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. 

All Together -- Humor, Math, Poetry

     Blogger and teacher Sue VanHattum (blogger at Math Mama Writes) has been a frequent and valuable contributor to this blog -- find stuff at this link -- and Sue has recently alerted me to a poetic posting that she found on Facebook -- written and drawn by artist-illustrator (and orthodontist) Grant Snider whose pithy and entertaining words and pictures are found at the website Incidental Comics.  Here is the opening portion of that visual-comic-poetic posting:

Opening lines of a visual poem by Grant Snider

Snider's complete "How To Be a Triangle" is found in Incidental Comics at this link.  Another recent posting -- "How to be a circle" -- is found at this link.

Poetry of Mathematics--David Eugene Smith, 1926

      Recently poetry-fan and occasional versifier Greg Coxson, a Research Engineer in the Department  Electrical and Computer Engineering at the US Naval Academy, sent me a link to an essay by mathematician and teacher David Eugene Smith (1869-1944) -- published in The Mathematics Teacher in 1926 and entitled THE POETRY OF MATHEMATICS.  Greg has been, over the years of this blog, a valuable contributor of information about mathy poems and poets -- and some poetry of his own.

     Early in the essay, Smith quotes Thoreau:

We have heard much about the poetry of mathematics, but very little of it has yet been sung.  The ancients had a juster notion of their poetic value than we.  The most distinct and beautiful statements of any truth must take at last the mathematical form. 

     Lots of quotes and viewpoints are offered in Smith's essay and, at the end he speaks of the role of teachers " . . .  mathematics may become and does become poetry in the enthusiasm of an inspired and an inspiring teacher."

The Secret Sits     by Robert Frost (1874-1963)

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

Lots more of Frost's words are available here.

The Geometry of Gerrymandering

gerrymandering: the practice of dividing or arranging 
a territorial unit into election districts in a way 
that gives one political party an unfair advantage in elections

       A recent Scientific American article by Manon Bischoff, "Geometry Reveals the Tricks Behind Gerrymandering," has reminded me of the horrors of this practice.  To express my thoughts about a particular concept, often a stanza that matches mathematical constraints helps me to carefully consider word choices and attempt clear and concise expression. The following syllable-square is a start toward expressing my point of view:

          For fair elections
          voting districts must
          be proportional,
          not maneuvered by
          gerrymandering.

This Scientific American author Manon Bischoff is an editor at Spektrum der Wissenschaft. She primarily covers mathematics and computer science and writes the column The Fabulous World of Mathematics. Bischoff studied physics at Technical University of Darmstadt in Germany and then worked as a research assistant at Johannes Gutenberg University Mainz in Germany.

Trying a Tritina

      Writer and scholar Marian Christie (born in Zimbabwe and now in Kent, England) has had a long term interest in mathematics and poetry and, during the last several years, she has created a blog -- Poetry and Mathematics -- in which she explores, with careful detail, some interesting and important links between these two arts.

     Christie's work has been featured several times in this blog and my posting today shows my attempt to learn from one of her postings.  At this link, on July 13, 2022, Christie posted "Turning in Circles -- the Tritina" and I have used her posting to learn the requirements for a tritina and, then, to try to write one.

     A tritina consists of ten lines -- three three-line stanzas with a final, separate line.  The stanzas have the same three end-words, rotated in the sequence 123, 312, 231, and a single final line containing all three end-words. 

     I have tried to write a tritina and offer my example below -- not because it is good but because it explores a pattern that I think might work well for students trying to write a poem in a math class.     

ARE THINGS DIFFERENT NOW IN SCHOOL?     a sample tritina     

Student Essay Contest -- Write about a Math-Woman

 Essay Contest -- Sponsored by AWM and Math for America

     Each year the Association for Women in Mathematics (AWM) and Math for America  co-sponsor a contest for essays written about the lives and works of contemporary women mathematicians and statisticians in academic, industrial, and government careers. 

     Each essay should be based primarily on an interview with a woman currently working in or retired from a mathematical sciences career. Participation is open to three groups -- middle school, high school, and undergraduate students.  Submissions open December 1 and continue to February 1, 2023.  Complete submission information may be found at this link.   (AND, 2022 winning essays may be found here.)

     I close with a poem about a math-woman -- "San Antonio, January, 1993" -- a poem inspired by my time at a long-ago mathematics conference and included in a chapbook of my mathy poems, My Dance is Mathematics (available at this link). 

Who is the GOD of ARITHMETIC?

     Recently I have learned (from poet and Capillano University professor Lisa Lajeunesse -- who enjoys linking mathematics and the arts) of the work of Canadian poet Lorna Crozier.  Author of more than a dozen poetry collections and recipient of five honorary degrees, Crozier is versatile and widely read.   Here is one of her fascinating poems:

     God of ARITHMETIC      by Lorna Crozier

     Most children no longer know who this god is. For one thing,
     he uses chalk as if time does everything but erase. In aban-
     doned country schools, he prints columns of numbers on the
     blackboards. There are no pupils to add them up and call
     out the answers though his pockets burn with stars to give
     away. His worshippers, in danger of dying out, recite the
     time tables like Hail Marys under their breath to prove their
     minds are still okay. No matter what they’ve lost—the word
     geranium, the birthdates of their children—they can do their
     sums. He wanted his only commandment to be included on
     the tablets Moses brought down from the mountain, but the
     others, bartering for space, thought it was only about arithme-
     tic and left it out. It would have changed the world. It would
     have made us kinder. Thou shalt carry the one, he intones to
     the small desks in empty classrooms, carry the one.

Copyright © Lorna Crozier. Originally published in God of Shadows (McClelland & Stewart/Random House, 2018). 

One Idea May Hide Another . . .

     One of the excitements I find in both mathematics and poetry is the continuing discovery of new meaning.  A first reading discovers something but subsequent readings discover more and more.  A poem by Kenneth Koch (1925-2002), "One Train May Hide Another," opens with "In a poem, one line may hide another line" -- focusing also on the idea that one thought may obscure another.

     Koch's poem is one that I first met lots of years ago when I was working with middle school students in a poetry class at a newly established Children's Museum in Bloomsburg, Pennsylvania.  At the time, the poem excited me by bringing back memories of traveling through western Pennsylvania as a child when my parents' car often needed to obey flashing red lights and stop while a train crossed our highway.  And sometimes there were parallel sets of tracks and the possibility that two trains might be passing our intersection in opposite directions at the same time. 

     I offer below the opening lines of the poem and a link to the complete poem; I post it with the hope that you also will enjoy it -- and will reflect on the ways that (in mathematics and elsewhere) one idea may hide -- or lead to -- another.   

How we learn Mathematics

      Recently I came across an interesting article about how we learn mathematics by Shaneen Suhail (a Masters student at JK Institute of Mathematical Sciences, Srinagar, India) -- and published online here in Kashmir Reader.   Suhail's thoughtful comments offer many ideas for teachers and students to consider -- and they include comparison of mathematics to poetry!

Like poetry, "mathematics says a lot with a little".  

The Secret Sits     by Robert Frost (1874-1963)

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

Lots more of Frost's words are available here.

Struggling to create -- slave and master . . .

      In the sonnet below, Edwin Arlington Robinson (1869-1935) speaks of the enslavement of a writer of poetry in the effort to explain ideas in a perfect form . . . an enslavement perhaps (or not) also shared by mathematicians.     Food for thought!

       SONNET     by Edward Arlington Robinson

       The master and the slave go hand in hand,
       Though touch be lost.  The poet is a slave,
       And there be kings do sorrowfully crave
       The joyance that a scullion may command.
       But, ah, the sonnet-slave must understand
       The mission of his bondage, or the grave
       May clasp his bones, or ever he shall save,
       The perfect word that is the poet's wand.

       The sonnet is a crown, whereof the rhymes
       Are for Thought's purest god the jewel-stones;
       But shapes and echoes that are never done
       Will haunt the workshop, as regret sometimes
       Will bring with human yearning to sad thrones
       The crash of battles that are never won.

From Robinson's COLLECTED POEMS:  THE CHILDREN OF THE NIGHT, CAPTAIN CRAIG (Macmillan, New York, 1915)

Struggling -- and then, after a while, Knowing

      Most of my experiences with solving mathematical problems have been challenging at first -- but often, after I explore and collect my thoughts, a pattern emerges.  The notion of "difficult at first" is vividly expressed in the following poem (found in the anthology Against Infinity (edited by Ernest Robson and Jet Wimp, now available at various used-book sites).

Geometry Test     by Larry Rubin

Thirty minutes, we had, to prove the theorem.
For twenty I sat staring at circles,
My inner angles frozen
When nothing came out equal.
The bisectors I drew were tilted wrong
While fear of the circular face of time
Stiffened my blood like clock-hands
Tracing arcs I never knew existed.
Suddenly that curve stretched perpendicular --
Longer that my longest transverse line --
Reaching beyond the limits of the page;
And the tallest segments of the intersected cone
Slit the seal of infinity.

My mind was washed like windshields after rain
And circles glided smoothly into place,
The arcs connecting in their shrunken frames,
I left that room, all theorems proved.

Halloween Counting Rhymes

 Here are links to a pair of fun counting rhymes:

"Five Little Pumpkins"

"Three Little Witches"

In Praise of the Irrational

     Japanese-American poet and retired math teacher Amy Uyematsu recently has published a new poetry collection, That Blue Trickster Time (What Books Press, 2022) and she has given me permission to share this fascinating mathy poem -- which vividly links the mathematical with the personal --  from that collection.

   In Praise of the Irrational     by Amy Uyematsu

        :  Kanpai (that's Japanese for “cheers”)

       Hooray for the illogical,
       this tale of built-in contradictions,
       each perilous paradox that can
       drive us bananas – and the curious
       ways we keep the faith.

       There's a logic to zero –
       ask any mathematician, poet or priest -
       but don’t expect them
       to explain.

       There's a profound dependability
       in the irrational instincts
       of women – yes us – all
       tenderness, guts, and a fierceness
       no man will ever fathom.  

Remote Schooling has hurt Math Learning

 Is it true that in any sequence
of thirty words in The Washington Post
at least two of the words will start with the same letter?

      Today's Washington Post has a story about recent declines in learning-assessment scores, especially in math -- both morale and persistence fell as students were remote from the watchful encouragement of in-person teachers.  

     Back in this blog posting in January, 2011, I offered poetic views of four of my important teachers.  Here is a repeat of one of those -- its lines remember Dr. Miriam C. Ayer  (d.1972), one of my mathematics professors at the University of Oklahoma in the late 1960s.  Even though I found it hard to like Ayer, I learned a great deal from her "Introduction to Topology" class.

     Nervous in class and tough
     to follow—she made errors
     on the blackboard yet demanded
     we write perfect mathematics
     in perfect English sentences. This was not
     an East Coast finishing school, and I hoped
     she’d be lenient with the Asian students
     even as fear made me work infinitely hard
     on papers that she gave back bright
     with red-ink from her difficult hand.
     No one before or since has read my words
     so carefully.

Communicating Mathematics with Poetry

     Each year MoMath (The National Museum of Mathematics) sponsors The Steven H. Strogatz Prize for Math Communication -- a contest for high school students; guidelines for next year's contest (deadline:  April 28, 2023) are available here.

      The 2022 Strogatz Prize winners include a poem -- "a proof of the function me" -- by Wyeth Renwick; here are its opening lines.

a proof of the function me     by Wyeth Renwick

          step one.
   find u.

          step two.
   add u to me and watch how the whole graph shifts upwards
   to make a u sized space where before it was only me
   until we're floating above the x-axis, u + me, an infinite
   line that stretches on past billions of little boxes
   on this graph paper grid.  let yourself think
   that maybe, just maybe, we were made for this - let yourself
   solve for the limits of the function and find that
   u + me approaches infinity.

          step three.
   square it all, square everything - make us into the parabola
   that my smile can't help but curve into when you pull
   our pinkies together and hold on real tight . . . 

 Renwick's complete poem is available here (click on poem-title).

The MoMath website offers these thoughtful comments about the poem:

     Wyeth Renwick’s poem is intriguingly ambiguous and open to interpretation: some of the judges read it as a love poem that winks at the reader with its use of mathematical concepts and language, while others saw it as a poetic animation of a human relationship, viewed as the graph of a function.  Either way, it makes math and poetry both seem more accessible to students who might otherwise not be drawn to these subjects.

Here is a link to previous postings in this blog that mention MoMath.

MacArthur Awards -- a Math-Woman, a Math-Poet

 SHE DOES MATH --

WE LIKE THAT! 

Recently the 2022 MacArthur Fellowship awards have been announced and the recipients include Melanie Matchett Wood of Harvard University, a a female mathematician who is a specialist in Number Theory and June Huh of Princeton University, a male mathematician who is credited with discovering underlying connections between disparate areas of mathematics and proving long-standing mathematical conjectures.  (This article about Huh tells of his high school ambition to be a poet BUT I have not been able to find online any of his poems.)

      While a high school student in Indianapolis,  Melanie Wood (then aged 16) became the first, and until 2004 the only female American to make the U.S. International Mathematical Olympiad Team, receiving silver medals in the 1998 and 1999 International Mathematical Olympiad.

     In honor of Melanie Matchett Wood and her work in Number Theory, here are the several lines from a poem on that topic by noted Czech mathematician Olga Taussky-Todd (1906-1995). (The complete poem is available here.)

          Number theory is like poetry
          they are both of the same kind
          they start a fire in your mind.
          Number theory is not just clever and smart
          it has a beauty that fills your heart.

Poetry and Mathematics -- Learning by Heart

     Many mathematical ideas are learned "by heart" -- that is, stored in  memory -- definitions, calculation, etc -- even for those who are not math-focused. 

      I grew up on a farm -- and, in addition to all of the learning opportunities related to farming, we had a book-case that included a set of Compton's encyclopedias, a collection of Aesop's Fables, and (my favorite treasure) Robert Louis Stevenson's A Child's Garden of Verses.   There are a number of these verses that I still know portions of "by heart" -- "My Shadow," "The Cow," "The Swing" -- and here is a two-line favorite:

       Happy Thought     by Robert Louis Stevenson (1850-1894)

       The world is so full of a number of things.
       I'm sure we should all be as happy as kings.

A Sonnet by William Rowan Hamilton

     Despite their similar lifespans, it is said that British mathematicians William Rowan Hamilton (1805-1865) and George Boole (1815-1864) had no significant interactions; however, both wrote poetry.  Back in my posting on 9/12/2022, I offered a sonnet by Boole.   Below, a sonnet by Hamilton -- found, along with a rich supply of poetry and science, at this MIT website.

A sonnet by William Rowan Hamilton

 

 

Math Jokes and Other Mathy Applications

     Each week I get an email from Feedspot that tells me of mathy blog postings that I may have missed and may be interested in.  One of the reminders that I particularly enjoyed today was to visit the blog of Boston Mathematician Tanya Khovanova;  the actual blogsite is at this link: Tanya Khovanova 's Math Blog.  Yesterday's posting involved some wordplay (math jokes); here are samples:

   I hate getting into debates about Möbius strips. They’re always one-sided.
        * * *
   4 out of 3 people have trouble with fractions.
        * * *
   Why was algebra so easy for the Romans? X was always 10.

When I visited Khovanova's blog, I searched for poetry -- one of my finds was a wedding poem composed by Gregory Adam Marton; here are its opening lines:

       In this summation, may there be no subtraction;
       May you multiply blissfully, and find no division;
       May the roots of the power of your love run deep;

 Marton's complete poem is available here.

Women in Mathematics -- Netherlands

      Below I offer a poetic quote from Marta Pieropan -- a faculty member at Utrecht University and a member of a European Women in Mathematics -- the Netherlands (EWM-NL), an activist organization supporting math-women.  They are involved, for example, in a Wikipedia Project and have developed a poster that celebrates math-women (and is available in several different languages, including English).

PROVING A THEOREM GIVES ME
THE SAME SATISFACTION
AS LAYING THE LAST TILE
OF A JIGSAW PUZZLE
THAT FINALLY REVEALS THE WHOLE PICTURE
AND HIGHLIGHTS THE RELATIONS
BETWEEN THE VARIOUS PARTS

Thank you, Marta Pieropan, for your poetic words (which I found here).

P.S.  Let us all remember that Tuesday, October 11, 2022 is this year's Ada Lovelace Day.  If you'd like to browse, here is a link to previous mentions of Ada Lovelace in this blog.

Is a poem like a theorem?

     Recently I have been musing over the question, "Is a poem like a theorem?"  Enriching my thinking has been a poem by Canadian-American poet Mark Strand (1934-2014), "The New Poetry Handbook."   I enjoyed the thought-stimulation that Strand's poem gave me and, as I read and reread, I explored changing the gender AND replacing "poem" by "theorem.  Not always perfectly sensible BUT thought-provoking!

Strand's complete poem of 21 stanzas is available at this link.