The magic of "i"

 An exciting math event occurred last week -- the opening of MoMath, 

a Manhattan museum that makes math fun.

 

Still thinking about complex and imaginary numbers (see Sue VanHattum's poem in the December 16 posting), I want to offer a couple of stanzas by Paul Hartal -- selected from "Voyage around the Square Root of Minus 1"  -- stanzas that are part of a lengthy consideration of connections between the arts and the sciences.  I do not always agree with Hartal's viewpoints -- but they are interesting to consider.

from  Voyage around the Square Root of Minus One     by Paul Hartal 

. . .  Mathematical equations are embedded
       with mysterious forces
       and their uncanny power transcends
       the cognitive faculties of the human mind.

Imagine new numbers

     As a child I wrote poems but abandoned the craft until many years later when I was a math professor; at that later time some of my poems related to ideas pertinent to my classroom.  For Number Theory classes "A Mathematician's Nightmare" gave a story to the unsolved Collatz conjecture; in Abstract Algebra "My Dance Is Mathematics" gave the mathematical history a human component.  
     My editor-colleague (Strange Attractors), Sarah Glaz, also has used poems for teaching --  for example, "The enigmatic number e."  And Marion Cohen brings many poems of her own and others into her college seminar course, "Truth & Beauty: Mathematics in Literature."  Add a west-coaster to these east-coast poet-teachers -- this time a California-based contributor: teacher, poet, and blogger (Math Mama Writes) Sue VanHattum.  VanHattum (or "Math Mama") is a community college math teacher interested in all levels of math learning.  Some of her own poems and selections from other mathy poets are available at the Wikispace, MathPoetry, that she started and maintains. Here is the poet's recent revision of a poem from that site, a poem about the invention (or discovery?) of imaginary numbers.

Imaginary Numbers Do the Trick      by Sue VanHattum    

The important 1 (multiplicative identity)

On this day 12/12/12, I have heard much media discussion concerning coincidences of number.  My own thoughts continue to examine the multiple meanings of "identity."  Here is a lovely tanka by Izumi Shikibu (b 976?) that focuses on the importance of one:

       This heart,
       longing for you,
       breaks
       to a thousand pieces--
       I wouldn't lose one.

From The Ink Dark Moon:  Love Poems by Ono no Komachi and Izumi Shikibu, Women of the Ancient Court of Japan (Vintage Books, 1990), translated by Jane Hirshfield with Mariko Aratani. 

Loss of Identity

     Some of the richness of a poem comes from the multiple meanings available for the poet's words.  We read "line" and think of the geometric straight thing and of the type of work a person does and of a particular list of products and  . . .   .    For mathematicians, a given term may have a precise mathematical specification that trumps all the others.  (See, for example, the discussion of "random" in the 5 December 2012 posting.)
     A math term that especially interests me poetically is "identity."  One has a unique "identity" and experiences "identity theft" or an "identity crisis"  --  each time I hear the word my cross-referencing brain links to the mathematical notion of identity.  In the integers, the element zero, 0, is an identity for addition since 0 added to any integer produces no change.  Likewise, 1 is an identity for multiplication since 1 multiplied by any integer produces no change.

That's so random! (NPR, OEDILF, etc.)

     One of the challenges I face in friendly conversations is not to overreact to a "misuse" of the word random.  When I hear someone use that word to describe events that are peculiar or haphazard my heart-rate rises in protest.  It is as if I am in math class where every term has one, quantifiable definition -- my use of random describes a situation when a variety of things may happen and all of them are equally likely.  Like when a fair coin is tossed, or a die.  Or when a lottery ticket is selected.
     Recently my attitude was aired nationally. Sort of.  On Friday, November 30, NPR's Evening Edition featured a discussion of random.  Written by commentator Neda Ulaby, "That's So Random:  The Evolution of an Odd Word" mentions the 1995 film "Clueless," a comedian (Spencer Thompson), the Hacker's Dictionary  -- and also includes comments from the Oxford English Dictionary's editor, Jesse Sheidlower. I am rethinking my stubborn position.

Rearranging words

After posting, on November 15, three stanzas by Darby Larson -- three of the more than six quadrillion stanzas that result from arrangements (permutations) of eighteen selected words --  I decided to try my own arranging.  Here are two results.

       noise is angry morning                          Arrangement 1
       surely hung suppose beads
       in windy eyes there's your what
       wake-up and the sway    

Bold women count

Last evening at a poetry reading at Kensington Row Bookshop, I read my poem about Sophia Kovalevsky (posted on June 24); hearing it out loud before an attentive audience helped me to sense a couple of edits I need to make.  Conversations after the reading drew my focus once again to bold women.  Mathematics has some of these women --  and wants more.  Here, in a poem with some numbers, Margaret Atwood celebrates a woman who is not only bold but who burns.  Many of Atwood's words apply to difficulties (including being misunderstood by men) faced by women in mathematics  -- women who have "talent / to peddle a thing so nebulous / and without material form." 

     Helen of Troy Does Countertop Dancing        by Margaret Atwood   

     The world is full of women
     who'd tell me I should be ashamed of myself
     if they had the chance. Quit dancing.
     Get some self-respect
     and a day job.

Lincoln and Euclid -- common notions

     This afternoon I enjoyed the recently-released film, Lincoln -- appreciating Sally Fields as Mary Todd, Tommy Lee Jones as Thaddeus Stevens and (especially) Daniel Day-Lewis as Abraham Lincoln. An absorbing drama -- inspiring and also informative.  With a slight mention of mathematics:  in a film conversation with two-young telegraph operators, Lincoln reflected on his study of Euclid and shared with the young men the first of Euclid's common notions:

     Things that are equal to the same thing are equal to each other. 

Women Scientists in America

That

one,

Mary

Gray,  is bold,

mathematical,

and female.  One of the founders

(one-nine-seven-one) of the Association for

Women in Mathematics and an attorney, a leader of our struggle to get

well-meaning men to confront the attitudes they inherited, to change -- so that "think

mathematically" does not mean the same as "think

like a man."  Mathematics has

myriad voices.

Awaken!

Hear all

of
us.                                   a Fibonacci poem by JoAnne Growney      

Thank you, Mary Gray

For today, Thanksgiving, I have wanted to prepare a special poetic tribute and thank-you to mathematician Mary Gray.  I have had yet not found time for complete preparation of that celebration.  But here are the opening words:  THANK YOU -- to a founder of  AWM (Association for Women in Mathematics) and a woman who has done much, much, much to further the opportunities and recognition for women in mathematics --  to Mary Gray.

A permutation puzzle -- the sestina

In a sestina, line-ending words are repeated in six six-line stanzas in a designated permutation of the words; the thirty-nine-line poem ends with a three-line “envoi” that includes all six of the line-ending words.  (After the first, a stanza's end-words take those of the preceding stanza and use them in this order:  the 6th, then the 1st, then the 5th, 2nd, 4th and, finally, the 3rd. In the envoi, two of the six words are used in each line.)  Here is a sestina by Lloyd Schwartz that uses only six words -- but its punctuation and italics cleverly shape variations of meaning. 

Rearranging words . . .

     If we count all possible arrangements of 18 words, the total number of these is 18! (18-factorial) and equal to 6,402,373,705,728,000 -- a collection of word-permutations that would be a burden, rather than a joy, to contemplate.  (This previous posting offers some small lists of permutations for review.)
     Poet Darby Larson boldly experiments in his verse and in a 2009 posting (found months ago at  darbylarson.blogspot.com but no longer there) I found these three stanzas -- three of the more-than-six-quadrillion possible arrangements of a particular list of eighteen words.  

Finding fault with a sphere . . .

     On November 9 I had the pleasure (hosted by Irina Mitrea and Maria Lorenz) of talking ("Thirteen Ways that Math and Poetry Connect") with the Math Club at Temple University and, on November 5, I visited Marion Cohen's "Mathematics in Literature" class at Arcadia University.  THANKS for these good times.

          This
          Fib
          poem
          says THANK-YOU
          to all those students
          from Arcadia and Temple 
          who participated in "math-poetry" with me --
          who held forth with sonnets, pantoums,
          squares, snowballs, and Fibs --
          poetry
          that rests
          on
          math.

      My Temple host, Irina Mitrea, and I share something else besides being women who love mathematics -- the Romanian poet, Nichita Stanescu (1933-83), is a favorite for both of us.  My October 23 posting ("On the Life of Ptolemy") offered one of Sean Cotter's recently published translations of poems by Stanescu and below I include more Stanescu-via-Cotter -- namely, two of the ten sections of "An Argument with Euclid."  These stanzas illustrate Stanescu at his best -- irreverently using mathematical terminology and expressing articulate anger at seen and unseen powers of oppression.

Symmetry in poetry

In Euclidean Geometry, objects retain their size and shape during rigid motions (also called symmetries); one of these is translation -- movement of an object from one place to another along a straight line path.  Here are a few lines by Alberta poet Alice Major that explore the paths of rhyme as a sound moves to and fro within a poem :

     Rhyme's tiles slide
               from line
     to line, a not-so-rigid motion --
     a knitted, shifting symmetry
               that matches 'tree' 

Word Play -- "Of Time and the Line"

Charles Bernstein, poet and teacher,  experiments with poetry  and prefers "opaque" and "impermeable" writing -- to awaken readers "from the hypnosis of absorption."  In the poem below he does, as mathematicians also do, multiplies ideas by playing with them -- here using "line."

     Of Time and the Line     by Charles Bernstein

     George Burns likes to insist that he always
     takes the straight lines; the cigar in his mouth
     is a way of leaving space between the
     lines for a laugh.  He weaves lines together
     by means of a picaresque narrative;

Storm Sandy -- and climate change

     That
     storm
     Sandy
     has caused more
     people to believe
     climate change is real and awful
     than the piles of statistics amassed by scientists --
     bad to worse since 1950  --
     ice caps melting, drought,
     sea levels
     rising.
     Oh,
     My!

This poem of mine, with its syllables counted by successive Fibonacci numbers, is a slight revision of one posted on 31 August 2012.  That earlier posting also links to climate change data and to other  FIBS.

Greatest common factor

Sometimes a mathematical phrase offers a splendid concentration of meaning in an otherwise non-mathematical poem.  This is the case in the poem below by Taylor Mali, teacher and slam poet. 

Undivided Attention     by Taylor Mali

A grand piano wrapped in quilted pads by movers,
tied up with canvas straps—like classical music’s
birthday gift to the criminally insane—
is gently nudged without its legs
out an eighth‐floor window on 62nd street. 

Geometry of Trees

     Donna Masini, one of my poetry teachers at Hunter College, offered this rule of thumb for use of a particular word in a poem:  the word should serve the poem in (at least) two ways -- in meaning and sound, or sound and motion, or motion and image, or  . ..  .
     Richard Wilbur (1921 - ) is a former US Poet Laureate (1987-88), a prolific translator, and one of my favorite poets -- and perhaps this is because he seems to maximize his word-choices with multiple uses.  When I read Wilbur, I see and hear and feel -- and, after multiple readings, these sensory impressions coalesce into understanding.  Here is one of his sonnets, a poem of the geometry of absence:

"On the Life of Ptolemy"

Poetry at its best uses words in new ways.  Mathematics sometimes does that also.  But for a poet to use mathematical terms in new ways can be risky.  Nichita Stanescu (Romania, 1933 - 1983) was a poet unafraid to take that risk.  Here is Sean Cotter's translation of Stanescu's "On the Life of Ptolemy" from the new and fine Stanescu collection, Wheel with a Single Spoke.

     On the Life of Ptolemy     by Nichita Stanescu

     Ptolemy believed in the straight line,
     It exists.
     Count its points and, if you can,
     tell me the number.

Seeking math-poets -- JMM, SanDiego 1-11-13

Call for Readers:
     The Journal of Humanistic Mathematics will host a reading of poetry-with-mathematics at the annual Joint Mathematics Meetings (JMM) on Friday, January 11, 5 - 7 PM in Room 3, Upper Level, San Diego Convention Center.  If you wish to attend the reading and participate, please send,  by December 1, 2012 (via e-mail, to Gizem Karaali (gizem.karaali@pomona.edu)) up to 3 poems that involve mathematics (in content or structure, or both) -- no more than 3 pages -- and a 25 word bio.

Teaching math (?maths) is complex

     In the midst of a teaching career in Bloomsburg University I spent a year in an administrative position -- the school needed time to search for a proper provost and I was deemed good enough for the interim.  My good fortune during that year was to work closely with Kalyan, a highly competent man, born in India, who went on (as I did not) to become a college president.  Kalyan and I liked each other and early in the year we shared our views that we were both from "work twice as hard" categories.  That is, a woman or a dark-skinned man needs to work twice as hard as a white man to achieve recognition as the performance-equal of that white man. 

Geometry . . . a way of seeing

Today's poem is not only a fine work of art, it is also -- for me-- a doorway to memory.   I first heard it in the poet's voice when he visited Bloomsburg University in the late 1980s,  and I was alerted to the reading and to James Galvin's work by my most dear friend, BU Professor of English Ervene Gulley (1943-2008).   Ervene had been a mathematics major as an undergraduate but moved on from abstract algebra to Shakespeare.  Her compassion, her broad-seeing view, and her fierce logic served her well in the study and teaching of literature.  And in friendship.  I miss her daily.  She, like Galvin, questioned life and probed its geometry.

Puzzle poems from Benjamin Banneker

Benjamin Banneker (1731 - 1806) was a free African American mathematician and almanac author -- also an astronomer, surveyor, and farmer. (I learned of his work through my friend Greg Coxson, an engineer, teacher, and fan of mathematical poetry -- and Coxson learned of Banneker through a school project of his son.)  Beyond building a wooden clock and helping to lay out the borders of Washington, DC, Banneker predicted the 1789 solar eclipse and included rhyming math puzzles in his almanac.  Coxson introduced me to a fine website, established by by John F. Mahoney of Washington, DC's Benjamin Banneker Academic High School, entitled The Mathematical Puzzles of Benjamin Banneker.
     Banneker's Almanack had an eclectic mix of astronomy/astrology, medical advice, weather prediction, and other things.  Here's a math-problem-poem from that Almanack -- found, along with others, at Mahoney's site: 

The best of the many

     Here I link to an article by David Alpaugh, "The New Math of Poetry," -- not brand-new, for it bears a date of February, 2010 , but I found it only recently and have been thinking about its description of the seemingly unrestrained quantity of poetry expected to be published on the Internet. What happens to poetry if each of us calls what she writes "poems" and publishes them online, making them as available as the lines penned by a Poet Laureate? 
     Most of what I feel about proliferation of poetry is excitement.  I love the democracy that lets all of us participate in poetry just as we all may run races, perhaps even taking a trophy in our neighborhood's turkey-day mile;  we do not pretend excellence but, simply, it is fun and good for us.  All of us who choose it can enjoy writing poems -- and experimentation with new forms -- and, from time to time, some surprising and splendid work will emerge. 

Surprise me!

Bob Grumman, a mathy poet whose work has appeared in this blog (21 June 2010) and a blogger, has recently been invited to write a Guest Blog for Scientific American.  Here is a wonderful sentence about poetry that I have taken from his posting on 22 September 2012 (the third of his guest postings).

           And I claim that nothing is more important for a poet 
               than finding new ways to surprise people with the familiar.

Visit Grumman's Guest Blog to find his illustrations of poetic surprise; after a pair of visual poems, ten x ten and Ellipsonnet, he discusses a poem by Louis Zukovsky in which the poet describes his poetics using the integral sign from calculus:

∫ 

Zukovsky's definite integral (which Grumman tells us is carefully copyright-protected) has the lower limit "speech" and upper limit "music." 

From the Scottish Cafe

     A poetry collection by Susan Case (see also 5 July 2011 and 5 August 2011 postings)  -- The Scottish Cafe (Slapering Hole Press, 2002) -- celebrates the lives and minds of a group of mathematicians in Poland during World War II.  The observations and insights of Case's poems add new dimension to the important story of The Scottish Book  -- a book in which the mathematicians recorded problems and their solutions.  

The view from here -- or there

From Nashville math teacher and blogger, Tad Wert, I learned of this poem, "Geometry, Lost Cove" by his Harpeth Hall School colleague, Georganne Harmon; in it, Harmon examines the contrasts in appearances when objects are seen from different distances. (And the mathematician goes on to say, Ah, yes -- in other words, some mappings of a space do not preserve distance.)

    Geometry, Lost Cove     by Georganne Harmon

    The ridge across this cove
    is straight as a ruled line,
    its bend as pure as an angle
    on a student’s quadrilled page.
    Beyond it another ridge lies
    straight-backed, as well,
    drawn off by its touch with sky.

Is Algebra Necessary?

     Anticipating my interest, several friends sent me links to a late-July opinion piece in The New York Times entitled "Is Algebra Necessary?" (written by an emeritus political science professor, Andrew Hacker).   I more-or-less agree with Hacker that algebra is not necessary in most daily lives or places of employment.  In fact, years ago I developed a non-algebra text, Mathematics in Daily Life,  for a course designed to satisfy a math-literacy requirement at Bloomsburg University.  On the other hand, my own fluency in the language of algebra opened doors to calculus and to physics and so many other rooms of knowledge that I have loved.
     Expressing algebraic issues in verse, we have this thoughtful poem by Jeannine Hall Gailey, Poet Laureate of Redmond, Washington (home of Microsoft). 

A poem for a math-friend

     On July 14, 2012, my good friend, Toni Carroll, passed on. I first knew Toni in the 1980s as a colleague in the department of mathematical sciences at Bloomsburg University.  Her warmth and inclusiveness drew many people to her and I was one of these.  In my view she also was fearless.  While I continued to contemplate action, she moved quickly toward righting an injustice.  I have learned from her to be a bit more brave.  

Variations of a line

In mathematics a line plays many roles -- as in this fine poem (which is a sonnet, more or less).

     Lines     by Martha Collins

     Draw a line. Write a line. There.
     Stay in line, hold the line, a glance
     between the lines is fine but don't
     turn corners, cross, cut in, go over
     or out, between two points of no
     return's a line of flight, between
     two points of view's a line of vision.

It Crossed My Mind

     In Elinor Gordon Blair --  my English teacher during my junior and senior years at Indiana Joint High School in Indiana, Pennsylvania -- I found a woman who became a life-long inspiration to me.  An insatiable reader and always curious, Elinor Blair seemed to learn from every thing that came along. Such an excellent strategy  -- and I learned it from her.  
     Mrs Blair -- is my habit to continue to call her by this formal name -- still lives in Indiana and she is 99 years old.  Three years ago she published a poetry collection, It Crossed My Mind.  These following stanzas from Blair's collection use imagery from geometry to describe the destructive way in which "skeletons of steel" have remade our American landscapes. 
     Thank you, Mrs. Blair, for these lines and for the ways you have enriched my life.

An instrument in the shape of a woman

     Celebrating math-women with poetry is a project to which I devoted several postings earlier this summer -- see, for example, these June and July entries.  Moreover, I am looking for more such poems to post.  Please contact me (e-mail address is at the bottom of this blog-site) with poems about math-women that you have written or found.
      Mathematician-astronomer Caroline Herschel (1750-1848) appeared in a poem by Siv Cedering on 21 July, 2012 and here she is again, this time celebrated by Adrienne Rich (1929-2012).

Fibs in NZ -- and climate change

     A few days ago, on August 21, it was Poet's Day in New Zealand and the blog sciencelens.com featured a math-poetry theme; that posting mentions the anthology, Strange Attractors:  Poems of Love and Mathematics (for which Sarah Glaz and I are co-editors) and offers several Fibs, poems whose syllable-counts follow the first six non-zero Fibonacci numbers (1, 1, 2, 3, 5, 8, . . .., with each succeeding number the sum of the two preceding). 

What is mathematics to animals?

In a playfully serious volume of verses by Eugene Ostashevsky we meet his alter ego, the "new philosopher" DJ Spinoza.  With the intelligence and bravery of the other philosopher-Spinoza (Baruch / Benedict, 1632 - 1677), Ostachevsky's Spinoza pokes a bit of fun at things that might be taken too seriously -- such as logic or mathematics or . . .  

Mindless chance

From the 2005 Summer issue of from  Prairie Schooner we have this haunting poem by Diane Mehta about the unknown probabilities of life and not-life.

    1 in 300     by Diane Mehta

    To lose at science is the accident of trying,

    for worse or, best, acceptable ways cells divide

    then swell into heart, spleen, spine

    for every satisfaction, and love also aligned 

Math humor

      Phyllis Diller (1917-20120), outspoken and funny, pioneering female comedian, died Monday, August 20.  Her self-deprecating humor was hugely hilarious -- and it helped the rest of us also not to take ourselves too seriously.

     In honor of Phyllis Diller and humor, I first offer a link to a "poem" from a favorite math-cartoonist -- Randall Munroe offers an amusing rhyming critique of the various majors (including math) available to undergraduates --  at xkcd.com.   And, below, I share several slightly funny math jokes adapted from ones found at Math Jokes 4 Mathy Folks and shaped into 4x4 or 5x5 syllable-square poems.

Worth of a horse

When my friend Kay and I visited the National Museum of the American Indian Museum in Washington last Wednesday, August 15, we particularly enjoyed the exhibit entitled "A Song for the Horse Nation." These displays explore the role of horses in Native American lives through stories and artifacts, through music and art.  Shown below is a photo of a sign that hangs in the exhibit.  I first intended to use the text on the sign -- with its many numbers -- as raw material for a poem.  But, as I have reviewed the sign since my visit -- including reading it aloud -- I have decided it is already a poem.  Here it is, for you:

Free vs Constraints -- Sandburg - Frost

One of the delights of investigation -- in library books or on the internet or walking about in the world -- is that one bit of information opens doors to lots of others.  And so, as I was learning about Eleanor Graham for Monday's posting, I found her essay entitled "The first time I saw Carl Sandburg he didn't see me" and was reminded in a new way of the ongoing debate about the value of formal constraints in poetry. 

Thirty and three

One of my poetry collections is a particular treasure because of its history.  My aunt, Ruth Margaret Simpson Robinson, graduated (as I also did) from Westminster College in New Wilmington, Pennsylvania.  At Westminster, a Chi Omega sorority sister of Aunt Ruth was Eleanor Graham Vance (1908-1985) who became a teacher and a writer; one of her biographical sketches mentions that she wrote for both children and adults, seeing many similarities between them.  Aunt Ruth passed on to me her personally-inscribed copy of  Eleanor Graham's 1939  collection, For These Moments, and in it I have found a poem with a tiny bit of arithmetic. I offer it here to you. 

Summing thin slices

This poem by recent (2008-2010) poet laureate Kay Ryan at first made me think of calculus, of integration, summing all the thin slices to find the area under a curve.  And then the poem moved me on. 

Spanish favorites

One of my favorite DC-area poet-people is Yvette Neisser Moreno -- who, besides giving us her own work, is active in translation of  Spanish-language poetry into English, most recently (with Patricia Bejarano Fisher) a Spanish and English edition of Venezuelan poet Maria Teresa Ogliastri’s South Pole/Polo Sur  (Settlement House, 2011).  Although I have not found any mathematical poems by Moreno, I learned from an interview that the Chilean Nobelist Pablo Neruda (1904-1973) is her favorite poet and I therefore present here the geometrically vivid opening opening stanza of Part XI of Neruda's well-known long poem, The Heights of Macchu Pichu: A Bilingual Edition (The Noonday Press, 1966). 

JHM -- many math poems

     Volume 2, Issue 2 (July 2012) of the Journal of Humanistic Mathematics has recently become available online -- and it has lots of poetry.  One valuable resource has been gathered by Charlotte Henderson, a participant in the January 2012 poetry reading at JMM in Boston; Charlotte offers a report on that reading and also has prepared a folder of the poems read there, collected for our ongoing enjoyment.  In this issue also there are poems by Florin Diacu, Ursula Whitcher, and Paige S. Orland and some kind words about this blog by Gregory E. Coxson (JoAnne Growney's Poetry-With-Mathematics Blog -- An Appreciation); many thanks, Greg.
      In the wake of the BRIDGES math-art conference at Towson University last week I also want to mention the lively blog posting about BRIDGES by Justin Lanier at Math Munch. 

For Hazlett -- an Exquisite Corpse poem

At the recent BRIDGES Math-Art Conference at Towson University, I led a Sunday afternoon Poetry-with-Mathematics Workshop.  One of our writing topics was women mathematicians and, using material from a richly varied website of biographies of math-women, supported by Agnes Scott College, we workshop participants read a bio of Olive Clio Hazlett (1890-1974) and each wrote sentences of the form "This woman . . . " which I have assembled and and slightly edited into the following poem.

Math super-hero

One day not long ago I told my Silver Spring neighbor, Nancy KapLon (nee Lon), of my interest in helping outstanding math-women to be more widely known.  Nancy told me about her wonderful and excellent favorite teacher -- geometer Jean Bee Chan of Sonoma State University in California. Nancy ('93) was a  first generation college student and Dr. Chan, as her mentor, guided her through the undergraduate experience to graduation with distinction and graduate school. Here is a syllable snowball, grown in Chan's honor. 

Math-women -- snowballing . . .

These syllable-snowball poems (increasing by one syllable from line to line)
note a few of the (living) math-women I admire.  

They are modest offerings --
not great poetry nor fully recognizing many accomplishments--  

but I want to start a ball rolling: 
look around you and notice the amazing math-women. 

She had a way with numbers

In Letters from a Floating World, artist and poet Siv Cedering (1939-2007) has given us a poignant portrait of astronomer (and math-woman) Caroline Herschel:
 
Letter from Caroline Herschel (1750-1848)     by Siv Cedering

William is away, and I am minding

the heavens. I have discovered

eight new comets and three nebulae

never before seen by man,

and I am preparing an Index to

Flamsteed's observations, together with

a catalogue of 560 stars omitted from

the British Catalogue, plus a list of errata

in that publication. William says 

An algorithm shapes a poem

Mathematics sometimes appears in poetry via patterns that follow the Fibonacci numbers. The pattern of Pascal's triangle also has been used.  In her intriguing collection, Do the Math  (Tupelo Press, 2008),  poet Emily Galvin (now also a California attorney) uses these and more.  Just as Euclid's Algorithm involves an interaction between two numbers, the following poem by Galvin applies the algorithm in a conversation between two voices.

Euclid's Algorithm    by Emily Galvin

These ten scenes happen on the blank stage.

A and B could be any two people, so long as

they've been together for longer than either

can remember.

More of Hypatia -- brave, smart woman

Poet and blogger Ellen Moody offers a lively and informative feature on poet Elizabeth Tollett (1694-1754); Tollett, too, wrote of forebears she admired, including Hypatia (c. 370 C. E. - 415 C.E.) -- who has been described as the first woman to make a substantial contribution to mathematics. In contrast with Anne Harding Woodworth's focus on the tortured death of Hypatia, Tollett's lines portray the struggles of her life.

    Hypatia     by Elizabeth Tollett

    What cruel laws depress the female kind,
    To humble cares and servile tasks confined!
    In gilded toys their florid bloom to spend,
    And empty glories that in age must end;
    For amorous youth to spread the artful snares,
    And by their triumphs to enlarge their cares. 

She died for mathematics

     Hypatia of Alexandria (in Greek: Υπατία) (c. 370 C.E. – 415 C.E.) was a popular Egyptian female philosopher, mathematician, astronomer/astrologer, and teacher in Egypt. Her father Theon, a mathematician and the last librarian of the Museum at Alexandria, educated her in literature, science and philosophy, and gave her credit for writing some of his mathematical treatises. 

What are the chances?

Ohioan Miles David Moore is an active participant in Washington, DC literary activities, including a reading series at Arlington's Iota Cafe.  The voice of his literary creation, Fatslug, adds jest and pathos to many readings.  In the poem below, Fatslug is victim of choice and chance:

Visit BRIDGES -- for (art and) poetry

This growing-then-melting syllable-snowball poem is offered in recognition of mathematician-and-poet Sarah Glaz and as a reminder of the poetry reading Glaz is organizing --  to be held at the 2012 BRIDGES Math-Art conference at Towson University, July 25-29.

SHE can solve any equation!

Today's New York Times offers a tribute to Mildred Spiewak Dresselhaus, a professor emerita of physics and engineering at MIT.  The Times article, by Natalie Angier, begins with this verse from the 1948 Hunter High School yearbook:

     MILDRED SPIEWAK

     Any equation she can solve;

     Every problem she can resolve.

     Mildred equals brains plus fun,

     In math and science she's second to none.    

Emily Dickinson -- and circumference

     Great poets may be investigated from many points of view.  For Emily Dickinson (1830-1886), some have noticed that her work employs particular terms from mathematics.  Including a much-quoted line -- "My business is circumference" --  in a letter to Colonel Thomas Wentworth Higginson, Dickinson is said to have used the word "circumference" in six letters and seventeen poems.  For example, the word appears in both of the poems offered below:

     633     by Emily Dickinson

     When Bells stop ringing—Church—begins
     The Positive—of Bells—
     When Cogs—stop—that's Circumference—
     The Ultimate—of Wheels.    

Remembering Sophia Kovalevsky

With Reason: A Portrait     by JoAnne Growney   (June 2012)

        Sophia Kovalevsky *    (1850-1891)

Because she was Russian  . . .
Because she had abundant curly hair . . .
Because she loved mathematics . . .
Because she was born in the 19th century . . .
Because lecture notes for calculus papered  her nursery walls . . .
Because her parents forbade her to leave home . . .
Because a woman could not travel abroad from Russia 
                    without her father or a husband . . .
Because she found a kind man to marry . . .
Because ideas came to her in torrents . . .
Because she married a man she did not love . . .

Seeking poems about math-women

In this blog I have previously posted poems that speak of the lives of these math-women:

     Sophie Germain (1776-1831)

     Florence Nightingale  (1820-1910)

     Amalie "Emmy" Noether  (1882-1935)

     Grace Murray Hopper (1906 - 1988)

And also a poem about four influential teachers of mine; three of them math-people; three of them women.

I want more poems about women in mathematics;   
send me yours (or those of others) -- 
write new ones; CELEBRATE women in mathematics:

women who are alive or ones that have passed; 

women of fame or those without; 

women out in front or those in quiet corners -- 

women we want to remember.

Sophie Germain dressed as a man to study math

One of the fine sources for biographies and other topics in the history of mathematics is MacTutor History of Mathematics archive, hosted by the University of St Andrews in Scotland.  Poet Brian McCabe cites this archive for historical information he used as background for his poems starring mathematicians -- found in his collection, Zero (Polygon, 2009).  Here is McCabe's poem for the outstanding French mathematician, Sophie Germain (1776-1831). 

Can mathematics maximize happiness?

     My post for last Monday (11 June 2012) offered a link I would like to repeat:  to an article by Judy Green, "How Many Women Mathematicians Can You Name?"  (first published in Math Horizons in 2001).  One of the seven names in Green's opening paragraph is "Sofia Kovalevskaia" (1850 - 1891); this prizewinning Russian mathematician (whose name appears with a variety of spellings, including "Sophia Kovalevsky" and "Sonya Kovalevskaya") was also a writer of literary work -- several novels, a play, a memoir, some poetry.  

Think Like a Man

     To publish mathematics,
     a woman must learn to think
     like a man, learn to write like
     a man, to use only her
     initials so reviewers
     guess she's a man!  Women must
     masquerade, pretend man-think --
   
     or can we build
     new attitudes,
     so all of us
     have fair chances?!        ("Square Attitudes"   by JoAnne Growney)  
 

Computer code -- is poetry?

Dubliner Eavan Boland is a master poet (and one of my favorites); Ireland shares her with the creative writing program at Stanford University.  In Against Love Poetry (Norton, 2001), we find Boland's tribute to the also-amazing master of language, Grace Murray Hopper (1906-1988).

                     Code          by Eavan Boland

             An Ode to Grace Murray Hopper  1906-88

    maker of a computer compiler and verifier of COBOL 

   Poet to poet.  I imagine you

     at the edge of language, at the start of summer

       in Wolfeboro, New Hampshire, writing code.

         You have no sense of time.  No sense of minutes even.

           They cannot reach inside your world,

             your gray work station

               with when yet now never and once.

                 You have missed the other seven.

                   This is the eight day of Creation.

Sum of moments

Here is a 3x3 square poem -- inspired by a recently-found margin-note I made in Differential and Integral Calculus (by Ross R Middlemiss) when it was my text for an introductory calculus course at Westminster College all those years ago:

          The sum of

          the moments

          is zero.

While the pages of text near the note go on with discussions and diagrams of slices and sums and limits -- they introduce the centroid, the moment of inertia, and the radius of gyration, and are importantly informative -- it is the margin-note that has today delighted me.  I wonder if the girl who wrote it saw it as I do today. I like the mystery.

Counting the dead

This poem by Joan Mazza heightens the impact of war-data by bringing it into the kitchen and the office -- juxtaposing war-numbers with the events of a pleasant day in central Virginia.  

Numbers for the Week       by Joan Mazza

This morning, it was twenty-eight degrees. I photographed
red oak leaves rimed with frost. I made chicken soup, canned
ten pint jars in the pressure cooker at fifteen pounds of pressure
for seventy-five minutes. On the stump near the compost pile,
I left the skin of fourteen chicken thighs for crows and woodpeckers.  

Arithmetic of war

     In his poem, "Arithmetic on the Frontier," Rudyard Kipling (1865-1936) wrote of Britain's nineteenth century military aggression in Afghanistan.  His words remind us of important questions:  what is the cost of a life lost in battle?  are some lives cheap and some more dear?

 
     Arithmetic on the Frontier     by Rudyard Kipling

     A great and glorious thing it is
         To learn, for seven years or so,
     The Lord knows what of that and this,
         Ere reckoned fit to face the foe --
     The flying bullet down the Pass,
     That whistles clear: "All flesh is grass."

Remembering Israel Lewis Schneider

     On Monday, October 17, 2011, Israel Lewis Schneider (1924-2011) --  Silver Spring poet and mechanical engineer -- passed away.  I did not learn of this death until yesterday -- when my colleague, Sarah Glaz, let me know that an e-mail to him had bounced back and I went online searching for him.

     It has been my pleasure to get to know "Lew" (who published poetry under the name, Israel Lewis) at local poetry readings where we connected over our common interest in poetry-with-mathematics.  Lew's poem, "I Find My Faith in the Flatness of Space," appeared in the anthology Strange Attractors:  Poems of Love and Mathematics (edited by Glaz and me) and his poem for two voices, "Cantor:  Not Eddie,"  appeared here in this blog on 24 July 2010.  Shortly after that July posting, Lew sent another poem for my review.  To celebrate the life of this kind, funny, and very talented man, I offer here that poem -- with its playful examination of mathematical and other identities -- "Who Steals My Trash . . . ":  

Crocheting mathematics

Charlotte Henderson majored in mathematics and English at Wellesley College and has applied her dual interests as an editor for A K Peters, Ltd (a science and technology publisher that is now part of CRC Press).  Several manuscripts on which she has worked at A K Peters have drawn her to the connections between mathematics and art, including needlework. She is particularly interested in the diverse possibilities of crochet, which she learned after working on Daina Taimina's book, Crocheting Adventures with Hyperbolic Planes.   Charlotte has turned this interest into art and into a poem: 

Taking Stock

Developing an inventory -- of what we have or have experienced, of what we see or imagine -- inevitably involves numbers and counting.  As in "Inventory" by Canadian poet Colin Morton, an adaptation or "free translation" of  "Inventaire" by Jacques Prevert.  Morton has a strong connection to mathematics --  his son is a mathematician at the Technical University of Lisbon.

  Inventory       by Colin Morton

  one lump of rock
  two houses
  three ruined foundations
  four gravediggers
  one garden
  some flowers

Before calculators we did more counting!

One of many sources of good poetry online is American Life in Poetry, collected by former U S Poet Laureate Ted Kooser.  In Column 368, Kooser offers "Numbers" by New Jersey poet, Jared Harel (first published Fall 2010 in The Cold Mountain Review).  Kooser's introduction notes, "My mother kept a handwritten record of every cent she spent from the day she and my father were married until the day she died. So it’s no wonder I especially like this poem  . . . " 

Natural numbers

     My just-previous posting tells of a Monday poetry reading I was able to attend.  On Monday, May 14, a poetry reading took place that I wanted to attend but missed; poet Gary Snyder read at the Folger Shakespeare Library. 
     Written in the 1950s and read by him here on YouTube, Gary Snyder's poem, "Hay for the Horses," involves a mathematical calculation: 

Poetry in DC -- counting sheep

The Washington, DC area offers a rich diversity of poetry events -- workshops and readings, contests and conferences.  An excellent way to find out what's happening is through the online listing, Beltway Poetry News, maintained by editor and poet Kim Roberts.  One of the very active DC poetry organizations is The Word Works whose board chairperson, Karren Alenier, is also a fine poet. 

Last week I enjoyed one of Karren's readings -- at Café Muse in Friendship Heights Village Center.  On May 7 Karren read from her recent collection, On a Bed of Gardenias:  Jane and Paul Bowles (Kattywompus Press, 2012).  These poems were exciting to hear --  they are part of an opera libretto that Karren is working on -- but not mathematical; thus, I turn back to one of her earlier poems, "Dialectic of the Census Takers," for presentation here. 

Ode to Alan Turing

In this week of announcements in the US about evolving views concerning human sexual preferences, it seems fit to offer a second poem (see also May 9) honoring British code-breaker and computer scientist, Alan Turing (1912-1954).  Here is "Ode to Alan Turing"  by Saskatchewan poet, Mari-Lou Rowley. 

A toast to Alan Turing

     Alan Turing (1912-1954) committed suicide at the age of 42. He was brilliant, arguably the best computer scientist of the twentieth century.  He is perhaps most famous for his code-breaking work at Bletchley Park during WWII; but he also made enormous significant contributions to the emerging fields of artificial intelligence and computing. And Alan Turing was gay. 

     More prose details will follow -- but first a poem for Turing by UK poet Matt Harvey : 

A square -- for everyone!

all     all

all     all

This square pun by Aram Saroyan appears in his Complete Minimal Poems  (Ugly Duckling Presse, 2007).  Other Saroyan poems may be found in the posts for 9 November 2010  and 30 November 2010 .

Pipher -- Math experiments, Pi

     'Tis a favorite project of mine

     A new value of pi to assign.

          I would fix it at 3

          For it's simpler, you see,

     Than 3 point 1  4  1  5  9.