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.  

 

Some students regret their major

      An article by Andrew Van Dam in the Washington POST earlier this month (available at this link) asserts that nearly 2 in 5 American college graduates regret their choice of major . . .  many humanities majors wish they had focused more on STEM subjects while engineering majors were the group most fully satisfied.  The article has made me think back to my own college days when it was the availability of scholarships rather than love of the sciences that led me there.

From Washington POST "Department of Data" (at this link)

 

     My own view is that education in several fields is far more enriching than focus in a single field -- that the humanities or social science major who wishes she had studied calculus and non-Euclidean geometry and then goes on to do that brings better preparation to her later field of study.  She has knowledge and perspectives to enrich her study of mathematics!

     Consideration of study preferences has led my thoughts to an interesting pair of poems by Duke University Professor Henry Petroski -- poems found in the 1979 anthology of mathematical poetry, Against Infinity (Primary Press, 1979, Edited by Ernest Robson & Jet Wimp).  

Math-Poetry Recordings on YouTube

     The arrival in 2020 of COVID caused a huge number of gatherings to take place online -- including mathematics conferences and poetry readings- -- and performances at many of these special events have been recorded on YouTube.  I offer below a few links to recordings and to further information.  Recording myself reading poems would probably not been one of my chosen activities but mathematician-poet Sarah Glaz, who has been an enthusiastic organizer of poetry events for the BRIDGES Math-Arts Conferences, has requested recorded samples from each participating poet.

     One way to start YouTube math-poetry explorations is to go to this link -- a link I found by searching for "poetry math" on YouTube.  In this blog, we have mentioned YouTube a bit in the past -- and the blog's SEARCH feature finds this list of previous postings that feature YouTube links.

Arts-based Math Education -- Meet one of the Stars

     Through BRIDGES Math-Arts Conferences I have become acquainted with the versatile Canadian scholar, Susan Gerofsky -- and I introduce you to her varied achievements with this biographical sketch.

Susan Gerofsky is an Associate Professor of Mathematics Education and Environmental Education at the University of British Columbia, Vancouver, BC, Canada. Her interdisciplinary research in curriculum studies is in embodied mathematics education through the arts, movement, gesture and voice, and she is a regular contributor to Bridges Math and Art. She is active as a poet, playwright, musician and filmmaker, and works with dance and fibre arts. You'll often find her cycling around town with a baritone horn or an accordion.

Gerofsky has introduced me to the use of combinatorial patterns in bell-ringing in the structure of poems.  Here, for example, is her "Desert Poem" -- based on the pattern "Plain Hunt on Four" or PH4.

Math Poetry Contest for Massachusetts Students

      Middle school, high school and college students in Massachusetts are invited to submit MATH POETRY in a contest sponsored by the American Mathematical Society.  The submission deadline is November 11 -- and lots of background information and  details for submission are offered at this link.

  A pattern of yearly contests has been interrupted by COVID -- however, looking back, I find two of the winning poems in the 2020 contest posted here, and a poster of winners for the 2019 contest is shown at this link.

The Poetry of Mathematician George Boole

      One of the interesting poetry collections on my shelves is The Poetry of George Boole by Desmond MacHale (Logic Press, Ireland, 2020 -- and published in the USA for Logic Press by Lulu.com).  This is not simply a poetry collection -- but poetry with commentary.  MacHale includes more than seventy surviving poems by the Irish mathematician Boole (1815-1864) -- and he also discusses Boole's views of the connections between Science and the Arts with an initial chapter is entitled "Poetry and Mathematics."  

     It is quite appropriate that Boole should relate poetry to mathematics since he was, primarily, a mathematician; his Boolean algebra is basic to the design of digital computer circuits)   Boole's own poetry, however, found most of its inspiration outside of math.  Here is his Sonnet 20 (Sonnet to the Number Three); written in May 1846 and suggesting that belief in the religious Trinity is connected with our interpretation of space in three dimensions.

Enriching Poetry with Mathematical Ideas

     An important leader in the community of writers who link mathematics and poetry is Sarah Glaz -- a scholar who is not only a mathematician and poet but also an organizer, participant, publicist, and recorder for numerous math-poetry events.  Glaz is an emeritus professor of mathematics at the University of Connecticut and her UConn webpage is a vast source of mathematical and poetry treasures.

     I first came to know Sarah well as we worked together on an important project -- gathering poems for the anthology Strange Attractors:  Poems of Love and Mathematics (A K Peters / CRC Press, 2008).  A preview of this collection is available here.   Here, from that collection, is one of my favorites -- a thoughtful poem about parenting and attitudes (love? or not?) toward mathematics:

Love Story     by Sarah Glaz

       If I ever write about you--
       he said--
       it will be a love story
       a story about
       how much you want to be loved.

       Father, do you love
       your little girl?
       I brought you
       a soup full
       of numbers
       formulas chopped to perfection
       integrals fried to a crisp 

From a poetic artist -- "New Math"

     Neha Misra, one of my neighbors (in Eastern Village cohousing in Silver Spring, Maryland) is both a poet and a visual artist; in a recent conversation, I asked Neha if she had any mathy poems -- and she  volunteered the following lines-- full of rich mathematical terminology paired with multiple -- and thoughtful --  meanings.  Thank you, Neha!

New Math        by Neha Misra
 
Because I once scored 49 out of 50
in a Mathematical Physics exam
that I was so proud of, still am.
I do not remember much of
signs of sines and cosines.
I remember the differential equations
were all fine, but I was in love
with the curves of integration—
 
Because I once taught a scared young boy
in the confident body of a man
to not let his exponential fear of math
come in the way of his waking dreams
of flying with numbers.
Paper and pen in our hands,
together we melted his fear of math
into the heart of zero
and he flew     
far   far           far             away from me
on the infinite new wings of those numbers—  

Dangerous Surprises of Exponential Growth

      In 1968, while I was in graduate school at the University of Oklahoma, the journal Science published "The Tragedy of the Commons" by Garrett Hardin.  Hardin's article describes a situation in which shared resources are overused and exploited -- leading to depletion of resources for the future.  In recent years there has been much criticism of Hardin's essay (and criticism of Hardin) -- but for me it served as a wake-up call to concerns about the environment.  With environmental difficulties growing exponentially -- and with many of us not fully aware of the growing rapidity of exponential growth, I have posed to students this problem:

An 8x8 syllable-square

We may be close to the end before we realize it . . .

Mathematics -- not isolated STARS but COMMUNITY

     In his 1940 book-length essay, A Mathematician's Apology, eminent British mathematician G. H Hardy minimizes the importance of those who communicate mathematics to those outside the research community   ... the book's opening paragraph is show below . . . it concludes with "Exposition, criticism, appreciation. is work for second rate minds."

The complete essay is available online here

Remembering Life on the Farm

      I grew up on a farm in western Pennsylvania -- and I think that farm life (at least as my father practiced it) was a strong introduction to mathematics.  Counting, calculating, predicting -- and, most of all, problem-solving -- prepared me for studies and for a complex world.  Today is the anniversary of my parents' marriage -- on August 24, 1939 -- and an important occasion for looking back!

     Last weekend I visited the farm (Meadow Lane Farm, now a golf course) and my rememberings drew me to this years-ago poem (previously posted here)

"Things to Count On" was included in my chapbook collection, My Dance is Mathematics  -- now out of print but available online here.   AND here is link to the results of a blog search for farm.

Celebrate poet Rita Dove

      In the KIDSPOST section of this morning's Washington Post I learned that next Sunday, August 28, is the birthday of poet Rita Dove (b. 1952) and Saturday, August 27 is the birthday of mathematician Giuseppe Peano (1858-1932).  Dove (who served as US Poet Laureate 1993-95) is author of one of my favorite mathy poems -- a poem about the EXCITEMENT of learning mathematics -- and I offer it below: 

from The Yellow House on The Corner (Carnegie Mellon University Press, 1980)

     Work by Rita Dove has also appeared in earlier postings in this blog.  This link leads to the results of a blog-search using her name.

HER Math Story

    “Her Math Story” is a platform of three women mathematicians (Julia Kroos, Tamara Grossmann and Joana Grah) who want to empower young women through “stories and blog entries to pursue studies and careers in maths, spark their curiosity and transmit enthusiasm for technical subjects”, as described on their website.  The first outcome of their collaboration with “Her Math Story” (HMS) is this interview with Professor Shanti Venetiaan. 

I learned the information above from the European Women in Mathematics – The Netherlands (EWM-NL) website where I also found this poetic quote by mathematician Marta Pieropan:

          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.          

Find some time . . . visit the EWM website . . . read . . . and reflect!

Do more to fight injustice!

     In this 5 x 3 syllable-rectangle we have an important and poetic reminder from Martin Luther King, Jr. (1929-1968); let us remember and act on his words:

                “Injustice
                  anywhere
                  is a threat
                  to justice
                  everywhere.”

 I have a dream . . .

Journal of Humanistic Mathematics -- latest issue

     Every six months a wonderful treasure appears in my email-box -- an announcement, with links, to the latest issue of the Journal of Humanistic Mathematics.  Here is a link to the Table of Contents for this latest (July 2022) issue.

     Gathered and edited by Mark Huber (Claremont McKenna College) and Gizem Karaali (Pomona College) this open access journal contains a variety of articles and fiction and poetry.  With topics such as "Math in the Time of COVID" and "A Report about a Speaker Series Connecting Mathematics and Religion," the journal offers both depth and variety as its contents explore the humanistic aspects of mathematics.  Following more than twenty articles, we come to these poems:

BRIDGES Conference 2022 -- Math-Poetry

      A couple of months ago (here in my June 8 posting) I offered a link to information about poetry to be offered at the 2022 Bridges Math-Arts Conference -- held last week in Finland.  This link leads to a series of YouTube recordings of Bridges mathy poems and this link (at the website of organizer Sarah Glaz) offers written information about Bridges poets as well as sample poems.  Visit, read and listen, learn, enjoy!

     One of my poems that is included on the Bridges poetry site is entitled "Three-fold Asylum" -- a poem that explores various roles of the number three.  I offer it below:

     Three-fold Asylum     by JoAnne Growney

     Third door left on level three, my room
     holds steel furniture—its items three:
     double platform bed (for dreamless sleep),

     square corner desk with three-castered chair
     that spins, loops, and glides from the barred door
     to the dark window that sees nowhere.

Looking back to an old poem -- "Expectations"

      Years ago I wrote this poem -- recently I have rediscovered it and, once again, pondered the role of time in my life.  Here, from the 1980's is "Expectations" -- a poem that appears in my collection, Intersections (Kadet Press, 1993).

     Expectations     by JoAnne Growney

          Don't let mathematics
          teach you to expect two
          to be more than one.

          It's sad but true that two
          can get too near,
          can interfere,
          can reduce each other
          to less than one,
          to less than half.    

Einstein Defining Special Relativity

     Today I share a poem by poet A. Van Jordan that takes math-science terminology and mixes it into personal situations -- and offers varied ideas to consider.  Born in Ohio, Van Jordan became interested in poetry while studying for a masters degree at Howard University and attending readings in Washington, DC.  

Einstein Defining Special Relativity     by A. Van Jordan

INSERT SHOT: Einstein’s notebook 1905—DAY 1: a theory that is based on two postulates (a) that the speed of light in all inertial frames is constant, independent of the source or observer. As in, the speed of light emitted from the truth is the same as that of a lie coming from the lamp of a face aglow with trust, and (b) the laws of physics are not changed in all inertial systems, which leads to the equivalence of mass and energy and of change in mass, dimension, and time; with increased velocity, space is compressed in the direction of the motion and time slows down. As when I look at Mileva, it’s as if I’ve been in a space ship traveling as close to the speed of light as possible, and when I return, years later, I’m younger than when I began the journey, but she’s grown older, less patient. Even a small amount of mass can be converted into enormous amounts of energy: I’ll whisper her name in her ear, and the blood flows like a mallet running across vibes. But another woman shoots me a flirting glance, and what was inseparable is now cleaved in two.

The poem above was found here at poets.org along with other samples of Van Jordan's work.  His poem "Quantum Lyrics" was included in this blog (at this link) back in February 2019.

Worried about Climate Change

     When working with students in poetry workshops I often ask them to write to satisfy a constraint -- perhaps a Fib or a square poem -- in order to help them focus their thoughts.  This morning -- in the middle of a heat wave -- I focused my thoughts squarely on my growing concerns about climate.

       Steamy weather.  I count
       the degrees.  I count on
       air conditioning.  But
       my cooling system adds
       to global warming.  What
       is the right thing to do?

 Here is a link to previous postings in this blog that offer climate concerns.

Amelia Earhart -- a brave and pioneering woman!

      Growing up on a farm in Western Pennsylvania, one of my heroes was Amelia Earhart (1897-1937) -- a brave and talented female who died too soon.  Fearlessly Earhart broke barriers for all women and my admiration for her led to the following poem (which is a tiny bit mathy -- since it contains several numbers).  The 125th anniversary of Earhart's birth occurs soon -- on July 24, 2022 -- and lots of years ago after reading about her life I wrote these lines to celebrate my appreciation for this remarkable woman.

Lost Star     by JoAnne Growney

Somewhere in Kansas,
seven years old,
belly slamming on ice --
a close call.

Set for collision
with a horse and cart,
that girl put down her head
and slid between the horse's legs.   

Poems with multiple choices of what to read . . .

      When you pick up something to read -- a newspaper article, instructions for a new appliance, or a poem, or whatever  -- in what order do you read it?  For many of us, reading is not a beginning-to-end process but a jumping around in which we survey the scope of what's to be read, look for internal highlights, focus on particular terms, etc.  A fascinating exploration of multiple ways of reading a particular poem is a treasure I have found in a blog that I visit often, Poetry and Mathematics by Marian Christie.

      Born in Zimbabwe and now living in the UK, mathy poet Marian Christie offers a delightful and informative blog that thoughtfully explores various ways in which the arts of mathematics and poetry are linked.  In this January, 2022 blog posting Christie examines what she calls a "multiple choice" poem -- that is a poem that offers multiple ways of reading what the page presents. The poem she considers is one written in 1597 by Henry Lok in honor of Elizabeth I; below I offer a diagram of that poem, copied from Christie's blog.

CoronaVirus Fibs

     The threats of the coronavirus seem less now, but are not gone.  And, as I go through files, I have found these Fibs -- expressing concerns from worried days.

Lots of previous blog postings with Fibs can be found at this link.

Poetry and the Fields Medal

     It has been exciting to learn that a woman -- Maryna Viazovska of Ukraine -- has won a Fields Medal (often called "the Nobel prize of mathematics"); Viazovska is one of four persons who have been recognized (announced on June 5) for her outstanding contributions to mathematics.  Fields medals were first awarded in 1936 and are awarded every four years to up to four mathematicians under the age of forty.  The only other female mathematician who has received this award was Maryam Mirzakhani in 2014.

One of my syllable-squares

     Also of much interest to me concerning this year's Fields Medal winners is that one of them, June Huh, was in high school interested in becoming a poet -- and dropped out of school to pursue that goal.  Later, however, in his university years, Huh began to see his future in mathematics.

Still Life with Mathematics

   The title of this blog post, "Still Life with Mathematics" is also the title of a mixed media artwork by Pacific Lutheran University math professor Jessica Sklar and displayed in Mathematical Art Galleries for the 2022 Joint Mathematics Meetings.  Included in the art (which Sklar describes as a tribute to her dissertation advisor and to mathematics) is Sklar's poem, "Disciple" -- first published here in the Journal of Humanistic Mathematics in 2017 and offered below;  Sklar describes it as "a love poem for mathematics."

     Disciple     by Jessica K. Sklar

     And when they ask why I love you,
     I divulge: in your universe,
     normality is special, naturality
     is contrived, fields can be infinite
     and singularities are as commonplace
     as odd primes.    

Learning from Poetry -- "The Courtesy of the Blind"

      Can difficulty with understanding mathematics be compared with physical blindness -- a difficulty that is biological rather than chosen?  This is a question that has come to my mind as a reaction to Wislawa Szymborska's poem (offered below) "The Courtesy of the Blind."  This Szymborska poem is part of a wonderful online collections of poetry, Poetry 180, a poem for each day of the 180-day public school year.  

Poem 119: The Courtesy of the Blind     by Wislawa Szymborska

Polish poet Wisława Szymborska (1923-2012)
was the 1996 recipient of the Nobel Prize in Literature
and the author of over 20 volumes of poetry.

     The poet reads his lines to the blind.
     He hadn’t guessed that it would be so hard.
     His voice trembles.
     His hands shake.

     He senses that every sentence
     is put to the test of darkness.
     He must muddle through alone,
     without colors or lights.

Remembering Alan Turing

      A posting from Mathigon on Twitter reminded me that today is the birthday of pioneering computer scientist Alan Turing (1912-1954); a bio of Turing may be found here at Mathigon.  This link leads to several poems that celebrate Turing . . .

           Do machines think?

                    Do we?

More about Turing's life and career may be found here.

Mathy Poems on YouTube

      In a recent posting -- 6/08/2022 -- I tell of mathematician-poet Sarah Glaz and link to her website that has a collection of links to works by various mathy poets that have participated in BRIDGES math-arts conferences.  Glaz not only offers connections to poet-information, she also offers links to YouTube recordings of poems -- and recently, to supply her with that, I worked with my granddaughter, Serena Growney, who has just finished her freshman year at high school and knows a lot more about using YouTube than I do.  Here's a link to our Growney-Growney YouTube collaboration.  (I had intended for Serena to focus on the book cover and not to catch my elbow, etc, in the background -- but perhaps all of that makes it more interesting.)  For viewers who like to see the text of a poem as well as to hear it, here is a link to a blog posting of "Things to Count On" -- and below I offer the text of the poem (a very new one), "A Tragic Mathematical Romance."

A Tragic Mathematical Romance        by JoAnne Growney

     Abscissa, my darling, what is the
     basis for your discontent?  When I
     calculate the
     distance between us, I
     even have trouble seeing it as
     finite – its growth has a steep
     graph, climbing out of my

Word-Play with Mathematics -- On-Stage

      One of the rewards from time spent with mathematics or from time spent with poetry is the array of multiple meanings that we find . . . usually not all-at-once but accumulating.  A master of word-play with mathematical terms and ideas is Mathematics Professor Colin Adams of Williams College.  Each time I attend the annual Joint Mathematics Meetings I look on the schedule for Mathematically Bent Theater -- with a presentation by Adams and the Mobiusbandaid Players. Here is a link to an interview with Adams; and here on YouTube are videos of some of the mathy presentations; EXPLORE and ENJOY!

To add a bit of poetry to this post, I offer below a photo of a visual poem by scientist and writer Bern Porter, found in the anthology Against Infinity.

"Formula" -- by Bern Porter

Against Infinity is an anthology of mathy poems edited by Ernest Robson and Jet Wimp and published by Primary Press in 1979 -- now out of print but available at used-book websites.  Here is a link to other selections from Against Infinity in earlier postings in this blog.

The Windmill Proof

      From Alice Major, Canadian poet and first Poet Laureate of the city of Edmonton, Alberta, I learned of Welsh computer science professor emeritus Stephen Payne's new poetry collection, The Windmill Proof.   Here is a sample poem by Payne which appears on the book's back cover. 

Learn more here about Stephen Payne; The Windmill Proof was published by HappenStance Press -- and is available for purchase at this link.  Here is a link to a review by Mat Riches and this link leads to a review by Adele Ward;  both reviews contains samples of mathy poems.

Many, many mathy poems -- THANK YOU, Sarah Glaz

      Sarah Glaz, mathematics professor emerita at the University of Connecticut, is also a poet.  AND, not only a poet but a coordinator of math-poetry activities for the annual BRIDGES Math-Arts conference.  This year's conference will be held in Finland, August 1-5, 2022.  This link leads to Glaz' announcement of the poetry program at BRIDGES 2022 -- and includes bios and sample poems by poets who plan to attend the conference AND also includes samples of work from some of us poets who have been part of BRIDGES in the past but will be unable to attend this year.  Below are the opening lines from a poem by Glaz that is inspired by the mathematical field of Ring Theory.

The entire poem is available via Glaz's profile at this link.

Work by Sarah Glaz has been featured in a variety of previous posts in this blog.  Here is a link.

The Mobius Strip -- in a LIMERICK

     Mathematics offers brief, condensed language for many big ideas.  Even for small problems -- such as the word problems of a beginning algebra class -- translation of the words into a mathematical equation offers the chance to express the problem precisely and to solve it using established procedures.    

     And brief mathematical forms also are popular in poetry -- the six-line Fib and the five-line rhyming stanza called a limerick both have wide appeal.  And, because of the brevity, the language must be concise.  At this webpage, maintained by Joachim Verhagen, are lots and lots of mathy limericks.  Here is a sample:

          The Moebius strip is a pain,
          When you cut it again and again,
               But if you should wedge
              A large disk round the edge
          Then you just get a PROjective plane.

This link leads to an interesting article about a Mobius strip made of light (see also the photo below); this link leads to a Wikipedia article about a real projective plane.  And more of Verhagen's Mobius strip limericks may be found here.  

A Mobius strip from this NOVA article

This link leads to a website with instruction for construction and playful activities with a Mobius strip.  To enjoy limericks found in earlier postings in this blog, follow this link.

All truths wait in all things . . .

       Tomorrow, May 31, is the 130th anniversary of the birth of American poet, Walt Whitman.  Below I include a few Whitman lines (with the mathy terms "logic" and "proves") that offer food for thought.

The rest of this poem and lots more by Whitman are found here at poets.org.

 Whitman's complete Song of Myself (52 poems) is available at this link.

A SEARCH using Whitman will lead to more of his work in in this blog.

Mathematics might be dangerous!

       Censorship of Math Texts: A Syllable-Square with Questions
    
       Florida educators have banned
       Lots of mathematics texts because
       The books’ problems-to-solve include some
       REAL problems – bias and racism!
       Are the banners blind to their bias?
       Do they fear exposure and critique?
       Do they worry that knowing the need
       for drastic changes may open doors
       to fair, equal treatment of us all?

Here is a link to a news article about the Florida censorship -- written by Moriah Balingit, from 5/9/2022 in the The Washington Post.

Crisscrossing Infinity

     Poet and painter and literary theorist Paul Hartal was born in Hungary, with higher-education experiences in Israel and the U.S. -- and is now a long-term Canadian.  Recently Hartal contacted me to share a couple of his poems that involved mathematical topics -- and I offer one of these below, "Crisscrossing Infinity." Hartal's poem refers to a war memorial constructed using the pattern that first appeared in the sculpture "Endless Column" by Romanian artist Constantin Brancusi (1876-1957) and is on display at New York's MA, Museum of Modern Art.

       Crisscrossing Infinity       by Paul Hartal

       In the city of Targu Jiu, Romania,
       an abstract sculpture rises
       30 meters high.
       It is made of 15 zinc and cast iron
       rhomboidal modules
       (plus a half unit).

Math-Poetry -- when distinct worlds collide . . .

     Carol Dorf has been a long-time leader in math poetry projects.  A now-retired secondary school math teacher from California, Carol is the poetry editor of  the online journal Talking Writing -- an online journal that has included a variety of mathy poems.   Recently, at the Joint Mathematics Meetings, Carol gave a presentation entitled "Poetry of Mathematical Definitions" -- the abstract for this talk begins with this provocative sentence:

Mathematical poetry begins when worlds we consider distinct collide.

Carol's poetry-editorship for Talking Writing has led to many math-related poems being published therein.  Here is a link to those poems and a bit of other math-related content;  the following list includes names of writers whose work has been included there:  Robin Chapman,    Marion Deutsche Cohen,    Allison Hedge Coke,    Mary Cresswell,    Catherine Daly,    Carol Dorf,    Iris Jamahl Dunkle,    Sarah Glaz,    JoAnne Growney,    Athena Kildegaard,    Larry Lesser,      Elizabeth Langosy , Marco Maisto,    Alice Major,    Katie Manning,    Daniel May,    David Morimoto,    Giavanna Munafo,    Karen Ohlson,    Eveline Pye,    Stephanie Strickland,    Amy Uyematsu,    Sue Brannan Walker,    and Jean Wolff.  Some of the poets have been featured more than once and to find all work by a particular author, SEARCH is recommended.

And here, from Talking Writing,  is one of Carol Dorf's fascinating poems:

       Lost Information     by Carol Dorf

       Visualize groups: there’s the babysitting co-op,
       with slips of scrip the children color during
       quarterly potlucks; and more than enough churches
       each with study evenings, and fundraising committees;