The Fruits of Undefinitions

     The poem "Undefined Terms" by poet-mathematician Katharine O'Brien (1901-1986) is a favorite of mine from long ago that I re-found recently here . . . for greatest enjoyment, read it aloud.

Undefined Terms     by Katharine O'Brien

A point is a point, a line is a line,
   a rose is a rose is a rose.
We thus undefine in the manner of Stein
   some terms in unrhyme and unprose.  

On these as foundation we lay definitions,
   the girders for walls and a roof.
We assume some conditions to fit requisitions
   and build us a logical proof.

Inauguration Day Poem

 Read by Youth Poet Laureate, Amanda Gorman,
an inspiring Biden-inauguration poem, "The Hill We Climb."

" . . . we lift our gaze, not to what stands between us,
                                               but to what stands before us . . ."

" . . . we will never again sow division . . ."

 

Remembering Martin Luther King, Jr

       Today as a nation we remember and pay tribute to Rev.  Martin Luther King, Jr. (1929-1968) -- Baptist minster, Civil Rights leader -- a brave man who was assassinated for his fearless and humanitarian views.  

Here are a few of his words.
 
          We must accept
          finite disappointment
          but never lose
          infinite hope.  
                                               Freedom is never
                                               voluntarily given
                                               by the oppressor;
                                               it must be demanded
                                               by the oppressed.

This link leads to previous posts in this blog that celebrate this hero. 

Bridges Math-Arts Conference 2021

Learn more here:  http://bridgesmathart.org/ 

Since 2009, interested contributors from mathematics and various arts -- poetry, music, theater, visual art . . . -- have gathered at an annual Bridges conference to celebrate and deepen math-art connections.  Due to Covid-19 the 2020 conference was virtual but so far, with hope, the 2021 conference is planned as an in-person conference in Finland.  Connecticut mathematician Sarah Glaz has been active in coordinating poetry events for the conference and here is a link to her announcement of the poetry program at Bridges 2021 -- including links to biographical sketches and poems by each participating poet.  My own poem therein honors mathematician Emmy Noether.

Here is a link to several postings in this blog that celebrate math women.

Number Personalities . . .

      Sometimes our experiences with objects or ideas leads us to assign them personalities -- a notion illustrated in the poem "Zero," by Sue Owen, a poem that lives on my shelf in the anthology Verse and Universe:  Poems about Science and Mathematics, edited by Kurt Brown (Milkweed Editions, 1998), and offered below.

Zero     by Sue Owen

       This is the story of zero,
       born to live a life
       of emptiness, only
       child of plus and minus.

       Its bones invisible
       so it could be seen through
       like an eye.
       With that vision, you could      

Poetic Mathy Quotes

      In India, National Mathematics Day is celebrated each year on December 22 -- the birthday of mathematician Srinivasa Ramanujan (1887-1920).  A couple of weeks ago, as this day was celebrated in India, a list of quotes about mathematics included the following:

Pure mathematics is, in its way, the poetry of logical ideas -- Albert Einstein

An equation means nothing to me unless it expresses a thought of God -- Srinivasa Ramanujan

Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers — Shakuntala Devi

Some mathematician, I believe, has said that true pleasure lies not in the discovery of truth, but in the search for it -- Leo Tolstoy

Math is fun. It teaches you life and death information like when you’re cold, you should go to a corner since it’s 90 degrees there  — Anonymous

Previous mentions of Ramanujan in this blog can be found at this link.

Numbers and Faces, a math-poetry anthology

 Celebrating the NEW year with a collection of OLD favorites!

      Twenty years ago in 2001, supported by a grant from EXXONMOBIL, the Humanistic Mathematics Network published:

 NUMBERS AND FACES
A Collection of Poems with Mathematical Imagery

This collection of 24 poems (which I edited) is out of print but is available here (as a pdf).  A screenshot of the Table of Contents appears below:

The Doomsday Rule

     My recently posted mention of Tristian Bangert's poem about John Horton Conway (1937-2020) sent me looking through my files for materials related to Conway's visit to Pennsylvania's Bloomsburg University in 1993.  During that visit, Conway entertained students with his explanation of the Doomsday Rule -- for calculating the day-of-the-week that corresponds to a particular date -- and I tried to capture his message (a lengthy one) in the following stanzas:

On What Day of the Week Were You Born?   

by JoAnne Growney

These lines were inspired by John H. Conway's presentation, "Calendar Calisthenics and Calculations," at Bloomsburg University on January 26, 1993.

A man that I met
named Conway, said "Why?"
should the hard be hard
when the hard can be easy
with just a bit of effort.    

Geometry Personalities

 When a triangle talks to a square, what does she say?

Among my favorites of mathy poems are poems by Guillevic (1907-1997) -- in which the poet gives personalities to mathematical objects -- and many of these are available in Geometries, Englished by Richard Sieburth, Ugly Duckling Presse Ltd., Brooklyn, NY; 2010.

Here, from the August, 1970 issue of Poetry Magazine is Guillevic's "Parallels" -- one of four of his poems translated from French by Teo Savory and  published there.

Searching this blog for previous connections to work by Guillevic 
leads to this link to a list of posts.

Counting Syllables for Christmas

     As I look ahead toward Christmas, I shape my thoughts into words with syllable-counts that match the Fibonacci numbers.

Holiday musing from JoAnne Growney

STAY SAFE!

Admiring John Conway with stories of numbers

     Recently I was contacted by Thomas Barr, Director of Programs at the American Mathematical Society who told me of poetry written by a student from Flagstaff, AZ; Tristian Bangert of Coconino Community College has written about the discovery by John Horton Conway (1937-2020) of the surreal numbers -- and I offer part of his poem below; contact information for the poet is offered at the end of this post:

from Conway     by Tristian Bangert

     There once was a man

     Who knew naught but numbers

     Joined by their presence

     The numbers, wondering

     "Where has your kind been? 

     Have you not wondered who was here before you?"  

Proofs in Poems -- the Sylow Theorems

     One of my valuable resources during this year 2020 has been the AMS PAGE A DAY CALENDAR by Evelyn Lamb -- published by the American Mathematical Society.
     Today, December 16, Lamb's calendar celebrates a collection of poems by British software engineer Patrick Stevens -- verses that together offer poetic proof of the Sylow theorems about the subgroups of a finite group.
     Here is a link to Stevens' collection of  "Slightly silly Sylow pseudo-sonnets" and these are the opening lines:

        Suppose we have a finite group called G.
        This group has size m times a power of p.
        We choose m to have coprimality:
        the power of p's the biggest we can see.
       . . .

This link leads to other mentions in this blog of Evelyn Lamb's math-poetry links.

Solving problems -- crimes and mathematics

     In childhood I loved novels that featured the girl-detective, Nancy Drew, and in adulthood I have continued to enjoy crime-solving fiction -- and have supposed that this is connected to my love of mathematics.  Recent news of the death of spy novelist John Le Carre (1931--December 12, 2020)  has stimulated my thinking about problem solvers and has led to this Fib:

        We 
        seek --  
        and find --
        truth that hides 
        in common views of  
        available information.

As you may already know, a "Fib" is a 6-line poem whose syllable counts match the first six Fibonacci numbers:  1, 1, 2, 3, 5, 8.  This link leads to additional Fibonacci-poetry connections.

How should a professor groom for math class?

     One of the rewards of many new endeavors is making new friends -- and one of the special connections I have made through math-poetry endeavors is Gregory Coxson, an engineering professor at the US Naval Academy.  Greg has frequently alerted me to new mathy poems and, this fall, he sent me an interesting poem that he had written, a thoughtful comment on looking beyond appearances to what is more important. 

My PDE Professor    by Gregory Coxson

He sometimes wore those marine corps sweaters
  The ones in army green, that look the best
On more triangular figures than his.
  And then those ridiculous epaulets
How did his wife let him out of the house?    

Gatherings of a retired teacher . . .

David Pleacher is a retired mathematics teacher who has maintained a math page on the Internet since 1998 -- and one of his rich and varied collections of resources includes mathy poems and songs, some by him and some by other authors.  Here are two samples:

by David Pleacher, found here

Celebrate Math Women . . . Write about them!!

     This message is a follow-up to a posting made on October 12 -- an announcement of the Student Essay Contest sponsored by the Association for Women in Mathematics and (as I have newly learned today) Math for America.

     Students in three categories -- middle school, high school, and undergraduate -- are invited to interview a math-woman and to write and submit a biographical essay that celebrates that woman.  The submission period for essays opened yesterday (12/1/2020) and continues until February 1, 2021.  Full details are available at this link.

  

For more, here is a link to the results of a blog search using "women" and "mathematics".

November is Native American Heritage Month

      Today, the day after Thanksgiving, is Native American Heritage Day -- a November event that was proclaimed in 2009 by President Obama and is part of Native American Indian Heritage Month (established in 1990 by President Bush.)  The disregard with which native Americans have been treated over many years has created huge wounds that will take long to heal.  Both mathematics and poetry can help to support justice and truth!  At present, the US Poet Laureate is Joy Harjo of the Muskogee Nation -- and Harjo is active in using the educational and healing powers of poetry.   Here is a link to some lines from Harjo's "Becoming Seventy" -- posted in this blog back in 2019.

     The website Poets.org helps us to celebrate Native American Heritage Month with a collection of poetic resources found at this link.  One of the poems offered -- which makes effective use of numbers in describing difficult situations -- is "Housing Conditions of One Hundred Fifty Chippewa Families" by Kimberly Blaeser.  I offer a few lines of that poem below -- followed by a link to the entire poem. 

Gather in Poems

 Gather in Poems -- a sort of Thanksgiving

     Last evening I attended a lovely virtual reading, "Gather in Poems," sponsored by the Academy of American Poets (advertised on Facebook) and moderated by  US Poet Laureate Joy Harjo.  One of the readers was a student poet -- high school junior Ethan Wang -- who shared a science-inspired poem by Rosebud Ben-Oni entitled "So They Say--They Finally Nailed--the Proton's Size--& Hope--Dies."  Here are a few lines from the poem -- and the entire poem may be found here.

. . .    I don’t believe hope dies
         just because old measurements got it
         wrong & there are no secret lives
         between protons & muons
         that cause the former to change
         in size,
         silencing all the music
         that drives us
         toward mystery
         rather than discovery.       . . .

One of the delightful--and free--services of the Academy of American Poets is free email delivery of "A Poem a Day."  Sign up here at https://poets.org.

Happy Fibonacci Day!

        Today, November 23 is Fibonacci Day . . . How are you celebrating?  Twitter poet Brian Bilston (@Brian_Bilston) has posted a Fibonacci poem -- with words-per-line counted by the Fibonacci numbers.  Here are its opening lines:

       I
       wrote
       a poem
       in a tweet
       but then each line grew
       to the word sum of the previous two
       until . . .

Use of the Fibonacci numbers in poetry has gotten frequent mention in this blog; here is a link to the results of a blog SEARCH using the term Fibonacci.  And find the rest of Brian's poem in this posting from August 31, 2020 -- or by browsing here on Twitter.

Shaping POETRY with GEOMETRY

Syllable-count constraints help me to think carefully about word choices as I construct a poem.  Here are square and triangular stanzas that came into my head recently while I was jogging.

In addition, when working with students,  I often find that they explore their ideas most easily when I suggest that they follow syllable-counting constraints.

Poetry and Mathematics -- opening doors . . .

Since 1998 The Bridges Organization has been offering conferences that publicize and celebrate links connecting mathematics and the arts.  Because of the Covid-19 pandemic, the 2020 conference was virtual -- but papers submitted to the conference are available online here.

One of the 2020 titles that has especially interested me is "Poetry in the Lesson of Mathematics" by Natalija Budinski and Zsolt Lavicza, available at this link.  The article describes a case study on how poetry can be used as a teaching tool in math classes -- helping students to understand complex mathematical concepts by writing about them using guidelines from poetry.

Links to additional Bridges articles by Budinski and by Lavicza are available via SEARCH here in the Bridges Archives.  And some of my earlier suggestions about using poetry in math classes are found in this posting.

In closing, a stanza from a long-ago poem of mine, "A Taste of Mathematics":

          She said, "A hot pepper
          is like mathematics--
          with strong flavor
          that takes over
          whatever
          it enters.

Venn Diagrams

      During these days of classifying people and points of view, my thoughts turn again and again to Venn Diagrams and I am then reminded of a thoughtful poem about math in grade-school days (by Pennsylvania poet and professor Marjorie Maddox) that I first read long ago -- and I offer it here:  

Learn about Venn Diagrams here

Venn Diagrams     

          by Marjorie Maddox   

There, stuck in that class,
chalking circles on a board 
       so high your toes ached,
an inch of sock exposed,
all for the sake of subsets,
        intersection.
That teacher with the tie too bright for day,
wide as your fingers spread  

Special Days for Mathematics

Today is the birthday of black mathematician, astronomer, almanac-writer and puzzle-maker Benjamin Banneker (1731-1806) -- and some of his puzzles were poems:  this link leads to this blog's previous postings of his work.

This week (November 9-14) is  2020 Maths Week in England.  Learn more, via an introductory video, here.

During these Covid-19 days of isolation I am particularly aware of distances that separate me from those I love . ..  and the numbers that keep track of it all.  Here are opening lines from the poem "Distances" by Peter Meinke that reflect on the changeable meanings of numbers. 

Varieties of SQUARE poems

     When writing a poem on a topic about which I feel strongly, I often like to use constraints -- such as patterns of syllable-counts or rhymes -- to help me to process my ideas carefully.   A recent post by mathematician-poet Marian Christie does a delightful job of showing how the square can be used to shape very fine poems.  Here is a link to Christie's post, "Mathematical forms in poetry:  Square poems" -- a posting which includes examples of acrostic poems and grid poems, palindromes, Latin squares and visual poetry.

     Below I offer one of Christie's own poems, "Earth Geometry" -- a poem that involves the square and the cube in its structure and thereby relates to ancient theories of matter and to a more current belief that the cube is a basic structure of the earth. (View Christie's full explanation here.)

Voting is on the calendar!

Poetry often surprises us by using familiar words in new ways -- and such is also the case with this cryptarithmetic puzzle -- offered by Evelyn Lamb in her AMS page-a-day calendar for tomorrow, Election Day.

               VOTES
           + VOTES
            CHANGE

In this puzzle (which Lamb credits to Manan Shah at mathmisery.com) each letter represents a base ten digit, no letter represents more than one digit at a time and no digit can be paired with more than one letter.  There are no leading zeroes; there are two solutions.  While you are waiting for results from the November 3 US election, this puzzle can help you pass the time in a way that's FUN!

Seeking wisdom in mathematical Haiku

 During these difficult pre-election coronavirus days I have been turning to poetry, and especially favoring -- for their brevity -- Haiku.  The January 2018 issue of the Journal of Humanistic Mathematics offers a folder "Math in Seventeen Syllables:  A Folder of Mathematical Haiku" -- with more than thirty poets sharing poetic insights using this ancient form.  Here is one, by Laura Kline, that spoke to me today:

          Peaceful living and
          Nicely balanced equations
          How we long for both

For more mathy Haiku, follow this link to the results of a blog-search using "Haiku".

Math Songs by Tom Lehrer -- Political, etc.

      All of the songs of musician and math-teacher and nonagenarian Tom Lehrer are now in the public domain (at this link).  His mathy item, "The Derivative Song," was included here in an early post in this blog.  Today I have particularly enjoyed his "Political Action Song" which begins with these words:

     Now when it comes to anything political,
     We're int'rested, we're militant, we're critical.
     Though it's not quite evident
     Who we represent,
     We take stands and issue statements by the score.
     Ev'ry candidate, we know,
     Though he won't admit it's so,
     Would give anything to be the one we're for, we're for,
     Would give anything to be the one we're for.     .  .  .    

Spirit of Delight . . .

        The true spirit of delight, the exaltation,

        the sense of being more than man,

        which is the touchstone of the highest excellence,

        is to be found in mathematics as surely as in poetry.

Bertrand Russell (1872-1970)