Which permutation of lines yields the best poem?

     A fascinating article about poet Jericho Brown (by Allison Glock in Garden and Gun magazine) reminded me of the vital role of line-arrangement in creating a poem.  (Emory University professor Brown has won the Pulitzer Prize in poetry for his collection The Tradition  (Copper Canyon Press, 2019)).
      Glock's article, "Jericho Rising," tells of various factors that have influenced Brown's poetry and describes his process of arranging lines, typed on separate strips of paper, into poems.  Three of the lines shown in the article are:

       What is the history of the wound? 

  We'll never see their faces or know their names.      

       And a grief so thick you could touch it.

THE STORY OF MATHEMATICS -- in a poem

     A mathy poem that I have learned about from Carol Dorf (poet and retired math teacher and poetry editor at talkingwriting.com) is "The Story of Mathematics" by poet and teacher Sarah Dickenson Snyder.  Offered below, "The Story of Mathematics" first appeared in the Spring 2020 issue of 300 Days of Sun -- it is a poem for which I have needed (and enjoyed) the challenge of several re-readings, both silent and aloud, to take it in.

     The Story of Mathematics    by Sarah Dickenson Snyder

     ​It starts with a shell –
     its curve and shine,

     the way a line peaks.
     It starts with a star

     and the arc
     between bone and light.

Counting . . . and more counting . . .

     Poet and retired math teacher and poetry editor (talkingwriting.com) Carol Dorf has been staying connected during the covid-19 pandemic by sharing poems.  Many of her emailed shares are works I know, but the item below came as new -- a mathy poem by David Ignatow (1914-1997) from his collection Against the Evidence: Selected Poems 1934-1994. (Wesleyan University Press, 1993).  Consider, with Ignatow, what is finite?  what is countable?

Information     by David Ignatow  

Links to mathy poems . . .

     The Annual Bridges Math-Arts Conference will not be meeting this year but mathematician Sarah Glaz has arranged for lots of math-poetic activity online -- go here and scroll down for links to poetry-presentations that she has arranged.  
     Glaz has gathered a Bridges 2020 Poetry Anthology (not yet published) that contains five of my mathy poems.  I read aloud two of them -- 

"Love Mathematics" and "A Baker's Dozen" -- here on YouTube.  

Thanks to my neighbor, Mark Willey, for help with the YouTube recording!

Doubling and redoubling . ..

     The mathematics of repeated doubling and concerns about COVID-19 have led Virginia dentist and poet Eric Forsbergh to write "A Fable" (offered below): 

     Fable     by Eric Forsbergh

     A child seeks the raja out.

     A grain of rice is held out on the child’s fingertip.
     The child seeks to live, someday to reproduce.

     “I ask this. One grain doubled,
     doubled again, on a chessboard every square.”
     The raja’s not alarmed.
     He sends a soldier out to get a loaded scoop.
     “Maybe a small pail.” he calls out as an afterthought.

A rhyme about a prime

     Tomorrow, May 16, is the birthday of Pafnuty Chebyshev (1821-1894), who was one of the founders of Russian mathematics and the first to prove (in 1850) a conjecture (about positive integers) made in 1845 by French mathematician Joseph Bertrand (1822-1900) and sometimes referred to as Bertrand's postulate.  This rhyming couplet celebrates that conjecture:

               Chebyshev said, and I'll say it again:
               There's always a prime between n and 2n.

Thanks to Evelyn Lamb's AMS Page-A-Day Calendar for its May 10 alert to the info above.

What would I do without NUMBERS?

     Sometimes familiar things that are very important are taken for granted.  Many of us do that with numbers . . . California poet and artist Mary Fabilli (1914-2011) considered their importance in the following thoughtful poem:

     Numbers     by Mary Fabilli

     What would I do
     without numbers?
     A 7 there and a 3 here,
     days in a month
     months in a year
     AD and BC
     and all such symbols

     the track of time

Geometry of a Shadow

     This morning while exercising I listened to an old CD that had been stored with materials I used when involved with the The Children's Museum (in Bloomsburg, PA).  The recording included selections from A Child's Garden of Verses by Robert Louis Stevenson (1850-1894) and as I listened to "My Shadow" I connected it with my blog -- a poem of geometry and mappings.  Here it is; enjoy!

     My Shadow    by Robert Louis Stevenson (1850–1894)
 
     I HAVE a little shadow that goes in and out with me,   
     And what can be the use of him is more than I can see.   
     He is very, very like me from the heels up to the head;   
     And I see him jump before me, when I jump into my bed. 

Squaring the circle . . . or not . . .

     Start with a CIRCLE -- is it possible, using only a straightedge and compass, to construct a SQUARE with the same area as the starting circle?  This problem, posed by ancient geometers, was long believed to be impossible, but not proven so until 1882 when Ferdinand von Lindemann proved that π is transcendental.
     Freelance editor and math-geek Sam Hartburn offers at her website a fun-to-read poem on this topic.  The first stanza is offered below, followed by a link to the full poem text -- and a recording. 

 (not) Squaring the Circle     by Sam Hartburn

          So I had this circle, but I wanted a square
          Don’t ask why, that’s my affair
          The crucial aspect of this little game
          Is that the area should stay the same
          Ruler and compass are the tools to use
          It’s been proven impossible, but that’s no excuse
          Many have tried it, but hey, I’m me
          I’m bound to find something that they couldn’t see

          So, here we go
                . . .

Hartburn's complete poem (and recording) may be found here.

Remembering Eavan Boland, Grace Hopper

     Irish poet Eavan Boland (1944-2020) died last week and news of her death has caused me to look back and remember.  In this year in which the US celebrates 100 years of women's suffrage, I am reminded of this poem in the Irish Times in which Boland celebrated 100 years of Irish women's suffrage, a poem entitled "Our future will become the past of other women."  Here is a brief excerpt from that poem:
                         A hundred years ago a woman’s vote
                         Becoming law became the right
                         Of Irish women. We remember them
                         As we celebrate this freedom.

One of my favorite of Boland's poems is her tribute to another master of language, Grace Murray Hopper (1906-1988) -- Hopper was a computer pioneer and a navy rear admiral.  Here is the opening stanza of Boland's poem:

Poetry and Math -- online audio -- 2020 census, etc

     Today (with poems in our pockets) we celebrate the final day of National Poetry Month and National Mathematics and Statistics Awareness Month and I offer to you two math-poetry links to browse and enjoy.
     This first link leads to an NPR Code Switch podcast that concerns the 2020 census -- "When Poets Decide Who Counts" -- and five poets-and-poems are presented in a discussion of the fairness/unfairness of the census-count.  (One of the poems, "American Arithmetic" by Natalie Diaz, has also appeared in this blog.)
     This next link leads to another podcast  -- this one entitled "What's math got to do with poetry?" and a creation of science writer Stephen Ornes, in his blog, Calculated.  (Thank you, Stephen, for inviting me to participate in your podcast and to read several poems.)

National Poem-in-your-Pocket Day -- April 30, 2020

     The following stanza by  award-winning children's author,  Beatrice Schenk de Regniers, (1914-2000), has led to an annual celebration in US schools of "Poem-in-your-Pocket" Day:

          Keep a poem in your pocket 
          and a picture in your head     
          and you'll never feel lonely
          at night when you're in bed.  

This year's Poem-in-your-Pocket Day will be celebrated on Thursday, April 30.  Here is a link to  "Counting and Math Rhymes" -- a website that offers a variety of choices for young people's pockets.  My own pocket -- and my mind, during these days of pandemic confusion -- will be holding lines from Carl Sandburg's "Arithmetic":

Considering my Point of View

       Today, on Earth Day, I am listening to news of the COVID-19 pandemic and wondering how to interpret what I hear . ..  

"Do you see the center . . . " by William Elliott

Elliott's poem appears on my shelf in the math-poetry anthology,  Against Infinity, edited by Ernest Robson and Jet Wimp (Primary Press, 1979).

The Geometry of Love

     A journal that I love to browse is the Journal of Humanistic Mathematics -- and recent quarantining has been a bit like my youthful experience of being "snowed in" and thus having extra time for reading.  At the JHM site, I was drawn to this article by Robert Hass, "John Cheever's Story 'The Geometry of Love'."  Before reading Haas' analysis, I sought to read the original story -- available here (a pdf-file of its appearance in 1966 in The Saturday Evening Post).
      Short story writer John Cheever (1912-1982) and JHM author Robert Haas explore (with some humor) the question: how can Euclidean geometry help us find our ideal world of truth and happiness.  Read and enjoy!
 
     Since this is a math-poetry blog, I add a tiny rhyme of mine:

               The Geometry of Love

               I like the intersection line
               that your plane makes with mine.

For lots and lots more fiction-with-mathematics, visit this wonderful website maintained by Alex Kasman of the College of Charleston.  

April 22 is EARTH DAY -- Remember the TREES

Can planting billions of trees save our planet?

Trees help cleanse the air by intercepting airborne particles, reducing heat, 
and absorbing pollutants such as carbon monoxide, sulphur dioxide, and nitrogen dioxide. 

Trees are sound barriers -- as effective as stone walls in stopping sound.

     Today this blog celebrates TREES via poetry by Australian visual artist and poet, Belinda Broughton -- her performance-poem "EDGES" has been part of an exhibition, Solastalgia at Fabrik, in Lobethal, South Australia -- and here in this video she performs the poem in front of a drawing that she created with charcoal from her recently burnt home, tragically part of Australia's recent and widespread outbreak of wildfires.  
     I include below, some of the opening and closing lines of Broughton's poem;  after these, I offer a link to the print version of the complete poem.

     Edges     by Belinda Broughton

     Who will speak for the trees? Who     will speak for the trees?
     Who will speak for the forest, for that part
     of the natural world? Because it’s all nature, let’s face it,
     even this crass world with its concrete and steel,
     its plastic paint and polluted pavements.
     It   is   nature.

Inclusion-Exclusion -- the power of the CIRCLE!

On my mind today, this poem by U.S. poet Edwin Markham (1852-1940):

          Outwitted     by Edwin Markham

          He drew a circle that shut me out--
               Heretic, rebel, a thing to flout.
          But Love and I had the wit to win:
               We drew a circle that took him in!

Find more of Markham's work here.

Haiku Poetry Day -- coming soon!

     My internet explorations find celebrations of Haiku Poetry Day described for both April 17 and April 18   -- my own recommendation is that you celebrate every day the beauty of language and meaning that can come when we thoughtfully limit our syllable-count.  I try to do that below.

Pandemic

Exponential growth:

small numbers doubling quickly--

a world upended!

Both mathematics and poetry honor concise language.  Here, from the Journal of Humanistic Mathematics is a wonderful collection  -- "Math in Seventeen Syllables:  A Folder of Mathematical Haiku," published in the January, 2018 issue.    ENJOY!  

Celebrate the lives of MATH-WOMEN via POEMS!

     This week I have learned that a lovely presentation of my poem, "With Reason  A Portrait of Sophia Kovalevsky," has been published in the April 2020 issue of Mathematics Teacher.

 The Kovalevsky poem is available here-- 

please read and enjoy!

      I have found that POEMS about mathematicians not only can serve to celebrate those lives but also provide a meaningful way to introduce these important people into math classes.  Here are several links to previously posted poems that speak of the lives of math-women:

   Sophie Germain (1776-1831)                      Florence Nightingale  (1820-1910)

   Amalie "Emmy" Noether  (1882-1935)      Grace Murray Hopper (1906 - 1988)

Readers may find more poems about special people by scrolling through postings or by using a blog-SEARCH.  Names available for SEARCH may be found in this document.  And here is a link to a blog-SEARCH using the terms "math women". 

Uncertainty persists . . .

      In these days of coronavirus uncertainty and risk, my thoughts are drawn again and again to this couplet:

The Secret Sits     by Robert Frost (1874-1963)

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

Lots more of Frost's words are available here.

And, as the coronavirus pandemic delays baseball season, here are additional Frost-thoughts:

     Poets are like baseball pitchers. 
     Both have their moments.  The intervals are the tough things.  

The Woman Who Bested the Men at Math

     An American Mathematical Society Page-a-Day Mathematics calendar, compiled by mathematician and free-lance writer Evelyn Lamb, has let me know today that tomorrow, April 4, marks the birthday of mathematician Philippa Garrett Fawcett (1868-1948), who became, "in 1890, the first woman to score the highest mark of all the candidates for the Mathematical Tripos at Cambridge University." 
     Learn more about Philippa Fawcett at this website, "Biographies of Women Mathematicians,: --  maintained by Emeritus Professor Larry Riddle at Agnes Scott College.  Riddle's biographic sketch of Fawcett includes a poem of anonymous origin that celebrates her 1890 achievement.  Here are its opening stanzas:

Math Poettary -- continuous, but not differentiable

     A few weeks ago I was introduced via email to Gauarav Bhatnagar, a mathematician now at Jawaharlal Nehru University in New Delhi, India.  In addition to varied and deep mathematical and educational interests, Bhatnagar likes to play with words; here are a couple examples of his poetic wordplay -- or, as he calls it, poettary.

        Continuous function     by Gaurav Bhatnagar

        A continuous function,
        draw it without
        picking up pencil
        from paper.

        At all points,
        the left hand limit 

She should have been on the Math Team

     National Poetry Month starts tomorrow and I hope that poetry can be a thoughtful focus for you in this time of crisis and confinement due to the coronavirus.  Join me in looking back to several previous posts of work by one of my favorite poets, Audre Lorde (1934-1992).

     "Hanging Fire"    about a girl who should have been on the Math Team
               "The Art of Response"
                         "Smelling the Wind" 

Lorde's collection, The Marvelous Arithmetics of Distance, may be found and browsed here.
For lots more poems about math-girls-and-women, go here.

Mathematics...underlies everything...said the poet

     I first met scientist-poet Mary Peelen via an 2019 interview of her by mathematician-poet Gizem Karaali in The Adroit Journal .  The conversation includes an introduction to Peelen's poetry collection, Quantum Heresies (Glass Lyre Press, 2019) in which she discusses her intent "to show how mathematics and physics underlie everything in my life . . ." Read more here.

       NUMBER THEORY     by Mary Peelen

       Forty one apples in the tree,
       red and round,

       praise awaiting gravity,
       wholly free of abstraction.

       When it comes to the primes
       and matters of religion,

       I defer to Pythagoras,
       his ancient cult and authority. 

SUNSET poem -- guided by a Fano diagram

GEOMETRY IN POETRY

Warning:  even if you are not a mathy person, you will like the poem offered below!

     When a writer picks up her pen and starts to write, the initial phrases may be simply a ramble -- a pouring out of thoughts that might be able to be shaped into a poem.  Over the centuries, writers have used syllable-counts and patterns of rhyme to help them shape their word into the best-possible expressions.
     Earlier in this blog (in this 2016 posting) is a poem created by Black Hills State University mathematician Daniel May using a geometric structure called a Fano Plane.  I offer below another similarly-structured creation by May -- and, after the poem, a bit of explanation.

Fano Plane diagram

Sunset : October 11th      by Daniel May

it's late in the day and we’ve climbed up this rise.
i stare, too closely, into the
leaving of the light streaming through the treetops 
          from the next ridge over.

later, i'll wonder if looking into the sun makes me crazy,
or gives me secret terrible knowledge.
my last willful act will be staring directly into our star, 
          and it will be like burial at sun.

Celebrating 10 Years of Math-Poetry Blogging

     This blog's first posting, "Poetry of Logical Ideas" -- found here, occurred ten years ago today on March 23, 2010.    This link leads to a list of topics, poets, and mathematicians contained in the 1200+ postings made since then.
 

Word Cloud for this blog -- created at https://tagcrowd.com.

Honor World Poetry Day on 3/21 with a Math Poem

On March 21 each year, UNESCO World Poetry Day! 

Browsing down through this blog will lead you to lots of poems to read to celebrate that special day. In addition, here's something new -- I offer below part of a fine poem that I recently found again in an old collection, Verse and Universe, (Edited by Kurt Brown, Milkweed Editions, 1998). 

from     Reasons for Numbers     by Lisel Mueller (1924-2020)

          1
          Because I exist

          2
          Because there must be a reason
          why I should cast a shadow

          3
          So that good can try to be better
          and become best
          and beginning grow into middle and end 

What does this math-poetry blog contain?

An alphabetical list of TOPICS

and NAMES of all of the poets and mathematicians

cited in this blog is available here.

Keeping Track -- poetry with numbers

      The very fine poetry of Jane Hirshfield has been featured in several earlier blog postings.  And below, again -- with some lines from "Ledger," the title poem for her new collection, out this month. These lines find, as Hirshfield often does, both life-truths and poetry in numbers.

     Ledger     by Jane Hirshfield

     Tchaikovsky’s Eugene Onegin is 3,592 measures.
     A voice kept far from feeling is heard as measured.
     What’s wanted in desperate times are desperate measures.
     Pushkin’s unfinished Onegin: 5,446 lines.   

Observe Pi-Day by writing in Pilish

      Many poets use constraints to shape their writing but few are as constrained as mathematician Mike Keith who has written many works in Pilish -- that is, a language in which the flow of words have lengths that follow the digits of Pi.  In honor of 2020's Pi-Day on 3.14, I have developed a small bit of Pilish, a poem of sorts, which I offer below.

 

 Entering the term "Pilish" into this blog's SEARCH box finds these earlier postings that celebrate Pi. 

 The first 50 decimal digits are 3.14159265358979323846264338327950288419716939937510 . . .

"Numbers and Faces" and 23 more math poems

     "Numbers and Faces" is the title of a poem by W. H. Auden -- and I also have used it as the title of a collection of poems that I gathered into a small anthology for the Humanistic Mathematics Network in 2001.  The collection is out of print BUT is available here as a pdf -- and the Table of Contents is shown below:

Learn of MATH WOMEN in POEMS!

 INTERNATIONAL DAY OF THE WOMAN

Sunday, March 8, 2020

      Often it is difficult to find time for history in mathematics courses.  One rather concise way that some of us introduce math personalities into the classroom is through poetry.  Today, as part of Women's History Month, I offer links back to a sample of poems in previous postings that celebrate math-women.

Amalie "Emmy" Noether (1882–1935)
     Following stanzas about Noether's life and achievements, the poem ends with these lines:
                    Today, history books proclaim that Noether 
                    is the greatest mathematician
                    her sex has produced. They say she was good
                    for a woman. 

New math poems -- recently found online

     A couple of days ago an email brought me the Table of Contents of the latest issue (Vol. 42, Issue 1) of  The Mathematical Intelligencer -- and it had links to two poems that I hope that you also will enjoy.
     First was "The Day I Receive My Ph.D." by Arkaye Kierulf of Cornell University. Kierulf's poem begins with these lines:
          I’ll head out into the streets to hand out
          My dissertation abstract like discount-hotel flyers.

          For Christmas I’ll send copies of my diploma to  . . .

For Kierulf's complete poem go here.

     Also in this same issue of the Intelligencer -- and available at this link -- is the poem, "Remembering e" by Robert J. MacG. Dawson of Halifax University in Nova Scotia.  Dawson's math-poetry has been featured in several previous posting's in this blog.  Visit and enjoy!

     Additional very rich sources of mathematical poetry are the twice-yearly issues of the Journal of Humanistic Mathematics (online here). The latest issue (January 2020) contains a folder of Statistical Poetry by Larry Lesser (many of Lesser's poems also are featured in this blog), and five additional poems:
     "Perfect (a poem)" by Joseph Chaney, "A Letter to Niccolò Fontana de Brescia" by Jessica Huey, "The Empress's Nose: A Parable, After Feynman" by Robert Dawson, "SIGINT signifier" by Terry Trowbridge, and "The Master Oiler" by Ernesto Estrada.
 

A MATH WOMAN acrostic poem

Can one describe a MATH WOMAN in 9 words?
and, what if those words' first letters must spell MATH WOMAN?
Try it -- it's fun!

       M  ultiplies
       A  xioms
       T  risects
       H  yperbolas

       W  rites
       O  rthogonal
       M  atrices
       A   voids
       N   egatives

Counting syllables, considering snowflakes

     From Larry Lesser, a professor at The University of Texas at El Paso (a researcher in math education) and a poet and songwriter and friend, today's poem offers a thoughtful reflection on the properties of a snowflake--and the fragility of thought and weather patterns.  But first (and also from Lesser), here's a clever "2019" stanza (in which each line has the number of syllables of the corresponding digit in that year):

                    Silence

                    is
                    sometimes the strongest thing we can say.

       SNOWFLAKE     by Lawrence Mark Lesser

        Some say
        ‘‘no two alike’’,
        others say
        ‘‘not too alike’’.

Which order is best -- or should I try them all?

This posting celebrates a new poetry collection -- 

Ringing the Changes by Stephanie Strickland 
(Counterpath, 2020).

This new collection starts with an idea from bell-ringing.  Some city towers have marvelous-sounding bells -- and sometimes these bells ring wonderful concerts for nearby inhabitants.  One of the traditional bell-ringing activities is called "ringing the changes" in which a collection of n bells are rung, in sequence, in all of the possible n-factorial bell-orders.  (Here, at Strickland's website, are some links to information about the art of bell-ringing.)

BUT, what if the goal were not to ring bells in sequence 

but to generate (for a reader) sequences of words (thoughtful poetic phrases)?

This sort of art is what Strickland brings to us in Ringing the Changes.

Those trains in word problems -- who rides them?

    A Problem in a Math Book     by Yehuda Amichai (1924-2000)

     I remember a problem in a math book
     about a train that leaves from place A and another train
     that leaves from place B. When will they meet?
     And no one ever asked what happens when they meet:
     will they stop or pass each other by, or maybe collide?
     And none of the problems was about a man who leaves from place A
     and a woman who leaves from place B. When will they meet, 

"Binary Heart" -- linking love and mathematics

      From the xkcd webcomic by Randall Munroe -- and also shown on the cover of Strange Attractors: Poems of Love and Mathematics, we have this reminder of upcoming Valentine's Day.

"Binary Heart" by Randall Munroe,
at https://xkcd.com/99/

     Munroe's clever drawings "of romance, sarcasm, math, and language" have appeared also in previous postings in this blog (here's a link) and his website is fun to visit.
     The anthology, Strange Attractors; Poems of Love and Mathematics-- edited by Sarah Glaz and me -- was published in 2008 by AK Peters and contains more than 150 poems of math and love (including another -- "Useless" -- by Munroe.)  More about Munroe is available here.

Valentine's Day -- a time for Love and Mathematics

     Perhaps you are looking for a mathy Valentine, 

or a Valentine for a mathy person . . . or both.  

This link leads to the results of a blog-search using VALENTINE

and offers lots of math-poetic possibilities.

Welcome DIVERSITY in mathematics

     As February on the calendar brings BLACK HISTORY month and March brings WOMEN'S HISTORY month, I invite you to explore the contributions of diverse groups to mathematics.  In this blog, I celebrate links between a rainbow of math-people and poetry -- for example, in this posting, "Mathematicians are not just white dudes, (which includes links to math-poetry by Benjamin Banneker and Scott Williams). 

Another prize-winning poem

     It was not until after my posting yesterday that I got permission from the third of the winners in the AMS 2020 student poetry contest to post his work.  Here is "The Number Won" by Austen Mazenko.   (And here is a link to a YouTube video of the January 18 event in which each of the winning poets reads their winning poem.)

Austen is a high school senior from Greenwood Village, CO. He loves words, numbers, and their patterns--and looks forward to pursuing mathematics in college next year.

THANK YOU to the American Mathematical Society for encouraging math-poetry!