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.

Seeing the World through a dual prism . . .

     Based in Melbourne, Australia, Tom Petsinis is a mathematics adviser at Deakin University and is author of nine poetry collections as well as theatrical works and books of fiction.  He also is involved in the worldwide BRIDGES organization --which meets annually to investigate and celebrate connections between mathematics and the arts.  This year's BRIDGES conference will be held July 27-31 in Halifax, Nova Scotia and next year's conference is planned for August 1-5, 2024 at Virginia Commonwealth University in Richmond, Virginia.

     Below is "Zero" -- a mathy poem by Petsinis which is also offered as a sample at this BRIDGES link (a link that advertises and celebrates those poets participating in the 2022 conference).

April -- Mathematics & Statistics Awareness Month

      Found at the website of the American Statistical Association this fine page of resources for Mathematics and Statistics Awareness Month for students and teachers.  

This photos shows resource topics available at the link given above.

     One of my own recent activities has been to revisit an old book, Poetry and Mathematics by Scott Buchanan (J. B. Lippincott, 1962), originally published in 1929.   Buchanan (1895-1968) was a philosopher who had majored in mathematics as an undergraduate; his career involved both teaching and consulting -- and work at a political think tank.  Here are some of his words:

Math in Song Lyrics -- Joni Mitchell

       One of the fun surprises I have had recently is to discover mathematics in the lyrics of a once-popular song -- in "Ray's Dad's Cadillac" by musical legend Joni Mitchell, recent recipient of the Library of Congress Gershwin Prize for Popular Song.

     Joni Mitchell -- who has recently come back to the stage after serious illness -- has surmounted barriers to female achievement and recognition as have many math-women.  She has indeed "looked at life from both sides now" . . .   Below I offer two mathy stanzas from her song -- "Ray's Dad's Cadillac."    (The complete lyrics are available at this link).

from   Ray's Dad's Cadillac     by Joni Mitchell     

Mental Math -- and links to Poetic Craft

     From Yellow Springs News (in Antioch, Ohio), an interesting mathy-poetic story by writer Ed Davis  -- entitled "Emergent Verse | A Poetry Workshop" -- in which is uses "Mental Math" by poet Maggie Dean and discusses the process of revising by moving toward brevity.   The process shown is one that often happens as I write a poem -- it begins with a wordy ramble and over time I am able to improve my word choices and say as much or more with fewer words.

Here's the second section of Dean's poem followed by Davis's revision -- a move toward conciseness  (nearly always a goal in mathematics).

Rhymes and Jokes for Mathy Folks

April 1 is April Fools Day.

April is National Poetry Month.

April is National Mathematics & Statistics Awareness Month.

CELEBRATE with a humorous Mathy Poem!

     An entertaining book by G. Patrick Vennebush --  Math Jokes 4 Mathy Folks (Robert Reed Publishers, 2010) was one part of a widely shared effort to humanize mathematics, to break down its apparent exclusiveness and severity.  (For samples and testimonials, go here.)  Since that 2010 publication, Vennebush (this link leads to info about his background and varied activities) has published additional joke books and offers a blog Math Jokes 4 Mathy Folks  -- an extension of the book-material that includes in its humor some poems; here is a sample:

This rhyme found here at Math Jokes 4 Mathy Folks -- scroll down.

MATHEMATICS and POETRY -- a balancing act!

     Recently I came across this article in Good Times -- a weekly newsletter from Santa Cruz County in California -- an article that features poet Gary Young and his two poet-sons -- one of whom (Cooper Young) chose to major in mathematics.  Quoting Cooper (from the Good Times article -- and referring to his father):

“He didn’t push poetry on me at all,” says Cooper, who recently graduated from Princeton University. “As I was growing up, poetry was always Jake’s interest. I was more of a science/math kind of guy. Then college came around and freshman year, I was looking for a fifth class. I figured I ought to know a little bit about what my father and my brother had dedicated their lives to. So I enrolled in a poetry class. And I really dug it.”

The poetry that I have found by Cooper Young is not mathy -- but it has led me to look back to one of my favorite mathematical poems  -- "To Divine Proportion," by Spanish poet Rafael Alberti (1902-99); I offer it below.

Antiparticular . . . and so on . . .

     Writer and St Mary's University (in Halifax) mathematics professor Robert Dawson enjoys composing both poetry and fiction -- and his work has been included in a number of previous postings in this blog.  Recently he has published several poems in Polar Starlight, a new Canadian magazine of speculative poetry; the poem below, "Antiparticular" -- in which Dawson plays with the meaning of "anti" -- appeared in the June 2022 issue.  (All issues of Polar Starlight are available online at this link.)

         Antiparticular     by Robert Dawson

     Physicists have produced, for many a day,
     Anti-electrons, even antiprotons,
     But nobody has yet, to my dismay,
     Claimed the discovery of antiphotons.
     They move (in theory) at the speed of dark,
     They carry lethargy but have no mass.

Writing a Proof in Verse -- with ChatGPT3

     Academician Punya Mishra (from Arizona State) is active in integrating various topics and learning patterns.  Back in 2020, at this link I featured his poem, "The Mathematical i"  -- and Mishra has recently shared with me some of his explorations with poetry created by artificial intelligence.

     Back in 2010, Mishra wrote a fascinating poem (The Infinity of Primes")  -- a poem that is also a proof -- which begins with these stanzas:

     Over numbers and their combinations if you sit and mull
     You will find that not one of them is uninteresting and dull.
     But it is a certain class of figures that most attention stirs
     Yes, I am speaking of those special ones, the prime numbers.

     Prime numbers are interesting, the mathematician posits,
     ‘Cos they make up all the others, the so-called composites.
     Here’s an imperfect analogy, a simple little working rule,
     Consider the prime to be an atom, then a composite’s a molecule. 

                        . . .               Mishra's complete 17-stanza poem is available here.

Mishra recently explored the the ability of ChatGPT3 to create a proof of the infinity of the set of primes;  The stanzas below offer a start of a proof-attempt; its completion and two other attempts are available at this link.

Poetry found in Scrabblegrams

      Poetry is often shaped by constraints -- syllable counts, patterns of rhythm and rhyme, and others -- and a writing constraint that has come to my attention recently is the "Scrabblegram."  I learned of the Scrabblegram in a blog posting by Marian Christie -- it is a collection of words that uses each of the 100 Scrabble-tile (including the pair of blank tiles, identified as needed) exactly once.

     Christie's blog introduced me to the work of David Cohen who -- using the Twitter handle @dc_scrabblegram -- posts a Scrabblegram daily.  Here is a link to Cohen's website.  And here is a mathy Scrabblegram verse that he posted on Twitter on World Maths Day, March 8, 2023.

A Scrabblegram from David Cohen.

Here is a link to another of David Cohen's Scrabblegrams -- this one features PI (and is also offered as a comment to my March 6 posting).        And here is one about the Fibonacci sequence.               

March is Women's History Month

Learn the history of MATH-WOMEN!

     A recently-released poetry collection that I have been excited to acquire is Jessy Randall's collection,  Mathematics for Ladies:  Poems on Women in Science (London: Goldsmiths Press, 2022).  I first met Jessy Randall's poetry when her poem ‘Elizabeth Cabot Agassiz (1822–1907)’ was published in the August, 2021 issue of Scientific American.

     After a thoughtful "Foreword" by Pippa Goldschmidt, we find 68 poetic snapshots of math women --going back as far as the 12th century and continuing into the the present.  Here is a sample:

CHARLOTTE ANGAS SCOTT (1858-1931)    by Jessy Randall

          When I was at college for mathematics
          I attended Cambridge lectures

          from behind a screen, of course.
          So the male students couldn't see me.

          (I might have distracted them.)   

International Women's Day

     Today, March 8, is International Women's Day -- a day to pause, recognize, and celebrate the achievements and abilities of women (and their equality with men).

In my poetry-stanza below I celebrate Laura Church -- my high school math teacher (in Indiana, PA)  a bold spokesperson for math-for-all back in the 1950s  AND the woman who led me into mathematics.

       Chalk in hand,
       she tosses her book,
       strides across the room,
       excited by trigonometry,
       excited that we,
       restless in our rows,
       caught some of it.
       Flamboyant, silver,
       fearless woman.

The stanza above is part of "The Ones I Best Remember" -- the full poem is available here.

Recognition and celebration of women in mathematics has increased dramatically since my high school days.  On of the important advocates is the Association for Women in Mathematics, founded in 1971, and often mentioned in this blog.  Here is a link to a poem that celebrates AWM.

Celebrate Pi-Day

 3 . 1 4 1 5 9 2 6 5 3  .  .  . 

March 14  -- that is, Pi-Day -- will soon be here.  One of the ways of celebrating  π  is with dessert pastries (pies)  -- but a  π-day  greeting often takes on the challenge of a message in Pilish -- a language whose word-lengths follow the digits of  π -- a challenge that students often enjoy!   An example:

Hug a tree, I shout -- hungering to defend trees and  . . .

FREE MINDS write and share . . .

     Last weekend I attended a very special event at Live Garra Theatre in Silver Spring -- an event featuring poetry and drama from ascending citizens -- described in the image below.

Two organizations that endeavor to improve the lives of incarcerated and recently incarcerated persons are The Free Minds Book Club and Freedom Reads libraries. 

Is a proof the opposite of a poem?

      One of the valuable online sources from the MAA (Mathematical Association of America) is the Math Values blog -- found at this link -- a blog that explores COMMUNICATION, COMMUNITY, INCLUSIVITY, and TEACHING and LEARNING.  Using the SEARCH feature, I entered "poetry" and found this variety of resources -- including mention of the Steven Strogatz Prize for Math Communication -- SHARE YOUR LOVE OF MATH WITH THE WORLD -- a contest for high school students with deadline April 28, 2023.  Entry categories include Art, Audio, Performance, Social Media, Video, and Writing.  Guidelines are available here.

     Back in June, 2021 at this link I shared a portion of the poem by Julia Schanen that won in the Writing category that year.  It's second line is the title of this blog posting -- and the complete poem is available here.  A 2022 Strogatz winner was Wyeth Renwick -- and this blog posting features his poem.

     I close with two of my favorite lines of poetry:

        The Secret Sits     by Robert Frost (1874-1963)

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

Math-Poetry Word Cloud

      On this February Friday I became curious once-again about the frequency of various mathy-poetic words used here in my blog -- and I went to the website https://www.wordclouds.com to ask for a picture of my word-frequency.  Entering my blog-link (https://poetrywithmathematics.blogspot.com) led to the photo below:

Word Cloud for https://poetrywithmathematics.blogspot.com. 

So many of the words are too small to read -- "love" and "teachers" are two that I was delighted to be able to find.

A previous blog-work-cloud from several years ago is found at this link.

Celebrate Black Mathematicians

     In January, at the National Joint Mathematics Meetings in Boston, the National Association of  Mathematicians gave this year's Lifetime Achievement Award to Scott Williams, one of the organization's founders back in 1969.  NAM is  nonprofit professional organization in the mathematical sciences with membership open to all interested persons who support promoting excellence in the mathematical sciences for all Americans and promoting the mathematical development of all underrepresented American minorities, especially African Americans. (Learn more about NAM at this link.)

     My connection with Scott Williams began at a program at the headquarters of the MAA (Mathematical Association of America) in Washington, DC and it has continued because of the interest we share in poetry as well as mathematics.  Scott's Facebook postings often include poems -- and work by him is included in the latest issue of the Journal of Humanistic Mathematics --  about which I posted last week (at this link). 

More Math-Poetry from JHM

     Every six months a new issue of the open-access online publication, Journal of Humanistic Mathematics, becomes available.  And -- among lots of other inclusions -- it offers a rich variety of mathy poems.   Here is a link to the table of contents of the latest issue -- and I strongly suggest that you visit and explore.  Math-poetry items, listed at the bottom of the TC, are shown in the screen-shot below:

Happy Valentine's Day

      A perfect way for math-poetry fans to celebrate Valentine's Day is to visit the anthology, Strange Attractors: Poems of Love and Mathematics (AK Peters/CRC Pres, 2008), edited by Sarah Glaz and me.  Here is a sample from that collection, a limerick;

     There Was a Young Maiden    by Bob Kurosaka*

       There was a young maiden named Lizt
       Whose mouth had a funny half-twist.
            She'd turned both her lips
            Into Mobius strips . . .
        'Til she's kissed you, you haven't been kissed!

     *Of Japanese heritage, Kurosaka was born in Lake George, NW -- he became a college teacher and author of science fiction and limericks.

     Here is a link to previous Valentine-related postings:  
this link leads to blog-search results for "Strange Attractors."

The Power of Words -- from June Jordan

      One of the very special privileges that I had while taking classes  at Hunter College (1999-2001) was to attend a poetry reading by June Jordan (1936-2002) -- a reading that introduced me to the power of her fearless voice and the importance of her words.

     Jordan often uses repetition and the precision of numbers to  build  strength in her poems; here is a sample -- the opening lines of "The Bombing of Baghdad":

THE BOMBING OF BAGHDAD    

     began and did not terminate for 42 days
     and 42 nights relentless minute after minute
     more than 110,000 times
     ae bombed Iraq we bombed Baghdad
     we bombed Basra/we bombed military
     installations we bombed the National Museum
     we bombed schools we bombed air raid
     shelters we bombed water we bombed
     electricity we bombed hospitals we
     bombed streets we bombed highways
     we bombed everything that moved/we
     bombed everything that did no move we
     bombed Baghdad
     a city of 5.5 million human beings .  . .

The complete poem may be found here at poets.org.

At this link are numerous recordings of Jordan reading her poems.   Here is a link to an article by Hunter College professor Donna Masini, "Writing and Teaching in a Time of Crisis:  Lessons from June Jordan" -- and here is a link to previous mentions of Jordan and her work in this blog.

Remembering Linda Pastan

     On January 30, the wonderful and versatile poet, Linda Pastan (1932-2023) died.  Here at the Poetry Foundation website is a brief bio of Pastan along with ninety-six of her poems -- including the mathy poems "Arithmetic Lesson: Infinity" and "Counting Backwards".   This link leads to previous mentions of Pastan and her work in tis blog.  And below, one of my favorites of her poems, "Algebra" -- which I also posted at this link back in November, 2013.

Algebra     by Linda Pastan

        I used to solve equations easily.
        If train A left Sioux Falls
        at nine o'clock, traveling
        at a fixed rate,
        I knew when it would meet train B.
        Now I wonder if the trains will crash;
        or else I picture naked limbs
        through Pullman windows, each
        a small vignette of longing.   

Celebrate Groundhog Day!

      Since my days as a girl on a farm near the town of Indiana, Pennsylvania -- not far from Punxsutawney, Pennsylvania -- I have long been familiar with Groundhog Day.  Here is a link that you can use to browse this blog's celebrations and memories of  this special holiday.

Daughters Can Also Be Heroic . . .

     A recent online Cultural Collective article featured the Chinese astronomer -- and mathematician and poet -- Wang Zhenyi (1768-1797) in an article entitled, "The Woman Genius Who Surpassed Da Vinci and History Forgot."   Although her poetry was mentioned, no samples were included -- here is a link to a stanza of hers that I posted back in February 2021 (a stanza that includes the title of this posting).  

     A well-known Qing dynasty scholar, Yuan Mei, commented on Wang’s poetry by saying it “had the flavor of a great pen, not of a female poet.”  Her poetry included her understanding of classics and history and experiences during her travels -- items such as scenery and the lives of those with whom she made acquaintances.   Here is a sample -- one of several of Zhenyi's poetic stanzas in Wikipedia:

       Transiting Tong Pass      by Wang Zhenyi

            So important is the doorway,
            occupying the throat of the mountain
            Looking down from the heaven,
            The sun sees Yellow river streaming.

Remembering Charles Simic

       Recently Pulitzer Prize-winning poet and former US poet laureate (2007-2008) Charles Simic has died.  Although Simic's poems were seldom mathy, he spoke as mathematicians do -- with precision and purpose.  Below I offer again one of his poems that speaks of Euclid (previously posted back in 2011). 

       The Chair     by Charles Simic

       The chair was once a student of Euclid.

       The book of its laws lay on its seat.
       The schoolhouse windows were open,
       So the wind turned the pages
       Whispering the glorious proofs.

       The sun set over the golden roofs.
       Everywhere the shadows lengthened,
       But Euclid kept quiet about that.

"The Chair" is found in Simic's collection Hotel Imsomnia (HBJ, 1992).  This link leads to a list of previous blog postings that feature Simic.   Here is a link to poets.org that features lots of Simic's poems and here at poetryfoundation.org are lots more.

A mathy poem from artificial intelligence

     A recent Facebook posting by Maryland poet and computer programmer Henry Crawford included a poem written by a robot -- and he shared with me the link for BETA.OPENAI.COM -- a free site, but one requiring the opening of an account.  I did that -- and began to explore.  Here is a screenshot of one of the results -- from when I entered the request "Write a poem using math words".

A poem composed by AI

Lots of additional information about AI is available in a free article/editorial (about ChatGPT)  by Gizem Karaali entitled "Artificial Intelligence, Basic Skills, and Quantitative Literacy" -- available at this link.  And here is a link to an interesting and related article in the NY Times, "How Smart Are the Robots Getting?" 

Poetry in Politics

      Numerical or alphabetical constraints often are used by writers to add shape and impact to their writing -- and such was the case in a recent speech by Hakeem Jeffries, New York Congressman and Democratic leader of the House of Representatives as he spoke on January 7 ;  Jeffries' speech went through the alphabet -- poetically directing his colleagues toward American Values instead of Autocracy, Benevolence over Bigotry . . . . all the way to Zealous Representation over Zero Sum Confrontation.  A wonderful illustration of the value of constraints in shaping ideas!

Create an abecedarian poem of your own: 
perhaps for a Valentine --
or to celebrate the coming of spring!

Here is a link to previous instances of abecedarian in this blog -- and below is a sample, my  abecedarian portrait of a mathematician.

A Lecture on the Cube

     Summer weeks spent teaching English to Romanian students have helped me to learn of several of the country's fine poets and to get involved in a bit of translating.  Romanian mathematics professor, Gabriel Prajitura (now at SUNY Brockport) -- whom I first met at Pennsylvania's Bucknell University when I was teaching nearby at Bloomsburg University -- worked with me to translate several mathy poems by Nichita Stanescu (1933-1983).  The Summer/Autumn 2004 issue of Circumference:  Poetry in Translation included "A lecture on the cube" and "A lecture on the circle."  My blog posting on April 18, 2014 -- available at this link -- shares "A lecture on the circle" -- and I offer the other below:

     A lecture on the cube     by Nichita Stanescu

        You take a piece of stone,
        chisel it with blood,
        grind it with Homer’s eye,
        burnish it with beams
        until the cube comes out perfect.       

Mathematics Sets Sail . . .

     Each time I open a new issue of Scientific American I am delighted to turn to "Meter", a poetry feature begun in 2020 and edited by longtime science writer, Dava Sobel.  One of my early favorites in "Meter" (found here in the February, 2020 issue) is "Mathematical Glossolalia" by Jennifer Gresham -- and Gresham has given me permission to include the poem here:

     Mathematical Glossolalia     by Jennifer Gresham

     As though time could have a hobby
     we speak in eigenvalues, the harmonious
     oscillations in the green flash before sunset.

     We interpret raised to the power to mean
     you were taken in by numbers
     as a young babe & your childhood

     can be classified irrational. Euclid,
     Euler, the empty set's a nest atop a piling.
     If two words diverge on the open seas &

     the dot product is without derivative, the intercept
     can be found only by Venn diagrams on the tongue.
     Swallowed by wave functions, turning back, theorems

     to explain the circumference of illusion, good heavens,
     the sailboat's isosceles never goes slack.

Jen Gresham is founder of Work for Humanity; she has a PhD in biochemistry from the University of Maryland.  "Mathematical Glossolalia" is from her 2005 collection, Diary of a Cell, winner of the Steel Toe Books poetry prize, is available here.  At this link, a bit of background about the word "glossolalia".

Applied Mathematics -- in Spoken Word Poetry

     Lots of mathy poems are available on YouTube -- for example, recordings by poetry participants in Bridges Math-Arts conferences are available;  here is a link to a webpage (maintained by Sarah Glaz) for 2022 Bridges poets and poems .  Today I have been fascinated by and want to share some words from an Applied Mathematics YouTube video by spoken word poet Dan Simpson, a UK writer, performer, producer, and educator.  A few lines from the poem appear below, followed by a link to the video performance.

I love the curvature of your wave form the way you deviate from the norm .  . .  when we touch it's an electric storm . . .  if you were described by numbers they would all be trying this but like Heisenberg you're uncertain  . . .  this verse is in a language that you can understand bringing maths and poetry together in double helix sounds . . .  statistically speaking I'll make you laugh sooner or later . . .

     Dan Simpson's complete and very entertaining YouTube performance of Applied Mathematics is available here.  Other mentions in this blog of Dan's poem and other YouTube recordings may be found at this link.

AMS 2023 Math-Poetry Contest Winners

     This week, January 4-7, in Boston MA, more than a dozen national mathematics organizations are holding national meetings -- at a conference called the Joint Mathematics Meetings (JMM).  This gathering includes a math-art exhibit and the celebration of winning poems in an math-poetry contest for students (sponsored by AMS, the American Mathematical Society).  The picture below is a portion of a poster that celebrates and publicizes the winning poems,  (The complete poems are available here at the AMS website.)

This is the top section of a poster of AMS 2023 winning mathy poems.

Celebrate the life of John Sims

      These days I am celebrating the life -- and mourning the passage -- of mathy-artist-writer and fighter for human rights, John Sims, who died last month of a heart attack at the young age of 54.  Here are three of the many headlines (with links to articles) that celebrate his life and mourn his death.  (I encourage readers also to search online for "John Sims" to learn more about his many, many ventures and achievements.}

From the Sarasota Herald-Tribune, John Sims, Sarasota-based conceptual artist and former Ringling professor, dies at 54

From ArtReview, John Sims, artist who confronted American racism has died

From Sarasota Magazine, Remembering Sarasota Artist John Sims  . . . "Sims, who died earlier this week, spent decades producing provocative art that touched on racism, mathematics and much more . . ."

From WUSF Public Media, John Sims, prominent Sarasota artist and former Ringling instructor, dies at 54

I first met John Sims early in 2010 at the Bowery Poetry Club in New York City.  He was poet-in-residence there and had invited mathy poets and artists to participate in a Sims project called  "Rhythm of Structure."   A booklet featuring exhibit items -- with a varied selection of poetry and art, by Sims and others (including a poem by me) -- is available online here.  Here is the cover with images of visual poetry by Sims.    

Ending the Year with Gratitude -- for Teachers!

     During his time as Poet Laureate of the United States, Billy Collins created Poetry 180 -- a project designed to encourage students to engage with poetry but providing a poem (accessible for high school students) for each of the 180 days of the school year.  Each week in my email, I get a message with links to five of these poems; one of the recent ones (poem 72, given below) has reminded me about the importance of teachers in my life -- teachers of poetry AND teachers of mathematics -- in shaping my learning and my personhood.   Here is  "Gratitude to Old Teachers" by Robert Bly:

   Poem 072: Gratitude to Old Teachers    by Robert Bly

          When we stride or stroll across the frozen lake,
          We place our feet where they have never been.
          We walk upon the unwalked. But we are uneasy.
          Who is down there but our old teachers?

          Water that once could take no human weight—
          We were students then—holds up our feet,
          And goes on ahead of us for a mile.
          Beneath us the teachers, and around us the stillness.

Bly's poem is from his collection, Eating the Honey of Words, (HarperCollins, NY, 1999).  Its presentation in Poetry 180 may be found at this link. 

Here is a link to previous mentions of "Poetry 180" in this blog.

A Cone with a Sphere on top

      The phrase used as title for this post, "A cone with a sphere on top" -- from a slightly-mathy poem by Katharine O'Brien (1901-1986), "Einstein and the Ice Cream Cone" -- has caused me to visualize a Christmas tree and so, in this holiday season, I offer it to you.  Enjoy!  And Happy Holidays!

     Einstein and the Ice Cream Cone     by Katharine O'Brien

     His first day at Princeton, the legend goes,
     he went for a stroll (in his rumpled clothes).
     He entered a coffee shop --- moment of doubt --
     then climbed on a stool and looked about.
     Beside him, a frosh, likewise strange and alone,
     consoling himself with an ice cream cone.   

Counting On . . .

     I was the oldest, the "responsible" one -- when I wanted to sleep in, my mother said, "Your father -- and our farm -- are counting on you."  Here is a bit of my poetic reaction:

     COUNTING ON

        One
        Two   two
        Three   three   three
        Four   four   four   four
        Five   five   five   five   five
        That's how it was growing --
        growing up
        on the farm
        milking cows
        gathering eggs
        scattering grains of corn
        for hens --
        counting   counting   counting . . .
        counting on.

Here is a link to several previous blog posts with poems related to COUNTING.

Patterns of the Wind

     Sometimes a poem contains just a sample of mathematics -- but a very memorable one.   Such is the case with "I Like the Wind" by Robert Wrigley in the 6 September 2010 issue of The New Yorker.  I offer below its opening lines.

       We are at or near that approximate line
       where a stiff breeze becomes
       or lapses from a considerable wind,
       and I like it here, the chimney smokes
       right-angled from west to east but still
       for brief intact stretches
       the plush animal tails of their fires. 

  (The poem continues here for 34 more lines.)

Short Poems

         Poetry, like mathematics, uses condensed language -- often saying quite a lot in just a few symbols.

          POEM     by Aram Saroyan 

          One two
          three there
          are three are
          never seen
          again.                 (from Complete Minimal Poems, Ugly Duckling Press, 2007)

          REFLECTIONS ON AN AMISH CHILDHOOD    by Billy Collins 

          I was
          a little square
          in a round hat.              (from Musical Tables,  Random House, 2022)

This link leads to a previous blog posting with a short (14 syllables) poem of mine AND
with links to poems celebrating five female mathematicians.

Writing -- a Path toward Knowing

     Advice for my grandchildren -- in the form of a Fib.  (Wish I had remembered to give it on November 23 -- which is Fibonacci day. ) 

 

    1            When

    1            I

    2            want to

    3            understand

    5            something difficult

    8            I grab my pen, write about it.

     I'm not sure when I made the discovery but by the time I was in graduate school  I knew that my learning pattern involved my fingers and my pen.  I copied definitions into a notebook, sometimes trying to rephrase them in my own words.  I elaborated the proofs of theorems . . . my fingers helped me remember.

November 23 is celebrated as Fibonacci day because when the date is written in the mm/dd format (11/23), the digits in the date form a Fibonacci sequence: 1,1,2,3. A Fibonacci sequence is a series of numbers where a number is the sum of the two numbers before it.  A Fib is a tiny poem whose lines have as syllable-counts the first 6 Fibonacci numbers.  

For more Fibonacci-related poems, follow this link.