestigious Fields Medal for her work related to the symmetry of curved surfaces. Judy Green adds important names in her article "How Many Women Mathematicians Can You Name?"
     For still more, visit my 2015 post "The culture for women in math and the sciences";  additionally, a search of this blog using "math women" will lead to a host of  names and links.  Enjoy!
     Here are the closing lines of a poem of mine about the brilliant mathematician, Emmy Noether (1883-1935):   

           In spite of Emmy's talents,
           always there were reasons
           not to give her rank
           or permanent employment.
           She's a pacifist, a woman.
           She's a woman and a Jew.
           Her abstract thinking
           is female and abstruse.

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

The full poem is available here.

Remembering Solomon Marcus

     Almost five years ago I received an email from Romanian mathematician Solomon Marcus in response to my posting of a translation of  a poem by Nichita Stanescu (1933-1983) entitled "Poetic Mathematics"  -- a poem that Stanescu dedicates to Marcus.  In his email, Marcus offers this:

          Nichita Stanescu published his "Poetic Mathematics" in January 1971, in the magazine ARGES, as a reply to my book "Mathematical Poetics" (in Romanian, 1970; in German in 1973, at Athenaeum Verlag, Frankfurt/Main).

Here is a link to an interview with Marcus last year (at age 90) and it tells of his ongoing literary interests.  Recently I learned the sad news of his death, last month at the age of 91.  Some interesting details of the way Marcus and Stanescu experimented with the uses of language are included in this 2008 article by Emilia Parpala and Rimona Afanaa and are illustrated in the following poem, "Ritual," in which Stanescu uses numbers to explore and extend the meaning of The Last Supper.

     Ritual     by Nichita Stanescu  (trans. Sean Cotter)

     I cry before the number five --
     the last supper, minus six.

From a math-friend and an Ohio poet

     One of the wonderful things about writing a blog about my paired passions of poetry and mathematics is that the blog connects me with fascinating and generous people whom I might not otherwise meet. One of these is Marylander Greg Coxson -- physicist, engineer, mathematician, Operations Researcher -- who took three years of Latin in high school and loves words.  With interests in art and poetry, Greg has organized exhibits of math-related art -- and is a regular recommender of mathy poems for this blog.
     A week or so ago Greg alerted me to an NPR interview with Ohio Poet Laureate Amit Majmudar (a radiologist as well as a poet) -- letting me know that Majmudar's poetry was rich with mathematical imagery.  Following Greg's lead, I found Majmudar's website and was able to contact both Majmudar and his publisher, Knopf, for permission to offer these mathematical poems.
     Here, from Amit Majmudar's new book Dothead, are two sections of the poem "Logomachia" -- sections alive with geometry and logic.  The first, "radiology," is visually vivid; the second, "the waltz of descartes and mohammed," is a sestina that plays with the logic of word-order.  

"The Giraffe" -- a poem for my pocket

     I've found the poem I want to carry in my pocket (and in my head) on "Poem in Your Pocket Day" -- coming soon on April 21. It includes at least one number; here it is:

       The Giraffe     by Ron Padgett

       The 2 f's
       in giraffe
       are like
       2 giraffes
       running through
       the word giraffe

       The 2 f's
       run through giraffe
       like 2 giraffes.    

A Diagonal . . . and so little time . . .

On my mind in recent days is the problem of "so little time."  About a year ago I posted a wonderful mathy poem by Californian Brenda Hillman about time.  The complete poem is available here; below I supply the opening lines:

       Time Problem     by Brenda Hillman

               The problem
                of time.      Of there not being 
                enough of it. ...

Over the six years of this blog, the most-visited post has been "Varieties of Triangles"  with poetry by Guillevic.  Here is another of that poet's charming geometric offerings:

 Diagonal   by Guillevic  (Englished by Richard Sieburth)

       To get where I have to go
       I claim right of way.

       Because I provide communication
       Between two angles

       I take precedence
       I take up residence.

       I cross first,
       Come what may.
 
"Diagonal" is found in Guillevic's Geometries,from Ugly Duckling Presse (2010). Buy it!

"The Computation"

     Here is a favorite poem of mine -- and it available with many others in the anthology, Strange Attractors:  Poems of Love and Mathematics (A K Peters, 2008), edited by Sarah Glaz and me.

     The Computation     by John Donne (1572-1631)

     For the first twenty years, since yesterday,
     I scarce believed thou couldst be gone away,
     For forty more, I fed on favours past,
         And forty on hopes, that thou wouldst, they might last.
     Tears drowned one hundred, and sighs blew out two,
         A thousand, I did neither think, nor do,
         Or not divide, all being one thought of you;
         Or in a thousand more, forgot that too.
     Yet call not this long life; but think that I
     Am, by being dead, immortal; can ghosts die?

How clever of Donne, writing all those years ago, to speak (indirectly, at least) to 2016's Math Awareness Month theme, "The Future of Prediction."

The Future of Prediction

     As well as being National Poetry Month, April is Mathematics Awareness Month and this year's theme is "The Future of Prediction."  In search of a poem on the theme, I found the following sonnet by poet Joyce Nower -- third in a section of 20 sonnets, "Meditations of Hypatia of Alexandria," in her collection, The Sister Chronicles and Other Poems (IUniverse, 2012), available in both print and electronic versions.

3.  Scales Can't Calculate*     by Joyce Nower

       Hypatia, Math, God One, can't plot the locus
       of soul and star, predict exactly where
       and when you die, whose hand deals death.  No hocus

Contemplating the heavens

English writer G. K. Chesterton (1874-1936) was a poet but was better known for his pithy sayings.   For example, we have the following statement (originally found here). 

         The
         difference
         between the poet
         and the mathematician
         is that the poet tries to get
         his head into the heavens
         while the mathematician
         tries to get the heavens
         into his head.

     Alas, Chesterton's comment obeys the common assumption that the male pronoun should be used for mathematicians.  Another poetic comment on mathematicians is found in a poem by Anthony Hecht -- "Mathematics Considered As a Vice" -- available here at PoetryFoundation.org.  Hecht's poem  offers a strongly negative view of the abstract nature of mathematics.
     Rivalry between mathematics and poetry comes to a head in April -- during which we will celebrate both "National Mathematics Awareness Month" and "National Poetry Month."

The Shape of the World -- a dream of equality

     One of the most vital components of the Washington DC poetry scene is Split This Rock -- an  organization that speaks and acts against injustice.  (Co-founder and Executive Director, Sarah Browning, is a long-time activist and a fine poet.)  One of STR's 2016 programs has been Al-Mutanabbi Street Starts Here DC 2016,  a book arts and cultural festival that commemorates the 2007 bombing of Baghdad’s historic bookselling street, and emphasizes free exchange of ideas and knowledge, in solidarity with the people of Iraq.  Several weeks ago at one of these events I met poet Dunya Mikhail and her translator, Kareem James Abu-Zeid, and was involved in discussion and reading from The Iraqi Nights (New Directions, 2015).  Here is a mathy poem from that collection.

       The Shape of the World      by Dunya Mikhail
                                           translated from the Arabic by Kareem James Abu-Zeid)
       If the world were flat
       like a flying carpet,
       our sorrow would have a beginning
       and an end.

       If the world were square,
       we'd lie low in a corner
       whenever the war
       plays hide and seek.

       If the world were round,
       our dreams would take turns
       on the Ferris wheel,
       and we'd all be equal.

     A link to the Arabic original version of this poem is shown at the bottom of Mikhail's webpage -- a link that also offers  a recording of her reading this poem, set to music.
     And please note that coming up soon is the  2016 Split This Rock Poetry Festival (April 14-17, 2016) with many excellent workshops and readings.  Learn about it here and register (online registration closes March 31).  See you there.

World Poetry Day -- Celebrate favorites!

     Down, down, down into the darkness of the grave
     Gently they go, the beautiful, the tender, the kind; 

     Quietly they go, the intelligent, the witty, the brave.

     I know. But I do not approve. And I am not resigned.

                      From "Dirge without Music" by Edna St Vincent Millay; offered by Hermann Weyl

                      in a Memorial Address for Amalie "Emmy" Noether on April 26, 1935 at Bryn Mawr College.

Poems that Count

On January 6 of this year I attended a wonderful poetry reading (sponsored by The Word Works) that featured the work of poets Tera Ragan and James Ragan (Tera's father). Their poetry is rich in imagery of their birthplaces -- near Pittsburgh -- and Czechoslovakia (where James' parents were born and a place they visited often).  Please enjoy these lovely and varied poems that include a few well-chosen numbers:   "Alcove" by Tera Vale Ragan; "Beckett Had Only One Student" and "The Eskimo's Twelve Expressions of White" by James Ragan.
                                                               
       Alcove     by Tera Vale Ragan

       Brick upon stone, a growing
                                        foundation,
       he builds a new family home up
       from the ground
                                        cement and marble
       tile to ceiling
       beam and red oak
                                        he paid for with cash.

A poem is an equation?

     Exiled Romanian poet Nina Cassian (1924-2014) spoke with a daring and imaginative voice that I have much admired.  And she occasionally used mathematical imagery in her work -- as in the following poem:

Controversy   by Nina Cassian
                                          (translated from Romanian by William Jay Smith)
I wrote a poem, an oblique poem,
a kind of calligram, I mean.
Someone said it was an equation
being solved behind a screen. 

Celebrate Math Women

     March is Women's History Month and, although this year's theme focuses on women in public service and government, my own thoughts tend toward women in mathematics.  My post on July 21, 2015 focuses on math women -- and a google search of the blog using "math women" will lead to a host of additional poems and links.  Enjoy!
     To celebrate math-women one must first be able to name them; here is a link to an important and relevant article by Judy Green, "How Many Women Mathematicians Can You Name?"

I am the girl voice,

Drafts scribed--thoughts stretched, smoothed, squared, sighed --

Catch here now my I.