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.

    

Inspired by Pi

     Last year, a few days after Pi-Day, my email had a link (Thanks, Paul Geiger!) to an example of Pilish -- this one a circle poem by Mike Keith that represents the initial 402 digits of Pi  -- and I have, at last, posted the poem below.  Keith's poem first appeared in the The Mathematical Intelligencer in 1986. 

     And here is a link to musical Pi --at the webpage of "The Derivatives" are math parodies written and performed by Bloomsburg University professors William Calhoun, Kevin Ferland, and Erik Wynters, including The Pi  Song (also known as 3.14159/Circle).

Arnold diffusion (and poets of Romania)

     I have had the good fortune to attend two BIRS Math / Creative Writing workshops in Banff (most recently in January 2016) and one of the organizers of these workshops has been Florin Diacu, a Romanian-Canadian mathematician-poet at Canada's University of Victoria. (For a bit more about my interest in Romanian poets, you may visit this posting from 2012 ; for still more, use "Romania" as a blog-search term.)
     Recently I discovered the following poem by Florin in the January 2014 issue of the Journal of Humanistic Mathematics and that online journal's open-access policy permits me to offer it here.  I have wondered whether it is prudent of me to present a poem about Arnold diffusion, a topic about which I have scant mathematical background.  But I like it, even though my understanding is incomplete; I hope you like it too.

The Marvelous Arithmetics of Distance

     Audre Lorde (1934-1992)  is one of my favorite poets; links to my previous postings of her work in this blog are given below.  Here is the opening poem from one of Lorde's collections, The Marvelous Arithmetics of Distance.

     Smelling the Wind       by Audre Lorde

     Rushing headlong
     into new silence
     your face
     dips on my horizon
     the name
     of a cherished dream  

Links to Favorites

     According to Google, these posts are the top ten favorites of visitors to this blog in the six years since my first posting in March, 2010.  Perhaps you will want to visit one of them.  Or use the SEARCH box to find something favorite of your own.   I invite your comments.  Which posts do you especially like?

Varieties of triangles -- by Guillevic     Oct 13, 2010

     Loving a mathematician (Valentine's Day and .. .)     Feb 12, 2011  

          Rhymes help to remember the digits of Pi     Sep 2, 2010

               "Mathematical" Limericks     Mar 29, 2010

                     Ray Bobo's mathematical poem Jul 14, 2010 
Poems of set paradox and spatial dimension   Feb 22, 2011
     Poems of Calculus   Apr 23, 2010

          Primes and a paradox   Aug 14, 2015
               Theorem-proof / Cut-up / poems   Nov 11, 2010
                     A Fractal Poem   Dec 28, 2014 

Newton, Einstein, Gravity, Poetry

     Recent discovery of gravitational waves has put Einstein (1878-1955) -- and even Newton (1643-1727) -- into recent news, and a visit to one of my favorite reference collections, James R. Newman's four-volume collection, The World of Mathematics, finds those two giants celebrated in verse:

Introductory quotes for Section 21 ("The New Law of Gravitation and the Old Law" by Sir Arthur Stanley Eddington) of Part V (on page 1073 of Volume Two) of James R. Newman's The World of Mathematics.

     Here are links to information about the poets named above:  Lord Byron (1788-1824),  Alexander Pope (1688-1744), and Sir John Collings Squire (1884-1958) -- and these links lead to previous blog postings that feature The World of Mathematics:  March 22, 2011 and August 2, 2011.

Euler formula poem

     Sometimes I try to write a poem that explains a mathematical concept -- it's a difficult task  My effort usually results in something that sounds more like a textbook paragraph than a poem.  And I was thereby hugely delighted (following a lead from Colm Mulcahy) to discover this poem by Grant Sanderson that has fun with a famous mathematical formula due to Euler:

e^iπ + 1 = 0     or, stated differently      e^iπ = -1

Euler Formula    by Grant Sanderson 

Famously
start with e,
raise to π
with an i,
we've been taught
by a lot
that you've got
minus one.

How Old Is the Rose-Red City?

     Most of Martin Gardner's fans are avid puzzler's -- my connection with him is also one of admiration (he was a thoughtful person who was a master at making connections among disparate things) but we are connected via poetry, including topics such as counting all possible rhyme schemes for a given stanza and the constraint-based poetry of OULIPO . . ..
     Gardner (1914-2010) was not a poet -- although he penned a quatrain or two, his great contribution was collecting and publicizing parodies and puzzle-verses by others.  Here is a link to Gardner's collection of poetic parodies, and here is a link to many of Gardner's puzzles, including the stanza below, "How Old is the Rose-Red City?" 

Visit JHM for Mathy Poems

     Today I'd like to direct you to the Journal of Humanistic Mathematics, an online open-access journal that features poetry in each issue.  The Table of Contents for the first issue of 2016 is now available here -- and I offer below a poem from Issue 1 of 2015.  (Before sharing the poem "Prisoner's Dilemma" by Raymond Greenwell I want also to mention that JHM is looking for investigative journalists and that today's "Poem of the Day" at Poets.org is "Evolution" by Linda Bierds and inspired by the work of Alan Turing.)
     I am particularly intrigued by Greenwell's poem because the Prisoner's Dilemma is a decision model close to my concerns about the environment. (More comments below.)

       Prisoner's Dilemma     by Raymond N. Greenwell

       Your best choice is my demise.
       My wise choice is your defeat.