Examining boundaries for Math-Women

Mathematician Ursula Whitcher is a versatile and interesting person -- and currently an editor for the American Mathematical Society's Mathematical Reviews.  It was my pleasure to meet and work with her at a conference on "Creative Writing in Mathematics . . ." in Banff in 2016.  Like me, Whitcher writes some poetry -- and here is one of her poems -- this one recognizing the isolation of math-woman Sophie Germain.

       Boundary Conditions     by Ursula Whitcher

               Royal Academy of Science, Paris, 1823

       This is her moment of triumph:
       a seat at the center, a node.
       Mademoiselle Germain sits silent,
       head upright, chaperoned.
       Academy members rise
       or dip; the speaker drones.   

Defending Poetry . . . .

With sadness I learned yesterday of the death of poet Meena Alexander (1951-2018) -- not only a fine poet but also one of my treasured teachers during my MFA studies at Hunter a bunch of years ago.  As I browsed the works of Alexander online I found here in World Literature Today her essay "What Use Is Poetry?" which includes reference to Shelley's "In Defence of Poetry." 

     Shelley's words led me to think of mathematics; perhaps you will, too:
          “It creates for us a being within our being. 
           It makes us inhabitants of a world to which 
           the familiar world is a chaos. It reproduces 
           the common universe of which we are portions and percipients, 
           and it purges from our inward sight the film of familiarity 
           which obscures from us the wonder of our being.”

The Heart's Arithmetic

     For me, the Christmas holiday season is a time for family gathering and a treasured time for that reason.  Today my thoughts turn to one of my favorite poems of family and mathematics -- a poem by much-too-soon-departed poet Wilmer Mills (1969-2011),  a poem first published in Poetry and also also found here at the Poetry Foundation website. 

     An Equation for My Children  by Wilmer Mills

     It may be esoteric and perverse
     That I consult Pythagoras to hear
     A music tuning in the universe.
     My interest in his math of star and sphere
     Has triggered theorems too far-fetched to solve.  

United by ice cream -- the sphere and cone

     During recent months I have been part of an online course that has helped me and a dozen others to learn steps for editing Wikipedia -- with the goal that we will be able to add biographies of "Women in Science and Mathematics" to that enormous online encyclopedia (in which, currently, less than 18% of the biographies feature women).    The course has led me to SEARCH Wikipedia using names of women I admire -- and it will be my intent to work toward addition of those missing.  One such woman -- a mathematics PhD, a talented teacher, a poet -- is Katharine O'Brien (1905-1986).  I introduce her below with one of her mathy poems (first published in The Mathematics Teacher in 1968).

     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.

By Claude Shannon -- a Poem for Rubik's Cube

     Below I present the opening lines of an 80-line (plus footnotes) poetic creation by Claude Shannon (1916-2001).  A mathematician, engineer and cryptographer, Shannon is often called "the father of information theory."  My own acquaintance with Shannon's work came through the topic of error-correction codes.  Shannon's poem on the Rubik Cube was first published here in a Scientific American blog posting by John Horgan.

     A Rubric on Rubik Cubics (1)     by Claude Shannon
   
     Strange imports come from Hungary:
     Count Dracula, and ZsaZsa G.,
     Now Erno Rubik's Magic Cube
     For PhD or country rube.
     This fiendish clever engineer
     Entrapped the music of the sphere.   

Chaos theory -- portrayed in poetry

     A poem I have long loved is "Chaos Theory" by poet (and fiction writer and scholar) Ronald Wallace -- and he has given me permission to offer it below.

Chaos Theory     by Ronald Wallace

    1. Sensitive Dependence on Initial Conditions

       For want of a nail the shoe was lost,
       for want of a shoe the horse was lost,
       and so on to the ultimate loss—a battle,
       a world. In other words, the breeze
       from this butterfly's golden wings
       could fan a tsunami in Indonesia
       or send a small chill across the neck 
       of an old love about to collapse in Kansas
       in an alcoholic stupor—her last.
       Everything is connected. Blame it on
       the butterfly, if you will. Or the gesture
       thirty years ago, the glance across
       the ninth-grade auditorium floor,   

Counting words with the Fibonacci numbers . . .

Today a poem by New York poet, Larissa Shmailo,

that explores aging with word-counts that match the Fibonacci numbers.

    none

    1(one) 

    1(ego)  

    two (I)

    I 2 threeeeeeeeee

    5 school, ruled 2 three   

Marriage in Quantum Mechanics

     Sometimes mathematical concepts also bring to mind phenomena in our everyday lives -- as in this poem by New Jersey poet Charlotte Mandel;  I hope you enjoy, as I did, Mandel's play with ideas and imagery. 

     In Quantum Mechanics, Marriage Is     by Charlotte Mandel

     discontinuous
     as rain
     chips into the lake,
     each linear strike
     sets another circle in the jostle
     as currents
     succeed.   

Thankful for . ..

          Now
          I
          give thanks --
          for your grace
          and empathy, for
          mathematics and poetry.

     When I offer a poetry class to people new to writing, often the first poem I ask them to write is a Fib -- I give them a topic (such as "winter" or "Thanksgiving" or "gardening" or . . .) and ask them to write lines whose syllable-counts match the first six Fibonacci numbers: 1, 1, 2, 3, 5, 8. Time and again these writers are pleased with the way that the numerical constraints shape their words into thoughtful meaning.
     This posting, "Poems with Fibonacci Number Patterns" offers more samples.  The six-line form (called a Fib and illustrated above) was invented in 2006 by Gregory Pincus.

Happy Thanksgiving!

Qualitative thinking in a quantitative era . . .

Chemistry Nobelist  Roald Hoffman also is a poet, 

and an advocate of holistic education.

Many thanks to Australian poet and STEAM advocate, Erica Jolly, 

for reminding me of the importance of Hoffmann's work.

HEIGHT     by Roald Hoffmann

The man
who said
when you're on top
of a mountain
you can't see it
was a miner. 

The tiny poem above is found here on Hoffmann's website.

A poet that makes math personal

     Mathematician-poet Marion Cohen has a new poetry collection just out -- The Project of Being Alive.  Here is a sample from that collection, a poem that highlights her relationship with mathematics:

      Statement     by Marion Deutsche Cohen

     A good teacher is supposed to teach students, not subjects.
     But I teach math.
     Whoever the students, math is the subject.
     If there were no students I’d probably still teach my subject.
     I’d teach and I’d learn
     all by myself.

Echoing Marion's thoughts, I think that many of us who love mathematics and/or love poetry, enjoy the challenge of reading and rereading -- and struggling to absorb difficult ideas. 

A FIRST-LOVE in math-poetry -- "Counting Rhymes"

     Still in my head are counting rhymes that I learned in childhood -- an early connection between mathematics and poetry that I think helped me to love both subjects.  Here is a link to a list of more than forty math-rhymes -- and including one that is also in Spanish.
     This rhyme is one that has been useful to me throughout both childhood and adulthood-- as I strive to remember which months have thirty days.

          Thirty days hath September,
          April, June, and November;
          All the rest have thirty-one,
          Excepting February alone,
          Which has twenty-eight in line,
          Till leap-year gives it twenty-nine.

AND, today's issue of the Washington Post has a cartoon by Tom Toles -- about recounting votes after last week's election -- that also involves a counting rhyme:  I offer part of the rhyme below but the visual is critical -- and available here.

          One, two, none for you.
          Three, four, they fell on the floor.
          Five, six, it takes some tricks . . .
          Seven, eight, to make America great.
               . . .
For a few more rhymes, check out this 2013 post, "Nursery Rhyme Mathematics."

Mathy poems at poets.org

 For a variety of mathy poems, here's a GREAT link to follow. 

Rhyming wordplay -- with math terms . . .

     Nineteenth century British poet Arthur Clement Hilton (1851-1877) died young but during his short life he wrote some lively verse.  Here is "Mathematics" -- from his collection The First Green, found here (p.134).

     Mathematics     by Arthur Clement Hilton

     I've really had enough of sums,
        I've done so very many,
     That now instead of doing sum
        I'd rather not do any.

     I've toiled until my fingers are
        With writing out of joint;
     And even now of Decimals
        I cannot see the point.  

Applied Science -- and Art

     Some days there is time to sort through piles of old stuff saved on a shelf -- and this morning's fun-find was a September 1993 issue of Poetry Magazine with this poem, "Applied Science," by Neal Bowers, a poem inspired by sculpture by George Greenamyer.

       Applied Science     by Neal Bowers
                        after George Greenamyer’s "Start to Finish"
       Because three left turns make a right,
       and the way down is the way up,
       the way in the way out,
       but most of all because
       the beginning is the end,

The Puzzle of Time

     Recently I have learned with sadness of the death last February of Romanian-Canadian mathematician Florin Diacu (1959-2018).  Florin also wrote poetry -- and helped to organize seminars in "Creative Writing in Mathematics" at the Banff International Research Station.  I met Diacu when I was privileged to attend these seminars -- and you may find my 2016 posting of his poem "Arnold Diffusion" at this link.  Today I remember him by sharing with readers his poem "Time" -- first published in the Journal of Humanistic Mathematics in 2012 and also available at this link.

       Time     by Florin Diacu

       Time drifts on the sea of illusions.

       Newton’s image of it was a line,
       unbounded and straight, like desire.
       Einstein called it dimension four:
       the lasting partner of space.

Five Little Pumpkins

 

Happy Halloween!

This children's rhyme is found at the DeepLearningToolKits(DLTK) website) and available at that site also with downloadable illustrations.  Enjoy!

Five Little Pumpkins

Five little pumpkins sitting on a gate.

The Prince of Algebra . . . and SAT scores

     An article in a recent issue of the Washington Post (perhaps this link will get you to it) told of a drop in SAT scores for the Class of 2018 -- and it has got me to thinking about various approaches to teaching and learning and about what test scores measure. Once -- a dozen or so years ago -- I got roped into helping with an SAT-prep course and was astounded to learn how much improvement was predicted for strategies relating to when to guess, when to give no answer, and so on.
     As I parented children moving through school, it seemed to me that one of the best features in their educational years was variety in their teachers.  We want -- in our math classes and throughout our schools -- to educate people who can keep on learning and who can respond to unexpected situations.  Multiple choice questions on SAT tests represent only one aspect of that variety.
     Teachers meet a variety of students -- and none of us are perfectly suited for them all.  One of the interesting students to whom I tried to be helpful speaks in the following poem, "The Prince of Algebra," also previously posted in this blog on January 10, 2014.

 The Prince of Algebra      by JoAnne Growney

       Madam Professor,
       let me introduce myself.
       I'm Albert James,
       whom you may know
       by my test score
       that's lower than my age.

Enter by Nov 9 -- Student Math-Poetry Contest

Contest sponsored by the American Mathematical Society

 for 

 junior-high students . . .  . senior-high students . . . college students 

 from Maryland 

WRITE A  POEM  with connections to  MATH  -- Send it to AMS

Here's a link to contest information:  www.ams.org/math-poetry  

This blog's posting for October 10 also gives some information about the student contest.

Describing a scene with numbers

     Lana Hechtman Ayers is a versatile and accomplished poet who also has a degree in mathematics --  in her poem below, she paints a picture with numbers.

       Algebra     by Lana Hechtman Ayers

       4 women
       of 3 generations
       are walking along
       2nd Street together
       in the rain
       without any number
       of umbrellas.

Read your Math-Poetry in Baltimore, 1/18/19

You are invited be part of a reading of math-linked poetry 

sponsored by the Journal of Humanistic Mathematics  and  SIGMAA-ARTS

at the 2019 Joint Mathematics Meetings (JMM)

Baltimore Convention Center  Room 301  

Friday, January 18, 2019  7 - 8:30 PM

 Celebrate MATH PEOPLE with poems! 

All interested in mathematical poetry/art are welcome.  Come to share your poems about famous or not-famous math personalities (the researcher, the teacher, the geek, the reluctant student, or whomever) – or join us simply to enjoy hearing the work of others!   Though we do not discourage last-minute decisions to participate, we encourage poets to 
          submit poetry (up to 3 poems, reading time up to 5 minutes) 
                    and a 40-word bio         in advance  (by early November)
so you can be listed in our printed program. Early submissions are encouraged, by November 1 would be GREAT -- but submissions will be considered into mid or late November.    Send submissions (and inquiries) to Gizem Karaali (gizem.karaali AT pomona.edu). Organizers of the event include JoAnne Growney, Gizem Karaali, Lawrence M. Lesser, and Douglas Norton.

Math-themed -- and seasonal -- Haiku

      Artist and computer scientist Stephen Luecking, now retired from teaching at DePaul University, has sent me some of his Haiku with mathematical imagery; enjoy!

fractals vein the leaves  

swirling in random descent  

autumn winds howling    

crystal hexagons  

drifting from darkening clouds  

earth sleeps in white gown  

Can numbers be a bridge to understanding. . . ?

Fifty-Fifty     by Carl Sandburg (1878-1967)

       What is there for us two
       to split fifty-fifty,
       to go halvers on?
            A Bible, a deck of cards?
            a farm, a frying pan?
            a porch, front steps to sit on?
       How can we be pals
            when you speak English
            and I speak English
            and you never understand me
            and I never understand you?

This poem is on my shelf in Sandburg's collection, Honey and Salt (Harcourt, Brace; 1963).

The music of twelve tones -- in poems

     Inspired by the musical composition strategy twelve-tone technique -- devised by Austrian composer Arnold Schoenberg (1974-1951), in which all 12 notes of the chromatic scale are sound as often as one another in a piece of music -- American poet Elizabeth Bartlett (1911-1994) has developed the twelve-tone poem.  In Bartlett's words:
       The poem consists of 12 lines, divided into couplets. 
       Each couplet contains 12 syllables, using the natural cadence of speech. 
       The accented sounds of the words are considered tones. 
       Only 12 tones are used throughout the poem, repeated various times. 
       As a result, the poem achieves a rare harmony that is purely lyrical, 
                    enriching its imagery and meaning

The following poem is on my shelf in Memory Is No Stranger (Ohio Univ. Press, 1981), a collection of Bartlett's twelve-tone poems; it also is found in the math-poetry anthology Against Infinity (Primary Press, 1979).

       The Infinite Present   by Elizabeth Bartlett

       Because I longed
       to comprehend the infinite  

Math-Poetry Contest for Maryland Students

Submission deadline:  November 9, 2018
Winners Announced:  December 12, 2018

Winning Poems Presented:  January 19, 2019

     The American Mathematical Society is conducting a math poetry contest for Maryland students–middle school, high school, and undergraduate students -- as part of the 2019 Joint Mathematics Meetings in Baltimore (Jan. 16-19, Baltimore Convention Center).   The contest is free to enter; information is at this link.  Winning poems will be printed on posters and poets will read them at the meeting as part of Mathemati-Con, a math festival for students.

          Write
          a
          thoughtful
          poem that
          shows ways math is most
          amazing -- a subject we love!

The stanza above is a Fib -- whose lines have syllables counted by the first six Fibonacci numbers.

A special Fibonacci poem

     A recent email from Marian Christie -- a nominally retired mathematics teacher from Aberdeenshire  -- alerted me to her very special sort of Fibonacci poem, one in which the number of letters-per-line follows the Fibonacci numbers AND the length of each word is a Fibonacci number AND the poem speaks about the objects counted by these Fibonacci numbers.

Pathways      by Marian Christie
–
O
I
am
not
going
anywhere
unaccompanied
by life’s patterns: a whorl
in a pinecone, branches on oak or elm trees, 
the petal count of a daisy, the helix at the heart of a chrysanthemum,
the shell of a nautilus swimming in the ocean. A sequence hides in the shape of
                                                                             probabilities, and in my own DNA. 

Poet's Note: In this poem the number of letters per line is determined by the Fibonacci sequence: the first line has zero letters while the last line, representing the twelfth number in the sequence, contains 89 letters. In addition, the letters of each word add up to a Fibonacci number.  

Christie's poem was first published on the UK-based website IndependentVariable.

Line and design -- poetry by Adrienne Rich

     A poem I first read during my high school years -- and have loved ever since -- is "Aunt Jennifer's Tigers" by Adrienne Rich (1929-2012).  Found along with that poem in Collected Early Poems 1950-1970  (W W Norton, 1994) is another poem by Rich that I also like a lot -- and offer below -- this one containing a bit of mathematics and a lot to reflect on . . .

          Boundary     by Adrienne Rich

          What has happened here will do
          To bite the living world in two,
          Half for me and half for you.
          Here at last I fix a line
          Severing the world’s design
          Too small to hold both yours and mine.
          There’s enormity in a hair
          Enough to lead men not to share
          Narrow confines of a sphere
          But put an ocean or a fence
          Between two opposite intents.
          A hair would span the difference.

The equal sign--and poetry--from Robert Recorde

  A poetic introduction of the equal sign (by Robert Recorde): 

This image is an excerpt from Recorde's The Whetstone of Witte (1557)

    Robert Recorde was born in Wales around 1510-12; he taught mathematics at both Oxford and Cambridge and got his MD from Cambridge in 1545 -- and became a physician to royalty.  He published a number of mathematical works -- one of the best known being The Whetstone of Witte (1557) -- a photographic copy of several of its pages is available here. He is lauded for the invention of the equal sign, first appearing, as shown above, in The Whetstone of Witte.  -- This article from 2015 in WalesOnline cites Recorde's greatest achievement to be making mathematics accessible to a general reader.   

Counting syllables . . . measuring memory

Political events of this past week (involving a candidate nominated by President 45 to serve on the Supreme Court) have triggered my thinking about the transience of memory.  Here is a Syllable-Snowball poem that includes some of these musings:

What happened back then?

My

sister

disagrees --

her version of

our  growing-up  lives

   so          often         discrepant

     from mine. Each new year -- 

  new           distances,

new    angles,

shape our

 views.

Name five!

     A recent mailing from the National Museum of Women in the Arts offered me this challenge:  name five female artists!  Including friends who are artists made this easy -- but I needed a bit of internet help to list five famous names.  This effort has suggests another challenge: 

 NAME (at least) FIVE FEMALE MATHEMATICIANS ! 

One way to meet math-women is through a variety of poems that celebrate them -- lots of poems about math-women are found in this blog.  The Search and Labels features (in right-hand column of blog) can be useful.  Here are several links to get started:

       A poem by Brian McCabe about Sophie Germain;

              a poem by Eavan Boland about Grace Murray Hopper;    

                     a poem by Carol Dorf about Ada Lovelace;

                            a poem of mine about Sofia Kovalevsky;

                                   a poem of mine about Emmy Noether

And this link leads to a great variety of math-women resources.

A few words in closing:

          14 Syllables

          A hen lays eggs
          one by one;
          the way you
          count life
          is life.

from JoAnne Growney's collection Red Has No Reason (Plain View Press, 2010).

Celebrate math students -- a Fibonacci poem!

     South Dakota mathematician Dan May teaches mathematics at Black Hills State University where he also leads workshops for middle school teachers, explores musicology and the connections between poetry and discrete mathematics. He has been involved in math-poetry activities at Bridges Math-Arts conferences but, more importantly, he has been involved with BEAM (Bridge to Enter Advanced Mathematics), a program offering varied academic assistance to underserved students, including a summer residential program. The following Fibonacci poem celebrates that adventure.

BEAM: A Fibonacci Poem     by Dan May

Now
you 
are home — 
Brooklyn, Queens, 
the Bronx, your boroughs. 
Only yesterday still at camp, 
learning knots and graphs, writing proofs on infinity. 
I taught you the one hundred and sixty-eight automorphisms of the Fano plane. 
You wear hijabs, or Jordans, or both. Diverse faces 
display the doubts of twelve-year-olds. 
But each of you, when 
you get it — 
your face 
lights 
Up.

Author’s Note: The poem’s syllable line count follows the 

Fibonacci sequence numbers 1, 1, 2, 3, 5, 8, 13, 21 forward and backward.  

This poem and several others of Dan May's math-linked poems may be found here.

A mathy poem for sale . . . in Kenya

     A vernacular poem by Kenyan writer Alexander Nderitu ("Kenya's Shakespeare") -- entitled "Mathabu ma Carey Francis" (in English, "The Mathematics of Carey Francis) -- is being auctioned by the poet for bids starting at a million Kenya shillings (a bit less than $1000 US).  Notable about this auction piece is that the background design on which the poem will appear is the poet's DNA sequence.

The opening stanza of Nderitu's poem 

From Wikipedia, this statement about Edward Carey Francis:  Edward Carey Francis (13 September 1897 – 27 July 1966) was a British mathematician and Anglican missionary to Kenya, where he became "arguably the most influential educationist in Kenya's modern history."  

Time and Precision . . . .

   California poet Carol Dorf is a semi-retired secondary school mathematics teacher who is an important force in poetry.  Not only a fine poet, Carol also is Poetry Editor of TalkingWriting, an online journal that sometimes features mathy poems.  It has been my pleasure to meet Carol and to read with her on several occasions, most recently at the 2017 Bridges Conference in Waterloo, Ontario.  The following poem is one that Carol read at Bridges 2018 and it is included in the Bridges Stockholm 2018 Poetry Anthology; it is a thoughtful reflection on the way that time -- and precision in its measurement -- varies in our lives.

Announce the Hour You Have Clocks For    by Carol Dorf
     

Time progresses through the bells 

announcing each moment of occupation: 

toilet, wash, dress, eat, work a, break, work b . . . 

eat, undress, wash, toilet. 

Schematic, yes. Our clocks' precision  

increases until the second, 

Meeting Math People via Poems

     Mathematics classes are crowded with vital material and it is hard to find time to also consider the PEOPLE of mathematics -- one way to do this is by offering poems.  In the September issue of Math Horizons, my brief article, "Mathematics and Poetry" offers a variety of samples -- introducing poems by mathematicians (including William Rowan Hamilton) and poems about mathematicians (Brian McCabe writing about Sophie Germaine, Cathryn Essinger writing about her super-logical brother).  
     Here are a pair of lines from Voltaire about mathematician and scientist Émilie Du Châtelet:

               She has, I assure you, a genius rare.
               With Horace and Newton, she can compare. 

     A wonderful poem to add to those quoted in the article is in the voice of a math student who protests discrimination; it is by Caribbean-American poet Audre Lorde (1934-1992) and entitled "Hanging Fire" -- the complete poem is posted here.

               I should have been on the Math Team
               my marks were better than his

Here is a link to a pdf of the Math Horizons article.  The article does not contain web-links, BUT each of the poems may be found by searching this blog using the poet's name.

Math Limerick Stories

     Mathematics teacher Josephine Johansen is a talented teacher who works to help her students LOVE mathematics.  Below are two stanzas from her illustrated tale, "The Algebra of Tree Wisdom" --written in limerick stanzas: 

Pat says "Say you put on your ring 

Then your necklace to you I bring 

Whichever you choose

To do first, you'll not lose

You'll still be dressed for your fling."

Pete adds "On the other hand

Putting shoes and socks on as planned

        Is not commutative

       Won’t switching order give

An outcome that would be unplanned."  

OEDILF -- with definitions in limerick form

     Since 2004, OEDILF, the Oxford English Dictionary in Limerick Form has been assembling limerick definitions of English words.  I learned about this amazing project in the Washington Post -- in a weekly column by Pat Myers entitled "The Style Invitational".  Each year, Myers invites readers to submit limericks that define terms in a particular alphabetic range.  This year's contest requested limericks that define words beginning with gl- to go-.  Follow this link (and scroll) down to see some of the winners (announced this past weekend).
     Alas, none of the winning limericks involved math terms, and so I offer here one of my non-winning submissions.

When you have time, visit OEDILF -- browse its limerick offerings and consider contributing some of your own. And, if you like, add limericks here via your comments below.

Something or Nothing -- Thinking about Zero

     The site of the 2019 Bridges Math-Arts conference has been announced  -- it will meet in Linz, Austria next July.  This link leads to the archives of the 2018 and earlier conferences.  Each recent year a poetry reading (coordinated by Sarah Glaz) has been part of the Bridges activities -- and this year a poetry anthology also was compiled.  Here is a poem by Canadian poet Alice Major that was featured both in this year's reading and in the anthology  -- a poem that also appears, along with other math and science poems, in Major's latest collection, Welcome to the Anthropocene. (University of Alberta Press, 2018).  Major's poem examines death and, as it does so, explores various meanings of zero.

Zero divided by zero     by Alice Major

There is no right answer.

The trains of logic crash, annihilate

certainty. Zero is just as good an answer

as one. Nothingness or loneliness.

There is no right answer.    

As a new school-year starts, a Latin Square poem

 With MATH in the middle, 

 here is a LATIN-SQUARE poem that starts and ends with GIRLS ! 

girls	do	great	math
do	math	girls	great
great	girls	math	do
math	great	do	girls