The hypotenuse of an isosceles triangle

Detroit poet, Philip Levine, has been selected as the new Poet Laureate of the United States. Selected by the librarian of Congress (James Billington), Levine follows poet W. S. Merwin in the honored position.  A Poet Laureate is responsible merely for giving readings in October and May but some laureates also use the position to proselytize for poetry.   Here, from Levine's early collection, What Work Is (Knopf, 1992), is a poem that looks back on a math-art moment in a middle-school classroom.

Can a mathematician see red?

Held late in July, this year's 2011 Bridges (Math-Arts) Conference in Coimbra, Portugal included a poetry reading for which I'd been invited to read but was, at the last minute, unable to attend. (See also 26 July 2011). Poets Sarah Glaz and Emily Grosholz each, however, read favorite selections from my work.  Glaz read one of my square poems, "The Bear Cave" (see 19 June 2011) and Grosholz read the poem shown below, "Can a Mathematician See Red?"

Banach's Match Box Problem

A poetry collection by Susan Case (see also 5 July 2011 posting)  -- The Scottish Cafe (Slapering Hole Press, 2002) -- celebrates the lives and minds of a group of mathematicians in Poland during World War II. Its observations and insights add a new dimension to the important story of the Scottish Book to which it refers -- a book in which the mathematicians reorded their problems and solutions. First published in a mimeographed edition in 1957 by Stanislaw Ulam, The Scottish book: mathematics from the Scottish Café (Birkhäuser, 1981) may now be seen and searched at GoogleBooks.  Case's collection includes statements of two of the Scottish Book's problems:  here, below, is "problem 193" -- which I offer as a "found poem."  A photo of its Scottish Book solution follows.

Cantor Ternary Set

The second issue of the Journal of Humanistic Mathematics has recently been posted -- with more new poems.  The first issue contained a poem by Philip Holmes about one of the most amazing collections of numbers in all of mathematics, the  Cantor Ternary Set.  This set, discovered by Henry John Stephen Smith (1826-1883) but popularized by Georg Cantor (1845-1918) consists of all the real numbers whose base 3 or ternary representations involve only the digits 0 and 2. Like a fishing net, the Cantor Ternary Set is mostly holes. "Gaps" by Philip Holmes spreads it out before us -- and reflects on what else it may represent:

Puzzle play

In volume 4 of The World of Mathematics (James R Newman, Editor; Dover 2003), in a section entitled "Amusements, Puzzles, and Fancies," is an essay by Edward Kasner and James R. Newman entitled "Pastimes of Past and Present Times." This piece is prefaced by a quote from Mark Twain: "Work consists of whatever a body is obliged to do, and play consists of whatever a body is not obliged to do." One of the characteristics that mathematicians and poets have in common  is that both enjoy mind-play -- mental adventures with ideas or numbers or words, dancing and shaping into some new thing.

Mathematical Induction -- principle, perhaps poem

One of my teachers -- I think it was Mr Smith in "College Algebra" during my freshman year at Westminster -- gave me these words to remember:

     When confronted
     with a statement
     that seems true
     for all positive integers
     the wise student
     uses mathematical induction
     as her proof technique. 

Bridges in Coimbra

     Newton's binomial is as beautiful as Venus de Milo.
     What happens is that few people notice it.

                -- Fernando Pessoa (as Álvaro de Campos) (1888-1935)
                    translated from the Portuguese by Francisco Craveiro

Little Infinite Poem

   Little Infinite Poem       by Federico Garcia Lorca

               For Luis Cardoza y Aragón

      To take the wrong road
   is to arrive at the snow,
   and to arrive at the snow
   is to get down on all fours for twenty centuries and eat
         the grasses of the cemeteries.

The wind, counting

     Who can ever forget
     listening to the wind go by
     counting its money
     and throwing it away?

Finding a square root

Here is an old poem (1849) by George Van Waters that offers instruction on finding a square root. This process was part of my junior high learning at the Keith School in Indiana, PA lots of years ago but I suppose the algorithm is seldom taught in 21st century classrooms.  (In case the poem's directions are unclear, additional instruction is offered here.)

I have dreamed geometry

   Descartes     by Jorge Luis Borges

   I am the only man on earth, but perhaps there is neither earth nor man.
   Perhaps a god is deceiving me.
   Perhaps a god has sentenced me to time, that lasting illusion.
   I dream the moon and I dream my eyes perceiving the moon.
   I have dreamed the morning and evening of the first day.

Seeking a universal language

Is mathematics a universal language?  Not only is this universality often postulated but also it was said  -- some decades back -- that devices were broadcasting into space the intial decimal digits of pi, expecting that other intelligent beings would surely recognize the sequence of digits.  Robert Gethner examines this arrogance in a poem.

Ancestry -- what counts

Etheridge Knight began writing poetry while an inmate at the Indiana State Prison and published his first collection, Poems from Prison, in 1968.  His poem "The Idea of Ancestry" shows us what a man in prison finds time to count:

   The Idea of Ancestry   by Etheridge Knight

          1
  
   Taped to the wall of my cell are 47 pictures: 47 black
   faces: my father, mother, grandmothers (1 dead), grand-
   fathers (both dead), brothers, sisters, uncles, aunts,
   cousins (1st and 2nd), nieces, and nephews. They stare
   across the space at me sprawling on my bunk. I know
   their dark eyes, they know mine. I know their style,
   they know mine. I am all of them, they are all of me;
   they are farmers, I am a thief, I am me, they are thee.

Mathematicians at work

     About her collecton, The Scottish Café (Slapering Hol Press, 2002), Susan Case offers this note:
     This series of poems is loosely based upon the experiences of the mathematicians of the Scottish Café, who lived and worked in Lvov, Poland (now L'viv, Ukraine), a center of Eastern European intellectual life before World War II, close to the area from which my own ancestors emigrated to the United States.  A book, known as the Scottish Book, was kept in the Café and used to write down some of their problems and solutions.  Whoever offered a proof might be awarded a prize.
     Here is "Fixed Points," the opening poem from Case's collection:

Mathematicians divide

One of my fine graduate courses at Hunter College was a "World Poetry" course taught by William Pitt Root.  One of our texts was Against Forgetting:  Twentieth-Century Poetry of Witness (W W Norton, 1993), edited by Carolyn Forché.  In this collection is found "To Myself," a poem that confronts fear, by Abba Kovner (1818-1987), a hero of anti-Nazi resistance. Kovner dares to open the poem with the word "Mathematicians."

5 x 5 and 6 x 6

Many poets have found the sonnet to be an ideal poetic form -- its iambic pentameter lines are like five heartbeats assembled in a single breath;  its fourteen lines are a good number for considering a matter carefully. My own frequent form is different -- not a sonnet but a square of some or another dimension.   Here are two of my recent syllable-squares.

     I squint with tension,
     puzzle over this:         
     dissatisfaction's
     itchy appetites
     are my happiness.

The Joys of Mathematics

   The Joys of Mathematics     by Peter Boyle

   At fifty I will begin my count towards the infinite numbers.

   At negative ninety nine I will start my walk towards the
      infinitesimally small.

Creation Myth on a Mobius Band

On the  website of Bert-Jaap Koops, I found this small poem by a poet I admire greatly, Howard Nemerov (1920-1991).

     Creation Myth on a Moebius Band   by Howard Nemerov

     This world’s just mad enough to have been made
     by the Being His beings into Being prayed.

Something for nothing

     Among my favorite mathematical ideas are the seeming-paradoxes -- notions that require a twist and a turn and a leap before one can say "aha."  Using a symbol for "nothing" is one of those leap-requiring ideas.  I don't remember when I first understood zero, but I have enjoyed watching my children -- and now grandchildren -- grapple with ideas of things that are absent rather than present. 
     Here, from Hailey Leithauser, is a poem  that celebrates the cipher. 

Circling -- with Rilke

Ranier Maria Rilke (1875-1926) was born in Prague but emigrated to Germany and is one of the great modern lyric poets.   The following Rilke poems draw on images of circles.

Found in Flatland

Over the years I have shared with friends and students my copy of Edwin Abbott's Flatland (first published in England in 1884) and, alas, not all of these other readers have matched my level of excitement with the small volume.  Even though the book's Victorian attitudes are mostly at odds with my own views, still the tiny book opened me to possibilities of new ways of seeing. Since observing the Flatlanders stuck in two dimensions from my advantageous three-dimensional position, I have wondered how I can now make the leap from three to four or more dimensions.

Stanescu - poetic mathematics

Today I found a link to a recent article, "Matematica şi poezia," that considers commonalities among the arts and mathematics and, therein, mentions a poem by Nichita Stanescu (1933-1984) which Gabriel Prajitura and I have translated.  The poem, "Poetic Mathematics," is dedicated to Romanian mathematician Solomon Marcus.  Here is Gabi's and my translation: 

Lagrange points

The Italian-French mathematician Josef Lagrange discovered the existence of five special "Lagrange points" (aka Lagrangian points) in the vicinity of two orbiting bodies where a third, smaller body can orbit at a fixed distance from the larger ones. More precisely, Lagrange Points mark positions where the gravitational pull of the two large bodies precisely cancels the centripetal acceleration required to rotate with them. Poet Catherine Daly considers these points in a poem:  

Counting on things -- a prose poem

Russell Edson is one of the contemporary masters of the prose poem (a poem whose words are organized into paragraphs rather than stanzas). A selection from May Swenson's prose poem (and short novel) "Giraffe" is available in the October 19 blog posting. Here is Edson's poem "One Two Three, One Two Three" -- which considers the secrets hidden inside one's head.  Another mind, even that of one of our children, is a mystery incompletely known to any of us.

Right Triangle

The shape of a poem influences our reading of it -- short lines cause reading with lots of pauses whereas we read long lines quickly to get the entire line completed in a single breath. Moreover, some poetry is intended to be primarily visual -- to be taken in as a seen-image rather than read.  UBU Web offers several example of early visual poetry and one may also explore the  UBU Web site for modern examples.  Visual poetry may also be termed "concrete" poetry; consider, for example, "Concrete Block" by Michael J. Garofalo:

Math lyrics -- Lehrer et al

Mathematicians with poetic tendency often use their word-talents to write song-lyrics rather than poems; a master of the song-writing art was/is Tom Lehrer.  As an undergraduate at Harvard in the 1940s,  Lehrer majored in mathematics; he is best known for songs he recorded in the 1950s and 1960s.  Here are Lehrer's lyrics for "The Derivative Song" -- written to be sung to the tune of "There'll Be Some Changes Made" (by Benton Overstreet, with original lyrics by Billy Higgins).

A square poem of Romania

When I'm working on a poem that resists my efforts to express what I must say, sometimes I turn to the square for a rescue -- that is, I attempt to find the best words by re-forming the poem as a square (same number of lines as syllables per line).  That is how I came to the following poem, "The Bear Cave,"  (a 9 x 9 square). 

Fear of math

California poet Carol Dorf is a high school math teacher (and has taught in a science museum) -- and images from math and science permeate her work.  An article on math anxiety (and its connections to the brain) in today's Washington Post brought to my mind this poem of hers: 

Once a student of Euclid

The Chair     by Charles Simic

The chair was once a student of Euclid.

The Bridges of Konigsberg

From the August 1997 issue of The Mathematical Intelligencer, we have this poem by Judith Saunders about a long-standing puzzle solved solved by the mathematical giant, Leonhard Euler (1707-1783).

Hikmet -- painting with numbers

Living is no laughing matter . . . 

These are words of Turkish poet, playwright, novelist and memoirist Nazim Hikmet (1902-63), who spent much of his life in prison or exile for his political beliefs.  In the following poem by Hikmet we see a portrait that builds from the numbers that characterize the landscape of Ibrahim Balaban's painting.  As you read Hikmet's poem, consider the value of numbers in portraiture.  Though they do not have the textures of color nor the movement of lines, numbers have shapes and edges that may much enrich our seeing. 

Spacetime

   Spacetime     by Miroslav Holub (1932-1998)

   When I grow up and you get small,
   then --

Personal geometry

We have recently passed the first anniversary of the death (6 May 2010) of Elena Shvarts, one of Russia's finest contemporary poets. Here is her "Poetica -- More Geometrico" (translated into English by Thomas Epstein).

Poems with permutations

     Below, in the May 16 posting, this blog considered all of the permutations of a few words -- in search of "the best" arrangement. Today we illustrate word-permutations in poems.
     First, a few lines from poet Gertrude Stein (1874-1946) -- who was masterful in her distortions of ordinary syntax and in her use of language in new ways. Stein played with both repetition and rearrangement; here is a brief example:

     Money is what words are.
     Words are what money is.
     Is money what words are.
     Are words what money is.

Which is the BEST order?

At Bartleby.com, we find  a quote from Samuel Taylor Coleridge (1772-1834) which says, in part " ... poetry—the best words in their best order." 

Consider the two orderings of the words "were" and "we." (To choose which is best is not possible until we know more of what the writer wishes to say.)

          We were!
          Were we?

Would rationalists wear sombreros?

This final section of "Six Significant Landscapes," by attorney and insurance executive (and poet) Wallace Stevens (1879-1955), playfully explores the limitations of rigid thinking. 

If p, then q.

     Today's posting (as also on April 13)  presents variations of the conditional statment -- a sentence of the form "If ___, then ___" in which mathematical theorems often are expressed. (For example, "If m is an odd integer, then m² is an odd integer.")   More generally, a conditional is a statement of the form "If p, then q" -- where p and q denote statements. Poet E. C. Jarvis plays with the language of logical statements and with the idiomatic phrase "Mind your p's and q's" in his poem, "A Simple Proposition." 

Poetry generators

Blogger edde addad had an undergraduate major in creative writing -- and later earned a PhD in computer science.  He has written about and created poetry-generating programs. addad is one of the contributors to the blog Gnoetry Daily -- which offers ongoing discussion and examples of collaborative human-computer poetry generation.  Here is  "Mystery" -- a poem generated by eGnoetry (assisted by addad!):

Permuting words and and enumerating poems

Caleb Emmons teaches mathematics at Pacific University.  Here is his very-clever description of the requirements for a poem to be a sestina -- spelled out in a poem that is itself a sestina.  (A sestina has 39 lines and its form depends on 6 words -- arrangements of which are the end-words of 6 6-line stanzas; these same words also appear, 2 per line, in the final 3-line stanza.) 

A jar in Tennessee

     Several of my early insights concerning the connections between poetry and mathematics grew from ideas presented by poet Jonathan Holden -- of whom interviewer Chris Ellis (in 2000) asked this question:
     Ellis:  You have drawn similarities between poetry and mathematics. Can you explain the association or similarity between poetry and math in a way the mathematically challenged can grasp?
     Holden: The "poetry and mathematics" analogy was simply to demonstrate, for those with some mathematical sophistication, that both languages "measure" things.

Forgetful Number

A lovely poem about more than a number . . .

    Forgetful Number  by Vasko Popa

    Once upon a time there was a number
    Pure and round like the sun
    But lonely very lonely

    It started to calculate by itself 

Perpendicularity -- a symmetric relation

     In 2010 both my October 13 and November 20 posts feature small poems by the French poet Guillevic (1909-97). Strongly drawn to his work, I have purchased the collection Geometries (Englished by Richard Sieburth, Ugly Duckling Presse, 2010); Guillevic has found in each geometric figure a personality and a voice. Buy the book and enjoy! Here is one of my favorites from the collection:    

Attitudes of Numbers

     I like Bruce Snider 's "The Certainty of Numbers" (which you may already have found online at The Poetry Foundation website, featured in the April 14  posting) even though I disagree with the initial attitude toward mathematics expressed by its narrator.  Writing a poem can be a voyage of discovery with the narrator's view flexing as the poem progresses.  
     Snider's poem brings to mind a view of mathematics that repeatedly bothers me:  I wonder why some people -- who would not complain about the fixendess of spellings of "cat" or "dog" or "sum" -- dislike mathematics for the so-called rigidity of  arithmetic facts such as "2 + 4 = 6."  ? ? ?

Earth Day, 2011

      My father, a farmer, was respectful of our earth's resources.  Replenish what you take, he taught.   But some of us consume without replacement as if the earth is infinite in its capacities. 
     When growth is exponential, we may not see its consequences before it is too late.  (Have we already destroyed the balances of nature?)  The following 8 x 8 syllable-square poem restates a oft-used math-textbook question -- and reminds us that little time may be left to solve environmental problems.   

Two and four and eight and birds

Pennsylvanian Craig Czury works as a travelling poet in schools, homeless shelters, prisons, mental hospitals, and community centers around the world.  Czury sent me the following translation, "Writing Sheet," by Willie Westwood of a poem by Jacques Prévert (1900-1977) -- the original French version  may be found at Westwood's site (scroll down).

Teaching math with a poem

Sarah Glaz is an algebraist (University of Connecticut) who uses poetry to teach mathematics. At her web page, scroll down to "Recent Articles" to see titles and links to three such papers.   One of the articles is "The Enigmatic Number e: A History in Verse and its Uses in the Mathematics Classroom" -- and it contains an annotated version of the poem whose opening stanzas are found below; it's found in the Digital Library of the Mathematical Association of America (MAA), Loci:  Convergence (April 2010). 

A picture should extend beyond its frame

Since April is Mathematics Awareness Month -- with theme "Unraveling Complex Systems" -- this blogger has been seeking out poems that embrace "complexity."  Today we have a selection by British poet, novelist, and critic John Fuller from his Newdigate prize-winning poem of 1960, "A Dialogue between Caliban and Ariel.". 

Finding poems with "numbers"

     Here's a quick and enjoyable activity:
     Go to the website for The Poetry Foundation.   Browse for a bit and, when you have completed your look-around, go to the search box toward the upper right and enter the word numbers, then click on the search button to bring a list of results.  On that new page, go to the left column menu and click on Poems.   Enjoy "Number Man" by Carl Sandburg and several other poems.
     When your time permits, search using a second mathematical term, and a third.  Bookmark the site.  April is National Poetry Month and Mathematics Awareness Month.  Celebrate!

Conditional statements

The "If ... , then ... ." statements of mathematical theorems are often termed "conditionals." We have, for example, the conditional, "If x < 3, then x² < 9."  And so on.  Formal conditional statements in a poem can give it the feel of mathematics, even if no mathematical terminology is used.  This is  illustrated in "Omens" by the Romanian poet Marin Sorescu (1936-1996); Sorescu's poem also treats us to word-play  -- with allusions that range from nursery rhymes to religious narratives. 

What can mathematics do?

For many, mathematics offers interpretive links between a mind and the truths it seeks to know,  the same role that a story plays in this poem -- "Story Water" -- by Jelaluddin Balkhi Rumi (1207 - 1273). 

A poetic perspective on algebra

     Last Monday (April 4), the Washington Post had an article concerning the value of Algebra II  as a predictor of college and work success.  Since then I have heard numerous successful people point out that they did not have the cited course.   Also on April 4, NPR had a feature on the advantages of being bilingual.   My own mind joined these two stories --  for me, algebra is a second language and has enabled my learning of lots of other things.
     Colette Inez 's poem "Forest Children" uses the language of poetry to speak of algebra (and of her concern for shrinking woodlands).

What color is 3?

     Long before there were six-digit hexadecimal codes for color (red #FF0000 or green #000800), there were paint-by-number craft activities.  And there is synaesthesia (syn -joined, aesthesia -sense),  a neurological condition in which two or more senses are connected. For example music might be "seen" in colours and patterns, or taste may have shapes, or letters and numbers have textures.
     Miroslav Holub (1923-98), Czech poet and research scientist (and one of my favorite poets) establishes number-color pairings in the following poem:

April -- month of poetry and mathematics

April is both National Poetry Month and Mathematics Awareness Month  (with theme this year being "Unraveling Complex Systems").  Today's poem by physicist Richard Feynmann (1918-1988) celebrates both poetry and complexity; from the Epilogue of  Feynman's book, What do you care what other people think?, we have these lines: 

Coleridge: A Mathematical Problem

 "A Mathematical Problem" by Samuel Taylor Coleridge (1772-1834) -- found online at Elite Skills Classics -- uses verse to describe construction of an equilateral triangle; Coleridge introduces the poem with a letter to his brother telling of his admiration of mathematics, a view rather rare among poets.   

The Nightmare of an Unsolved Problem

Back in the 1980s when I first met the Collatz conjecture in a number theory textbook it was stated this way:
     Start with any whole number  n :
          If  n  is even, reduce it by half, obtaining  n/2.
          If n is odd, increase it by half and round up to the nearest whole number, obtaining  3n/2 + 1/2 = (3n+1)/2.   Collatz' conjecture asserts that, no matter what the starting number, iteration of this increase-decrease process will each time reach the number 1.   

Numbers are more than numbers

Today, a poem in three parts, "Trouble with Numbers" -- from the collection Mathematics and Other Poems by William Wall. 

Celebrating Newman's "World of Mathematics"

Lionel Deimel is a database and Web site designer, a steam locomotive enthusiast, a cat lover, an essayist and a poet who maintains an eclectic website entitled Lionel Deimel’s Farrago.  There I found a small poem about one of my most-valued literary treasures, The World of Mathematics, a four-volume collection compiled with commentaries and notes by James R Newman, first printed in 1956. The range of topics is vast and the primary requirement for reading is not calculus but curiosity.  Sections of Volume 4 include "Mathematics in Literature," "Mathematics as a Culture Clue," and "A Mathematical Theory of Art." (You should not be without this fine collection.)    Here is Deimel's poem: 

Counting: 1, 2, 3, 4, 5, . . .

At Peter Cameron's Blog, "Counting the things that need to be counted," the July 14, 2010 entry contains a reflective poem entitled "Millenium" which meditates on the ten digits in stanzas whose lengths count them.  Here are the opening stanzas: 

Who are our prophets?

Here is the opening sentence of an article, "Mathematicians and Poets," by Cai Tianxin, a mathematics professor at Zhejiang University -- it appears in the April 2011 issue of Notices of the AMS:

     "Mathematicans and poets exist in our world as uncanny prophets."  

9 9-square stanzas

In the current (March 21, 2011) issue of The New Yorker (pages 46-47) may be found the poem "Green Farmhouse Chairs" by Donald Hall.  Hall's fine nostalgic poem consists of 9 stanzas; each stanza is "square" -- and has 9 lines with 9 syllables per line.   Enjoy!

Remembering Pi-day, a day late

Yesterday (3-14) was Pi-day, but my recent thoughts have been focused on my math-teacher son Eric (who has acute pancreatitis) and his family -- and I forgot to post this poem on the proper day.  Thanks to Lana Hechtman Ayers for these opening lines of  "Circumference:  A love poem." 

Teaching Math

When I was a new professor in the 1970s at Bloomsburg University (then Bloomsburg State College) my colleague PH and I discussed our teaching efforts and compared them with the ways we had been taught. We agreed that our university teachers seemed simply to dump mathematics on us in any manner whatever -- believing, it seemed, that those who were "smart enough" would pick it up.  (And other students should study sociology or communications  or the like.)  We and all around us worked to improve our teaching techniques and yet many years later it seems to continue that the privileged -- whether of wealth or education or gender or birthplace or whatever -- seldom see their advantages over those who are different.  And sometimes those of us who try the hardest fail our students because we do too much.  This latter idea led me to write this poem.

Numerology

On her website Deanna Rubin describes herself this way, "I have a degree in Technical Writing and Computer Science from Carnegie Mellon University, and my head is full of random numbers."  Illustrating this latter claim is her poem, "Numerology":    

Journal of Humanistic Mathematics -- V1, Issue 1

A new door has opened for those of us interested in the humanistic aspects of mathematics.  Under the able leadership of editors Mark Huber (Claremont McKenna College) and Gizem Karaali (Pomona College), the idea of the former Humanistic Mathematics Network Journal has been revived and Volume 1 Issue 1 of the Journal of Humanistic Mathematics is now available online.  The inaugural issue contains several poems, including the following one by Caleb Emmons, "Seeing Pine Trees,"  in which Emmons characterizes the views of a poet and a mathematician as two halves of one whole. 

Perfect as soap bubbles

An alert to today's poem came from Greg Coxson, a University of Wisconsin-educated, Silver Spring-based, radar engineer who loves mathematics and poetry.  The poem is by Howard Nemerov  (1920-1991) and it builds to a presentation of its perfect mathematical image near its end.  

Immense polygons of evening

Sometimes one wonderful line makes me fall in love with a poem. I offer the following -- in which the title first draws me in and then "immense polygons of evening" delights me even more.  Here, by Paula Closson Buck, is "A Betrayal of Integers," which uses mathematical terminology as the perfect mix of seasonings for a gourmet dish. 

Counting rhymes -- Catalan, Bell numbers

     In mathematics, the Catalan numbers (named for Belgian mathematician Eugène Charles Catalan, 1814–1894, and beginning with 1, 1, 2, 5, 14, 42, 132, 429, . . . ) and the Bell numbers (named for the Scottish mathematician Eric Temple Bell, 1883-1960, and beginning with 1, 1, 2, 5, 15, 52, 203, 877,  . . . ),  provide answers to a variety of mathematical counting-problems, including counting the number of rhyme schemes for stanzas of poetry.  In English, earliest classification of rhyme schemes dates back to George Puttenham and his treatise, The Arte of English Poesie (published around 1590). 

Poems of set paradox and spatial dimension

Universal Paradox     by Sandra DeLozier Coleman

     One gigantic set made of all that there is
     Boggles the mind with paradoxes.
     For it is greater than all, but smaller than this —
     The set which consists of the subsets of it.

Black History Month -- celebrate Haynes and Hughes

Living on the border of Washington DC I am exposed to items of local history for our nation's capital.  One such item involves the "discovery" of Langston Hughes (1902-1967) by poet Vachel Lindsay (1879 - 1931) at the Marriott Wardman Park Hotel, a leading conference hotel in the city.   A second story is a mathematical one.  Martha Euphnemia Lofton Haynes (1890-1980), a fourth-generation Washingtonian, was the first black woman to earn a PhD in mathematics -- conferred in 1943 by Catholic University. 

Srinivasa Ramanujan

One of the most intriguing tales in the modern history of mathematics involves Indian-born mathematician and genius Srinivasa Ramanujan (1887-1920) who traveled to England to work with G H Hardy (1877-1947).  Poet Jonathan Holden, who writes often of matters mathematical, offers this portrait of the Indian prodigy: 

Thinking about Thinking

The question of what it means to think is never far from my focus -- and is particularly on my mind during these days that the computer Watson is competing on the TV game show, Jeopardy.   Here is a poem I like a lot -- "New Math" by Cole Swensen  -- in which the poet (writing more than 20 years ago) considers the limits of computation (and whether it could aid persons unable to recognize faces). 

Puzzles, puzzlers, and parody

     For lots of fun, go to plus online magazine at this link to find a poem that requires a knight's tour of a chess board for you to unscramble its words and read its eight lines.

Loving a mathematician (Valentine's Day and . . . )

A perfect way to celebrate Valentine's Day -- especially for you who enjoy mathematics --  read (aloud and to each other) some "poems of love and mathematics." Such is easily possible, for the anthology, Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008), edited by Sarah Glaz and me, contains words on the topic by more than 150 poetic voices.  

Dividing by Zero

Fairy godmothers have their magic wands and mathematician have division by zero as a way to make the impossible happen -- for example, we can show that 2 equals 3:

How much math does a math-poem need?

Poems offered in this blog vary in the levels of mathematics they contain.  One mathematical reader commented privately that in some of the poems the use of mathematical terms is "purely decorative."  Indeed, some people have particular expectations for poetry that relates to mathematics -- they want the content to use mathematical notation or to present a mathematical truth. Such as, perhaps, this abbreviated statement of the four-color theorem (formulated as a 4x4 square): 

Electronic poetry -- Stephanie Strickland

     Computers offer new opportunities for poetry -- permitting new types of poems.  Animated perhaps, or hypertext, or vast manuscripts of which we can see at most a fragment -- the possibilities are many.  Stephanie Strickland is one of the pioneers of electronic literature -- and this post was sparked by my experiences at her presentations at Georgetown University on February 1.  

AWP avoids mathematics

I am currently attending the 2011 AWP* Conference and am disappointed that none of the sessions involves connections of writing with mathematics -- this disappointment has prodded me to write the Fib that I include below. (Recall that a Fib is a poem whose successive line-syllable counts follow the **Fibonacci seqence -- the numbers that count the petals on a flower, the spirals of seedheads on a pine cone or pineapple, and many other natural things.) 

Painting tragedy with numbers

Although words such as "massacre" and "victim" and "buried" help us to understand the effects of disaster and injustice, sometimes the most vivid descriptions of horrific events are painted with numbers -- 6 million slain, 4-year-old girl raped, 11 days without food.   One of the strong poetic voices of the twentieth century was June Jordan (1936-2002).  Works in her collection, Kissing God Goodbye  (Anchor Books, 1997), speak out for all victims, in Baghdad or Belfast, in Lebanon or Algeria.  In the following poem from that 1997 collection, Jordan uses numbers to heighten her portrayal of tragedy in Bosnia. 

Romanian poets -- Cassian and Barbu

Born in 1924, in Galati, Romania, Nina Cassian has published over fifty books -- besides poetry, she has works of fiction and books for children. Since 1985 she has lived in exile in the United States. Among those Cassian credits with strong influences on her poetry is mathematician / poet Dan Barbilian / Ion Barbu (1895-1961).  This poem by Cassian illustrates those mathematical influences:

Sonnet for a geometry teacher

Wisconsin poet Ronald Wallace has fun with math-words in the following sonnet that celebrates a teacher of plane geometry. 

Poems starring mathematicians - 8

Even though Johnny Depp played a mathematician in his recent film, The Tourist, we don't learn much about what mathematicians think or do from that story. Poetry offers more insight. Mathematician and writer Sherman Stein gives us this portrayal:

Self-portrait with numbers

Visual poet Geof Huth  lives and blogs in Schenectady, NY.  In 2010 he turned 50 and early in 2011 he sent me (via snail mail, on smooth white paper) a letter.  The letter is a poem; the poem is a celebration of life, a sort of self-portrait, using numbers.  Geof gave me permission to post it here.

Poem and parody -- isomorphic?

In mathematics, algebraic systems that have different objects but the same structure are described as isomorphic.  The parody in poetry illustrates the same idea -- a new poem is created that matches the form of a chosen poem, but uses different words.  For example, here are the opening stanzas of a poem published in 1799 by Robert Southey (1777-1843) that was later parodied by Lewis Carroll (1832-1898) in Alice's Adventures in Wonderland.

Integrals -- a poem

Integrals    by Jonathan Holden

     Erect, arched in disdain,
the integrals drift from left
across white windless pages
to the right,
serene as swans. 

Hyperbolic effects

Last month I went to the Hyperbolic Crochet Coral Reef Exhibit at the Smithsonian Museum of Natural History -- for a photo scroll down to the end of this post -- and that visit provoked me to begin searching for the term "hyperbolic" in poems.   I came close when I found "hyperbola" in a poem by Jonathan Holden and hyperbole in a sonnet by Elizabeth Barrett Browning: 

Poetry inspired by Chaos

Poet Robin Chapman studies the language learning of children -- and has collaborated with physics professor Julien Sprott on a lovely and fascinating collection The Art and Poetry of Chaos:  Images from a Complex World (World Scientific, 2005).  In the following poem Chapman offers (as she does throughout the poetry of the collection) a human interpretation of technical terminology.  

Dr King's dream and Black math students

Today is our public celebration of the January 15 birthday of Martin Luther King, Jr (1929-1968) who was both preacher and poet in the "I have a dream" speech he delivered on the steps at the Lincoln Memorial in Washington D.C. on August 28, 1963. 

Rather like an elephant

What is mathematics?
          These days I am outside of mathematics looking in and my views of the subject are more complex than during the days when I was a professor and mathematician. Back in my math-prof days -- when I moaned about those who held the view that mathematics is merely computation -- I tried to explain to uncompreheding friends the role of calculation within mathematics with this analogy:  computation is to mathematics as spelling is to poetry.  But those for whom computation is all of their mathematics do not accept this argument.  Indeed, I myself now have the notion that one can navigate life competently without algebra -- much as I get along without Spanish or Chinese. But I regret not knowing them -- they are, like algebra, among the world's important languages.

Geometry and autism

We do not easily describe what goes on inside our own heads and have still greater difficulty seeing into the minds of others.  Pennsylvania poet Barbara Crooker uses images from geometry to help us to see into autism. 

Tribute to four teachers

Many people offer advice about education--and, in particular, about mathematics education.  I'm skeptical of general pronouncements because my encounters with learning (as student or teacher or parent) have been singular:  one mind meeting another mind for a period of exchange.  Here's a poem that recalls four of my teachers, three of them teachers of mathematics. 

Which are "real" numbers?

The adjective "real" in the term "real number" causes confusion for many whose mathematics is casual rather than intense.  I like the mathematical definition of a number as real iff it corresponds to a point on the number line -- for this gives the abstract number a geometric counterpart (an attachment to reality) -- but there are others for whom the reality of a number depends on its emotional connections, perhaps used in ways that poet Ginger Andrews uses numbers in the following poem.  

Mathematics and race

Sherman Alexie is a Spokane / Coeur d’Alene Indian from Wellpinit, Washington. Besides several collections of poetry, Alexie has published novels and short-stories; he wrote the screen-play for the 1998 film, Smoke Signals. Here, in verse, he deals with the mathematics of racial identity:

New poems from old -- by permutation

     One of the founding members of the Oulipo, Jean Lescure (1912-2005), devised categories of permutations of selected words of a poem to form a new poem; three of these rearrangements are illustrated below using the opening stanza of "Mathematics or the Gift of Tongues" by Anna Hempstead Branch (1875-1937). Here is the original stanza from Branch's poem:  

From 2010 -- titles and dates of posts

List of postings  March 23 - December 31, 2010
A scroll through the 12 months of titles below may lead you to topics and poets/poems of interest. Also helpful may be the SEARCH box at the top of the right-hand column; there you may enter names or terms that you would like to find herein.
    Dec 31  The year ends -- and we go on . . .
    Dec 30  Mathematicians are NOT entitled to arrogance
    Dec 28  Teaching Numbers
    Dec 26  Where are the Women?
    Dec 21  A Square for the Season
    Dec 20  "M" is for Mathematics and . . .  

The year ends -- and we go on . . .

Immortal Helix     by Archibald MacLeish  (1892-1982)

HEREUNDER Jacob Schmidt who, man and bones,
Has been his hundred times around the sun. 

Mathematicians are NOT entitled to arrogance

Godfrey Harold “G. H.” Hardy (1877 – 1947) was an English mathematician known for his achievements in number theory and mathematical analysis. One of Hardy's lasting contributions is his 1940 essay, ;A Mathematician's Apology, which offers his self-portrait of the mind of a working mathematician. Here, written in lines and stanzas -- as a found poem -- is the opening paragraph of Hardy's essay:

Teaching Numbers

Californian Gary Soto  writes for both children and adults and much of his work suits both groups.  Here from A Fire in My Hands (Houghton Mifflin, 2006) is "Teaching Numbers":

Where are the Women?

Here is a small square poem about a paradox that's been on my mind recently.

               Little Women

               In school, many
               gifted math girls. 
               Later, so few
               famed math women!

A Square for the Season

          Now,  near the Solstice,
          we turn on  bright lights
          and  give gifts.  Oh, Sun,
          please shorten our nights
          with  your  quick  return.

Season's Greetings
     to mathematicians, to poets, and to all who inspire them-- 
          from JoAnne Growney.

"M" is for Mathematics and . . .

Today's poem by Miroslav Holub (1923-98) is square, having 5 lines of 5 letters each; it describes the letter M by using what is "not M" -- a style of reasoning often used to good effect in both poetry and mathematics.        

An Elegy from Argentina

Mathematicians are mourning the too-soon death of Cora Sadosky (1940-2010) on December 3.  Born in Argentina, Sadosky earned her doctoral degree at the University of Chicago in 1965 and published more than fifty papers in harmonic analysis and operator theory. A strong advocate for women in mathematics (1993-95 president of AWM) and active in promoting greater participation of African-Americans in mathematics, Sadosky was a long-time faculty member at Howard University.
     Here, in recognition of the contributions of Cora Sadosky, is "An Elegy" by Argentinian poet Mirta Rosenberg.  Using Rosenberg's words for her mother, we celebrate a foremother in mathematics:

Can we trust numbers?

Poet Lucia Perillo was honored Monday evening, December 13 at the Library of Congress -- as her collection Inseminating the Elephant won the 2010 Bobbit National Prize for Poetry.  It was my good fortune to be there to hear her read.  She is direct and upretentious, tough and witty.  An evening of good poetry read well.  Perillo has an undergraduate degree in wildlife management and her deep understandings of the natural world are evident in her poems.  In  an earlier collection, we find "In Light of the Absent Constant," a Perillo poem of science and number: