A Proof in a Poem . . .

     I was led to this information by a recent (11/23/23) posting by @OxUniMaths on  𝕏 (at https://twitter.com/home)

     Mathematicians Germano Cardano and Nicolo Tartaglia  lived in Italy in the 16th century.  When Cardano tried to persuade Tartaglia to tell him the solution method for  to cubic equations, he received a description that he calls a poem. Andrew Wiles discusses this situation in a YouTube video, as part of his talk on the Langlands program.  The posting by @OxUniMaths on  𝕏 offers a brief section of that talk -- and includes this translation (from the original Italian) of Tartaglia's poem:

Tartaglia considers solving a cubic

To the right (above), Wiles has noted a symbolic translation of Tartaglia's words.  In his discussion of the poem, Wiles also notes that back in the 16th century all math was written using words.  

Write about a MATH-WOMAN -- and WIN!

     Years ago -- when I was the only woman in the Bloomsburg University mathematics department --  I wrote a poem, "My Dance is Mathematics," about the mathematician Emmy Noether -- and it contained the following lines:

               If a woman's dance is mathematics,
               She dances alone.

But things are changing!  Founded in 1971, AWM (Association for Women in Mathematics) has been actively celebrating the lives of female mathematicians  -- and one of AWM's current and far-reaching activities is a STUDENT ESSAY CONTEST for which students -- in middle-school, high-school, and college categories -- are invited to interview a female mathematician and write about her.  The essay-submission period is December 1, 2023 - February 1, 2024.  Questions may be directed to AWM Essay Contest Organizer, Dr. Johanna Franklin (johanna.n.franklin@hofstra.edu). 

ADDING -- a List Poem

      Via an X (Twitter) posting by poet and blogger Marian Christie (@marian_v_o), I learned about a blog by writer Mike Ferguson entitled Gravy from the Gazebo -- available at this link.  Ferguson has posted a series of mathy list poems -- starting on November 10 with "Adding list poem".  The poem's opening lines are offered below and the complete poem is found at this link. 

The poem is introduced with these words:   Love a list poem, this is my latest – the kind of content and ideas I would like to introduce to students for writing their own:

Opening lines of a poem by Mike Ferguson -- the rest is here.

Ferguson next offered more lists: "Subtracting list poem" at this link AND "Multiplying list poem" at this link AND "Dividing list poem" at this link.

Read.  Reread.  Share.  Write your poetic response.  Share!

A Mathy-Poetic Trajectory

      Carol Dorf is a retired math teacher and poet -- and at New Verse News I have discovered one of her recent mathy poems, "TRAJECTORY," posted on 10/09/2023.   I offer its opening lines below.

from   TRAJECTORY     by Carol Dorf

          The problem set gives us: a stone, force, an angle.
          Given this, predict when the stone will hit the ground.
          Outside the book this problem grows more complex
          even if there are no dragons to interfere with the trajectory.
          Imagine a missile. No don’t. There’s no need to imagine:
          haven’t you opened the paper today? Imagine a war
          where children’s bodies form the location of the necessary
          violence. Don’t authorities always say necessary?

                . . . . .              Dorf's complete TRAJECTORY is available at this link.

Carol Dorf is a Zoeglossia fellow, whose poetry has been published in several chapbooks and in a wide variety of journals; and she is a founding poetry editor of Talking Writing.  

Here is a link to the New Verse News website -- a collection of many, many poems.  This link leads to poems at that site by Carol Dorf, including "Trajectory." 

Take a Tour -- of Mathy Poems

       Recently I have discovered (at the website of the American Mathematical Society, AMS) a blog posting that features my blog.  Entitled "A Tour of Intersections:  Poetry with Mathematics," the posting by math and science writer Rachel Crowell.  Below I post a sample:

"MATH WOMAN"  -- acrostic poem by JoAnne Growney

This link leads to the AMS postings by Crowell that features my poems.

AND . . .  readers are invited to EXPLORE THIS  BLOG for more!

AND

CREATE mathy poems!  and share them with joannegrowney (at) gmail (dot) com.

Upcoming AMS Math-Poetry Contest

 Middle School Students

High School Students

College Students

Share YOUR POEMS via the 2024 Math-Poetry Contest

sponsored by the American Mathematical Society

Submit between November 27, 2023 and February 2, 2024

Detailed instructions for contest entries are found AT THIS LINK!  

The Thirst to Know HOW MANY?

    One of the important math-poetry projects that I have been involved in is Strange Attractors:  Poems of Love and Mathematics, a poetry anthology collected and edited by mathematician-poet Sarah Glaz and me -- published by AK Peters/CRC Press in 2008 and now available on Kindle and at various online used-book sites.

     A poem in Strange Attractors that I have been drawn to again recently is "Ode to Numbers" by Chilean poet Pablo Neruda (1904-1973).  Here are its opening lines: 

from  Ode to Numbers     by Pablo Neruda

          Oh, the thirst to know
          how many!
          The hunger
          to know
          how many
          stars in the sky!   

Zero Man of India

     An interesting story that Google led me to is told in this article about "Zero Man of India" --  the article tells of  Shahbaz Khan, famously known as Shahbaz Hakbari, a multifaceted individual with talent in poetry, prose, mathematics, and education -- well-educated AND he he is a widely celebrated teacher.

"Mathematics and poetry may seem like two different worlds, but both require creativity, imagination, and thinking outside the box," Shahbaz Khan explained.

The article "Zero Man of India" contains many mentions of Khan/Hakbari's life as a poet -- but has no poems.  Nonetheless, the phrases quoted are poetic -- and, below, I have given two of them the shapes of  poems.

Remembering Louise Gluck

        Poet-Laureate of the United States (2003-2004), winner of the 2020 Nobel Prize in Literature, Louise Glück died recently.  (10/13/23)  (A biographical sketch and many of Glück's  poems are available here at poets.org.)  The quotation below -- sharing her desire "to make something never heard before"  -- links closely to the desires of those of us in mathematics, to create the new.

A quote given with Gluck's obituary in The Washington Post

This 2020 blog posting features Gluck's "Parable of the Swans" and here, at poetryfoundation.org, is "A Fable" -- a poem about two women and one baby.

An infinite design -- in a poem

Like a circle, the "lazy 8" or infinity symbol -- shown below --never ends.

Recently it was a delight to me to find -- here in the Harpy Hybrid Review -- the following diagram-poem by Philip Wexler entitled "INFINITY".   And I have enjoyed reading and rereading -- exploring the ways that shape and meaning intertwine.

Celebrate Ada Lovelace -- and all women in STEM

     The second Tuesday in October -- this year, Tuesday, October 10 -- is Ada Lovelace Day..  Details of the celebration planned by The Royal Institution of Science are available here at this link.  A careful biography of this pioneering female mathematician -- Ada Lovelace (1815-1852) -- is available here.

"Ada Lovelace Day (ALD) is an international celebration of the achievements of women in science, technology, engineering and maths (STEM). It aims to increase the profile of women in STEM and, in doing so, create new role models who will encourage more girls into STEM careers and support women already working in STEM."  Quote from https://findingada.com/.

Although her father, poet Lord Byron, had no interest in mathematics, Ada's mother, Lady Byron, was supportive as was astronomer-mathematician Mary Somerville (1780-1872) -- who became a longtime friend and math-encourager. (Lots more details of Lovelace's math-life are available here at the St Andrews Math-History website and her pioneering work with the Analytical Engine is featured here.)

      Below is a poem by Twitter poet Brian Bilston (@brian_bilston) that celebrates Ada Lovelace.

Indigenous Peoples Day

      Today (October 9, 2023) is Indigenous Peoples Day -- and I call attention to a thought-provoking activist poem by Linda Hogan, a member of the Chickasaw Nation and an important contributor to indigenous literature.  Here are the opening lines of Hogan's "Embodied."

     I am embodied first by the numbers
     given by my grandparents,
     no choice but to sign the Dawes Act.

Hogan's complete poem is available here in World LIterature Today. 

A portion of Hogan's poem was also posted here in this blog -- back in 2020.

Sunflower Swirls

     From Sharon Jones at Connell Co-op College in Manchester, UK, I have learned about National Poetry Day -- an event organised by Forward Arts Foundation and held on the first Thursday of October -- an annual celebration encouraging everyone to make, experience, and share poetry with family and friends.  Today, October 5, I celebrate the day by offering one of Sharon Jones' poems.

Turing's Sunflowers       by Sharon Jones

I am perplexed by mathematics.

The numbers and patterns make no sense to me.

I am transfixed by the yellow blaze of sunflowers.

Like you.

Celebrating a WINNING Woman!

     The International Congress of Mathematicians meets every four years (next in 2026) and, at these meetings, awards the Fields Medal --  an award given to two or three or four outstanding mathematicians aged 40 or younger.  The year 2014 was the first in which a woman won this medal -- "For her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces." -- she was Maryam Mirzakhani (1977-2017) -- who died too young of breast cancer.

     In her collection, Mathematics for Ladies:  Poems on Women in Science (Goldsmiths Press, 2022), Jessy Randall has a poem that celebrates Mirzakhani -- and I offer it below.

     MARYAM MIRZAKHANI (1977-2017)      by Jessy Randall   

Geometry in Poetry

     Poet Marian Christie's blog, Poetry and Mathematics -- found at https://marianchristiepoetry.net/ -- is a website I much enjoy visiting; there I learn many many new things.  (Here is a link that leads to a list of my previous postings that feature Christie and her work.)

    The idea that the shape of a poem may be part of its message is not new -- but Christie has brought more than line-length and syllable-count into the picture and today I focus on her Circular Poems.  

A Circular poem by Marian Christie

Poetry on the Side . . .

     My friend Gregory Coxson (engineering professor at the US Naval Academy) is an explorer of new ideas and I enjoy his frequent emails that share his discovered math-poetry connections.  Recently Coxson introduced me to the website of retired Virginia Tech professor Ezra Brown and, following the link Inspirational and Fun Stuff, I found this interesting collection of number-related Haiku --  beginning with a recollection of September 11. 

Day of Horror

There is no doubt that
on September Eleventh
God sat down and cried.

“I worked hard…”

Bach was prolific:
One thousand compositions
and twenty children.  

Chat GPT writes about Emmy Noether

       Learning about AI and exploring its possibilities has been an interesting recent activity for me.  One of my own favorite math-related poems is a poem I wrote many years ago about mathematician Emmy Noether -- and that poem, "My Dance is Mathematics," is available here in this blog at this link.  I offer below a poem from ChatGPT;  my instructions were:  write a poem about Emmy Noether -- and I got this:

     In realms of math where brilliance takes its flight,
     There dwells a star whose radiance shines so bright,
     Emmy Noether, a name of boundless grace,
     A mathematician whose legacy we embrace.

     Born in Erlangen, a spark in her eyes,
     She defied the norms, reached for the skies,
     In a time when women faced a daunting door,
     She pushed it open, forevermore.  

Attitudes toward Mathematics

     A wonderful place to visit is PLANET INFINITY -- a website maintained by Rashmi Kathuria, math teacher from Delhi, India.  Exploring this site I found, in the posting for July 24. 2012, the following poem.   Rashmi Kathuria introduces the poem with the following statement.   

     "Yesterday one of my school student came to me and shared her self composed poem on her feelings regarding Mathematics. Shreeya composed it when she was in grade 8."

A posting of student poetry from Planet Infinity.

Mathematics is a beautiful subject. It is the way in which it is taught and learnt makes it difficult or boring.    -- Rashmi Kathuria

Poetry of Science

     One of the interesting regular online postings is a new science poem EVERY FRIDAY -- offered by Sam Illingworth via an email subscription or in his  Poetry of Science blog.  Recently I have found and valued Illingworth's interview late in 2020 with poet Donald Beagle, author of the poetry collection, Driving into the Dreamtime (Library Partners Press, 2020).

     One of Beagle's publications involved editing a poetry collection by James Radcliffe Squires (1917-1993) -- a collection in which many of the poems are informed by science.  Here is a sample from Squires' collection Where the Compass Spins -- now presented in Radcliffe Squires: Selected Poems; edited by Donald Beagle).

          “…We are one motion and we see
          Another. Then we overtake two flying birds
          And at the crisis of the wan parabola
          Assume their speed. Thus motion dies…”

The lines above are from Squires' poem “The Subway Bridge, Charles Station to Kendall.”  This same poem concludes by touching upon the Einsteinian concept of the gravitational bending of light: “Faring with the straightness that curves. The line / Of brightness bending as it nears the sun.”    When you have an available hour, visit and enjoy the whole of Illingworth's 2020 posting about Donald Beagle's poetry.

Is reading POETRY like reading MATHEMATICS?

Back in June I found an interesting article online by USAToday Entertainment Editor Pamela Avila  that raises questions about how to read poetry -- questions that are similar to those asked about reading mathematics.  I offer samples below:  

Here are words from poet Clint Smith, author of new poetry collection Above Ground and writer for The Atlantic:

"Sometimes we're taught to read poetry as if it's a code that we have to unlock or that it's a puzzle or a geometric proof with a specific answer," says  "I don't think that that's what poems are or should be."  ("Counting Descent" is a mathy poem that explores Smith's family history.)

The beauty of a poem can lie in not knowing. 

Steam Powered Poetry

       Some of us -- perhaps because of the structure of our minds, perhaps because of our education -- focus strongly on a few key ideas.  And some of us -- perhaps this is common among teachers -- focus on the linking of ideas that we encounter.   My own learning activity seems to be hybrid and to focus on linking and integrating -- perhaps stemming from my childhood mix of rural and urban environments, perhaps from my interests in both mathematics and poetry.

    It is a delight for me to learn of growing numbers of teachers who are combining STEAM subjects with the arts -- and one of the outstanding contributors to this effort is children's author and teacher Heidi Bee Roemer.  Roemer is one of the contributors to the website Steam Powered Poetry and recently I found on YouTube her poem. "Going Bananas" -- about mean, median, and mode .  A text version of "Going Bananas" may be found in this April 2021 posting.

Here is a link to a broad selection of steam powered poetry videos.

A Nine-Sided Diamond

   One of my much-appreciated math-poetry connections is with Scott W. Williams, a Professor of Mathematics at SUNY Buffalo and author of many scholarly papers and many poems.  In a recent issue of the Journal of Humanistic Mathematics (JHM) I found (and valued reading) his "Impossible Haiku" -- a series of Haiku-stanzas that play with the Collatz Conjecture -- an unproven belief that for any starting number these two steps, performed in appropriate succession, eventually reach the number 1:

   If the number is odd, multiply by 3 and add 1; if the number is even, divide it by 2. 

Williams' "Impossible Haiku" may be found at this link.      Another mathy poem by Williams (found here at his website) that I especially value is the one that I offer below -- a poem dedicated to his mother.

THE NINE-SIDED DIAMOND by Scott Williams 

Hunger -- portrayed in poetry and numbers

      Since 2003, SPLIT THIS ROCK has been an activist poetry organization that protests war and injustice.   Besides readings and conferences, Split this Rock also connects members by emailing a POEM OF THE WEEK series.  Most often, these poems are not mathematical in nature -- but one of the recent offerings is a verbal picture that uses numbers -- "meat market" by New York multidisciplinary artist Lara Attallah.  I include a portion of this poem below.   

    meat market    by Lara Atallah

             after Lebanon, a country with one of the worst economic crises since the nineteenth century

    the price of bread has gone up again. throngs of cars
    slouch towards shuttering gas stations. the currency, a farce

    with each swing of the gavel, numbers
    soar. fifty thousand pounds by day’s end,  

MAA Math Values Blog values poetry!

     I am a long-time member of the Mathematical Association of America (MAA) -- an organization (with administrative offices in Washington, DC)  whose mission is "to advance the understanding of mathematics and its impact on our world."   The MAA website states:

Our members include university, college, middle, and high school mathematics faculty; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in government, business, and industry. We welcome all who are interested in the mathematical sciences.

     An important feature on the MAA website is their Math Values blog -- which has frequent postings from diverse voices within mathematics; these postings include important mathematical information and also math's connections to the larger world -- including teaching and learning, the arts, practical math-applications  . . .and more . . . 

     Recently in the Math Values blog I came across this posting (from June 2023) by Czech poet and artist Radoslav Rochallyi of what he calls VECTOR poetry; here is a screen-shot of a sample -- a poem developed from the phrase: “Time is pouring out of my broken watch glass. You look ahead, and you're right. Because the potential of the past is just … a sandcastle.”

Shaping a Poem with Fibonacci numbers

      One of my favorite websites to visit is this varied and thoughtful "Poetry and Mathematics"  collection of postings by Marian Christie.

     Throughout history, people who write poems have often been aided by constraints.  When we sit down to write, writing the words that first occur to us -- then shaping the word into extended meanings but following a pattern of rhythm or rhyme or word-count . . . or . . .  .  For many poets the sonnet, for example, has been a poetic structure that shapes thoughts into special arrangements of words.

     In long-ago days, when print and screen versions of poems were not easily available, rhyme schemes were an important aid -- helping one's memory to keep a poem in one's head.  Now, aided by widely available print and online visibility, poetry has moved into new forms -- including a variety of visual arrangements.  

A Template for Student Math Poems

      Earlier this month, mathematician, songwriter, and poet Larry Lesser posted a link on Facebook to an article (found here at "The Conversation") about ways that Penn State University Professor Ricardo Martinez combines mathematics and poetry in a course entitled "The Ways Math and Poetry Can Open Your Eyes to the World."   When asked, "What prompted the idea for the course?", Martinex responded:

I have always enjoyed writing poetry. As a high school mathematics teacher, I recall telling my students that everything is and can be connected to math, even creative writing. Then, as a graduate student, I read about people using “I am” poem templates for young people to express who they are through a series of “I am” statements, and I thought to myself, where is the “I am” math poem template? So I created one.

Here is a portion of a template that Martinez has created to use with students: 

Lost Women of Science

     One of the fascinating websites that I have found recently "Lost Women of Science" -- a podcast series available at https://www.lostwomenofscience.org/.  This site has lots of bios and I browsed among them using the search term "mathematics".  One of the fascinating stories that I found is that of Naomi Livesay -- who played a key role in the Manhattan project.

Learn more about Naomi Livesay at this link.

     These recent considerations of women in science have led me to recall a blog posting that I made back in June of 2012 that featured this poem of mine (with stanzas that are syllable-squares):

Math Biographies at the University of St. Andrews

     One of the very informative and math-related Twitter postings that I follow is @StA_Maths_Stats --which features postings from the School of Mathematics and Statistics at the University of St Andrews in Scotland.  These include postings that feature mathematicians.  Today's Mathematicians of the day posting features a list of math people (with links to bios) who were born or died on August 10  -- and it includes this quote from Oswald Veblen, topologist and geometer from the United States who died on this date in 1960:

Mathematics is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry.

My search at the St. Andrews website for occurrences of the word "poem" led to a list of 179 responses.  Here is the poem I found at the first item on that list:

Life described by counting -- "My Math"

      One of my art-and-poetry friends, Kyi May Kaung alerted me to the online journal, Glass -- and I had lots of fun browsing in the archives . . . . and found (in Volume 1, Issue 2) a mathy poem-- which I offer below.

      My Math     by Allan Peterson

          Two egrets and three gulls are five,
          ten with shadows, doubles of the night in daylight,
          plus two for the red hawks watching.
          This is my math, just as I was multiplied by the bear
          and her cubs crossing at Chama,
          by the swarm of winged ants and the warblers
          that came frenzied for them.
          If I wait for the fall migration, if I am my integer
          while being stalked by bacteria,
          I might calculate an uneasiness of earth, including
          the skink that hides in the dryer vent,
          a continent about to shift in its chair, but I am impatient,
          still counting deliberately on my fingers and stars.

Another poem by Peterson with lots of numbers may be found here at poetryfoundations.org.

Creative, Mathy, Poetic -- Mathematickles

       The website of author and screenwriter Betsy Franco contains a great variety of literary links (including this link to this interview of Franco by Oprah).  Her writing includes poetry -- including collections of mathy poems for kids:  Counting Our Way to the 100th Day   and Mathematickles -- small mathy stanzas that are a bit like Haiku.

Here is a sample from Mathematickles: 

Mathematickles are math haiku that tickle your brain. Fun words take the place of numbers in all sorts of math problems. Math becomes playful, beautiful, sassy, and creative in this whimsical romp through the seasons! 

Mathematickles -- by Betsy Franco

 

The geometry of pleasure . . . .

     My late-July days have been wonderfully busy with family activities -- time with my children and grandchildren (and not much time for this blog).  Poetry that I have recently enjoyed is this selection at poets.org from "Pink Waves" by Sawaka Nakayasu.  Many thoughts have been stimulated by its opening and its final lines:

          it was a wave, it was infectious  . . . .
                      . . . .  geometry of pleasure  

Winning Math-Communication with Haiku

     Each spring at MoMath (The National Museum of Mathematics in New York City) a contest is held -- for the Stephen Strogatz Prize for Math Communication -- inviting entries in Art, Audio, Performance, Social media, Video, and Writing.  This year's deadline was April 28, 2023 and winners are posted at this link.  (Info about mathematician Stephen Strogatz is available here.)

     This year's winner in the Writing category was "An Exploration of Communicating Math Concepts Through Haiku" by Anaya Willabus  -- a selection from her runner-up entry is shown below and the complete creation by Willabus is available here.

Winning math communication by Anaya Willabus

Previous mentions in this blog of the Strogatz Prize may be found at this link.

Remembering Amy Uyematsu . . .

     This is a time of sadness in the math-poetry community as we  mourn the loss of poet and retired mathematics teacher, Amy Uyematsu (1947-1923).  Here is a link to an obituary that celebrates her life and scrolling down at this link leads to information about Uymatsu's scheduled contribution to an upcoming BRIDGES Math-Arts Conference.

     It was my delight to connect with Amy lots of years ago and I have featured her and her work often in this blog (This link leads to Blog-SEARCH results for Uyematsu.)  

     A frequently-discussed question in math circles is "Is mathematics discovered or invented?" -- and below I offer the opening stanzas of Uymatsu's poem, "The Invention of Mathematics."  The entire poem is available here in my blog posting for September 29, 2010.

The Invention of Mathematics        by Amy Uyematsu

                         A man who is not somewhat of a poet
                         can never be a mathematician.
                                      Karl Weierstrass, German mathematics teacher

     / one

               one is the only true number
               the I in the eye
               each baby the god
               in a mother's sigh       

A LIMERICK defining "FACTOR"

      As a follow-up to my recent posting about OEDILF (Omnificent English Dictionary in Limerick Form), I can't resist posting my limerick that appears on that site.  Years ago when I first learned of the dictionary I submitted several limerick-definitions but the only one that has survived is this definition of "factor":

This limerick is found here at the OEDILF site. 

Mathy Limericks . . .

     One of the fun-to-visit poetry resources on the internet is the Omnificent English Dictionary in Limerick Form, a website resource that has for a goal the inclusion of at least one limerick for each meaning of each and every word in the English language.  Here is a link to an earlier mention of OEDILF in this blog and here, from the OEDILF site, are a pair of limericks about Calculus -- limericks that are currently awaiting dictionary approval.

          "Was it Newton or Leibniz?" I asked
          My professor. He smiled and then tasked
               Me to find more about
               My small calculus doubt.
          I researched and the truth was unmasked.     

A Pioneering Woman

      Born in Washington DC in 1924, Evelyn Boyd Granville graduated from Smith College in 1945 and in 1949 became the second African-American woman to receive a PhD from an American university -- from Yale.  She worked primarily in computing.  (July 7 update:  from this morning's Washington Post I have sadly learned that Granville has passed -- on June 27, 2023).

Details of Granville's achievements may be found here and here.

Math Class -- Express POINT OF VIEW with a POEM

       Often students in a math class feel hesitant about expressing their point of view about the subject -- and these attitudes may emerge more easily via a writing assignment.  A writing format that many students respond to easily is an acrostic poem.  Such a poem is obtained by first selecting a relevant math term -- perhaps INTEGER or ADDITION or EXPONENT or  . . . and using each of its letters as the first letter of a line of poetry.  Here is a brief sample using MATH --  one of many examples I found as the result of an internet search using the terms "acrostic poem on mathematics".

Available at this link

Go here for lots more:   Acrostic Poem On Mathematics - Bing images

TRITINA -- a tiny SESTINA

     In several previous postings (collected at this link) this blog has considered the poetry form called a sestina:    a sestina has 39 lines and its form depends on 6 words -- arrangements of which are the end-words of 6 6-line stanzas; these same words also appear, 2 per line, in the final 3-line stanza.

     The American poet Marie Ponsot (1921-2019) invented the tritina, which she described as the square root of the sestina.   the tritina is a ten-line poem and, instead of six repeated words, you choose three, which appear at the end of each line in the following sequence: 123, 312, 231; there is a final line, which acts as the envoi -- and includes all three words in the order they appeared in the first stanza.  Poinsot has said -- and I agree -- poetic forms like the tritina are "instruments of discovery . . . they pull things out of you."  Read more here in an article by poet Timar Yoseloff.)

   

BRIDGES Math-Poetry in Halifax -- July 27-31, 2023

     BRIDGES, an annual conference that celebrates connections between mathematics and the arts, will be held this year in Halifax Nova Scotia, July 27-31.  (Conference information available at this link.)  A poetry reading is one of the special event at BRIDGES and Sarah Glaz, retired math professor and poet, is one of the chief organizers of the event.  Here at her University of Connecticut website, Glaz has posted information about the July 30 reading along with bios and sample poems from each of the poets.   For poets not part of this early registration, an Open Mic will be available (if interested, contact Glaz -- contact information is available here at her website.)

Here is a CENTO I have composed using a line of poetry from each of the sample poems (found online at this link) by the 2023 BRIDGES poets:

HELLO, Numbers

     As a child, I learned to love numbers via counting rhymes (of which many are found at this Lit2Go website);  -- often I reinforced my number-memory by reciting  rhyming verses such as "One, two, buckle my shoe" and "Baa, Baa, Black Sheep" and enjoying the trick in "Going to St. Ives."  University of Arkansas mathematician Edmund Harriss (whom I met a bunch of years ago at a conference in Banff) and co-authors Houston Hughes (poet) and Brian Rea (visual artist) have a book -- HELLO NUMBERS! (published in 2020 by The Experiment).  This book, like those old rhymes, gives young readers the opportunity for fun with numbers as they learn.

Here's a sample:  

    Learning meets wonder
           when you invite numbers to come play in your imagination!

       First think of One peeking out from the night
       Like a point, or a dot, or a shimmering light.

Syllable Squares

        Poetry and

       Mathematics

       are languages

       that can aid us

               to think

               new thoughts.

Inventing Zero

     A Pennsylvania friend who is now in Oklahoma, Sharon Solloway -- whom I got to know when we were both faculty members at Bloomsburg University (now part of Commonwealth University)  --  shared with me on Facebook the following mathy poem,  "Inventing Zero" by Canadian astronomer Rebecca Elson (1960-1999).  Found in Elson's collection,  A  Responsibility to Awe (Carcanet Classics, 2018)  "Inventing Zero" is available along with other samples of Elson's work here at this link.

       Inventing Zero      by Rebecca Elson

               First it was lines in the sand,
               The tangents, intersections,
               Things that never met,
               And you with your big stick,
               Calling it geometry,   

Number Patterns in Nature

     Naval Academy engineering professor and math-poetry fan Gregory Coxson has recently introduced me to poetry by Mattie Quesenberry Smith at VMI (for a bio of Smith, go to this page, scroll down, click on BIO) -- she and I have connected and she has shared with me several of her mathy poems; here is one about the Fibonacci numbers -- a number pattern found in nature:  

     Fibonacci Found It       by Mattie Quesenberry Smith

        It is spring on House Mountain,
          And I am wondering how
          Fibonacci found it
          And believed that it matters,
          That sequence of numbers
          Hinging on what precedes them,   
          Running this springtime show.
          Soon spring will be sanguine,
          Shouting from steep shadows,
          And the eight-petaled bloodroot,
          A robust and pure lion
          Rooted in his bloody rhizome,
          Is a rare know-it-all.
          A leaf encircles his stem.
          Its strange, veined palm
          Shields him from blood’s loss.

 ”Fibonacci Found It” was first published in Thirty Days: The Best of the Tupelo Press 30/30 Project’s First Year,” edited by Marie Gauthier, Tupelo Press, 2015. Reprint rights are retained by author.

Choosing the GEOMETRIC SHAPE of a poem

      Structural constraints often govern the patterns we find in poetry -- well-known in poetic history are rhythm-and-rhyme patterns including the sonnet and the villanelle and the limerick, and the syllable-counting pattern of some Haiku.  Because many poems were shared orally, rather than in writing, patterns of counting and sound helped to ease the challenges of remembering.

     For me a wonderful source for learning about new poetic forms is the blog of poet Marian Christie -- a writer and scholar, born in Zimbawe and now living in England , who has studied and taught both mathematics and poetry.  In her very fine blog, Poetry and Mathematics, found here, Christie explores many of the influences that mathematics can have on poetry -- including, here in a recent posting, some effects transmitted by the SHAPE of a poem.

EDGES -- as well as VERTICES -- are IMPORTANT!

G. H. Hardy (1877-1947) was a prominent English mathematician, well-known to mathematicians for his achievements in analysis and number theory -- and for his mentorship of the Indian mathematician, Srinivasa Ramanajuan.  For most people outside of mathematics, Hardy is better known for his 1940 expository essay, A Mathematician's Apology; here are Hardy's opening sentences:

Stimulate Math Class Discussion with Poems

     Sometimes teachers want to understand more about their students' attitudes and concerns about learning a particular subject.  Often, rather than asking direct questions like, "What is your difficulty?" or "Why don't you like geometry?" it can be useful to stimulate discussion with a poem.   The website of the Academy of American Poets, offers at this link a wide selection of poems about school subjects.  Scrolling down through this long list, eventually one comes to Poems for Math Class -- with poems for Algebra, Calculus, and Geometry.  

     One of the Academy's suggested poems is "Calculations" by Brenda Cardenas  -- I offer the first stanza below -- the complete poem is included here in this posting from November, 2017.  

          from    Calculations      by Brenda Cárdenas    

Measuring Infinity

      One of my recent excitements has been to learn about a current exhibit at New York's Guggenheim Museum, " Gego:  Measuring Infinity".  At the Guggenheim website for the exhibit, we learn:

Gego, or Gertrud Goldschmidt (b. 1912, Hamburg; d. 1994, Caracas), first trained as an architect and engineer at the Technische Hochschule Stuttgart (now Universität Stuttgart). Fleeing Nazi persecution in 1939, she immigrated to Venezuela, where she settled permanently, fully embarking on an artistic career in the 1950s that would span more than four decades. In two- and three-dimensional works across a variety of mediums, Gego explored the relationship between line, space, and volume. 

After visits to the Guggenheim website, I wanted more -- and I purchased a featured book, also entitled Gego: Measuring Infinity, and available at this link.  On page 19 of this lovely book, a bit of poetry.  Written in homage to Gego in 1979 by Venezuelan poet Alfredo Silva Estrado (1933-2009), the poem speaks of Gego's experimentation with structure, space, light, shadow, line, and grid.  Quoting from the Guggenheim book, we have Estrado's words:

Mathematician of the Day

     On this date, May 16, in the year 1718, the talented Maria Agnesi was born.  A great source of historical information about mathematics and mathematicians is MacTutor, a math-history website maintained by the School of Mathematics and Statistics, University of St Andrews, Scotland.  One of the services that MacTutor provides is a list of names and information about mathematicians born on each day of the year.  For example, this link leads to the listing for May 16 -- and to lots of info about Agnesi.  Here, in a 7x7 syllable-square, is a brief sketch of  her life:

Maria Agnesi's life --

a complicated story --

wealthy and intelligent, 

in love with mathematics,

also very talented--

wrote a teaching text about 

differential calculus.

This 2018 Scientific American blog posting by Evelyn Lamb discusses a curve from calculus, often called (somewhat misleadingly) "the witch of Agnesi."   Previous mentions of Agnesi in this blog may be found at this link.

Exploring the truth with a FIB

     Recently I have been reconnected with British-Israeli mathematician-educator, Yossi Elran  (whom I met at a conference in Banff several years ago).  Elran is well known for his puzzle-book, Lewis Carroll's Cats And Rats... And Other Puzzles With Interesting Tails (World Scientific, 2021).  He is in the process of writing a sequel to this book and it will include some math-poetry; probably some Fibs (poems  -- often with just 6 lines -- with syllable-counts per line that follow the Fibonacci numbers).   Elran's recent email query about Fibs helped me to remember that I had one waiting to be posted, a Fib about missed opportunities and status for women.  Here is is:

Exploring the truth with a FIB        by JoAnne Growney

Celebrate Hypatia

     Consilience is an online journal (edited by Sam Illingworth) that explores "the spaces where the sciences and the arts meet" -- and in the recent Issue 12 I have found a very special poem by British science writer Isabel Thomas that celebrates the pioneering math-woman, Hypatia of Alexandria (died 415 AD), one of the first women whose study and teaching of mathematics, astronomy and philosophy has been documented.  I offer several stanzas of "Rimae Hypatia" -- followed by a link to the complete poem.  

     Rimae Hypatia       by Isabel Thomas

                   The Rimae Hypatia is a lunar fissure named for Hypatia.

          In the greatest library of the ancient world
          Hypatia 
          turned her mind to 
          algebra, astronomy, geometry,
          examining the world from different angles.    

Poetry and Mathematics are NOT Opposites

     Recently I found online -- at the Spectrum Magazine website -- a collection of poems by Florida poet Phillip Whidden.  One of these poems is entitled "Mathematics" -- and I offer its thoughtful and thought-provoking opening lines here. 

from   MATHEMATICS     by Phillip Whidden

        Mathematics is not the prose part of the mind, logical, 
                as in meaning the opposite of poetry,
        Not just set out in indented paragraphs of abstraction.
        This is a city where the streets are innocent of collisions,
        Where the options are always 0/1,
        Are right, left, straight,
        Though the results can rise
        Out in a gyring arc from a heliport,
        Up in a sweep from the long rectangle of the airport runway,
        Ocean liners pulling away in parabolas from straight-edged docks
        And nothing ever in reverse.
                 . . . . 

The rest of "Mathematics" and four other poems by Widden -- including "Super Binomial Byronic Poets" (which also has a bit of math) -- are available here. 

Geometry and Sewing

     The mathematical ideas that I have mastered over the years spread out and infiltrate whatever I do and experience -- when the newspaper carrier throws my bagged Washington Post newspaper on the the porch in front of my second floor door, I wonder -- is the paper's curved path an arc of a circle, or a parabola?  Or ??? 

     Today, as I was sorting old newspapers and magazines into piles for saving or recycling or trashing, my items-to-sort included lots of copies of The New Yorker -- and the issue from May 16, 2022 had a page marked;  I opened it to find the poem "FEATHERWEIGHT" by Chase Twichell.   This poem reminded me how much my sewing activity connects to mathematics.  I offer below the poem's opening stanzas -- followed by a link to the complete poem online (both print and audio versions).

        FEATHERWEIGHT     by Chase Twichell

            At fourteen, I taught myself to sew
            on a Singer Featherweight,

Poets for Science -- Poetry Exhibit

     In 2017 poet Jane Hirschfeld curated an exhibit entitled "Poets for Science".  It was featured in Washington, DC on Earth Day, April 22, 2017, when demonstrators around the world participated in a March for Science, a call to support and safeguard the scientific community.  Since 2017 the exhibit has been hosted by various locations.  (More information at this link.)

     The Poets for Science Exhibition features a Special Collection of human-sized poems banners, with each poem in the collection specifically chosen by Hirshfeld to demonstrate the connection between poetry and a particular area of science, from the Hubble Telescope and MRI machines to childhood cognitive development, biology, ecology, and natural history.  

     Connection between poetry and mathematics is exhibited by the poem "Pi" by Nobel-prize-winning poet Wislawa Szymborska (1923-2012)  (translated from Polish by Clare Cavanaugh and Stanislaw Baranczak (1946-2014)).  I offer a portion of the poem below (followed by a link to the complete poem).

Pi     by Wislawa Szymborska  (translated by Barańczak and Cavanagh)

Where Will the Parallels Meet?

      One of my favorite poets -- with a varied selection of mathy poems -- is the Czech poet Miroslav Holub (1923-28), an immunologist as well as a poet and one who also wrote about the horrors of World War II.

     Here is one of his poems that I gathered in this 2001 collection Numbers and Faces:  A Collection of Poems with Mathematical Imagery, entitled "The Parallel Syndrome."

The Parallel Syndrome   by Miroslav Holub  (translated by Ewald Osers)

          Two parallels
          always meet
          when we draw them by our own hand.

          The question is only
          whether in front of us
          or behind us.

          Whether that train in the distance
          is coming
          or going.

The collection named above, in which Holub's poem appears, is available here.
This link leads to results of a blog search for previously posted poems by Holub..

Once upon a Prime . . .

      British Mathematician Sarah B. Hart is receiving wide-spread publicity and praise in recent days for the publication of her book Once Upon a Prime:  The Wondrous Connections Between Mathematics and Literature (Flatiron Books:  New York, 2023).  (Here is a link to an enthusiastic review in The New York Times by Jordan Ellenberg.)   

     My copy of Hart's book arrived last week and I have been enjoying not only the information but the point of view.  Hart's opening chapter is "One, Two, Buckle My Shoe:  The Patterns of Poetry" and, for those of you who don't have the book yet, an excerpt from opening pages of the chapter is included here in an article in Literary Hub.

Running . . . Again . . .

      Today one of my friends from graduate-school days in Oklahoma is running in the Boston Marathon and, while following her progress on my I-phone, I have been thinking about the role of running in my own life; for me, running has been a way of releasing tension -- some exercise and good breathing.   Years ago Theodore Roethke's villanelle "The Waking" (available here) inspired me to write "Running" -- and I offer it below:

    Running      Response (by JoAnne Growney) to “The Waking” by Theodore Roethke 

       My sleep is brief.  I rise to run again,
       to flee the doubts that catch me when I'm still.
       I live by going faster than I can.

       I feel by doing.  What's to understand?
       I eat and drink and never have my fill.
       My sleep is brief.  I rise to run again.