What nobody else has thought

     Albert Szent-Gyorgyi (1893-1986) was a Hungarian Biochemist who discovered Vitamin C and won the 1937 Nobel Prize for Medicine.  Szent-Gyorgi offered this summary of the research process:  discovery is seeing what everyone has seen and thinking what noone else has thought. Mathematicians and poets join research scientists in that quest to see and say something new.     I was reminded of Szent-Gyorgyi's view when I read this little poem, "The Roasted Swan Sings," by Mark Baechtel in the anthology, Cabin Fever (WordWorks, 2003):

A wedding song -- shaped by mathematics

This posting includes a stanza from of "A Wedding on Earth" by Annie Finch.  In the poet's words: the poem has 11 stanzas with 11 lines for a total of 121 lines, this number symbolizing the two single members of a pair joining into a 2, which is the prevailing theme of the poem; and each stanza combining [averaging] the stanza of Spenser's epithalamion (18 lines)  with Sappho's stanza (4 lines).

Poets who Count

For some poets, counting is part of the language of the poem. For others, counting determines the structure. Here are two poems of the former sort -- "Counting" by British poet Philip Larkin (1922-1985) and "Adding It Up" by New England poet Philip Booth (1925-2007) -- followed by opening stanzas of a poem for which counting is part of both content and structure:  "Millennium" by mathematician Peter Cameron .

Trouble with Math in School

     Sad and lonely experiences seem to produce more poems than joyful ones.  And so it is easier to find a poem about a trouble in a math class than success there.  Jane Kenyon (1947-1995) was a poet and translator whose work I admire.  Here is her math-class poem:

The infinitude of ecstacy -- a la Israel Lewis

Israel Lewis is the pen name of a polymath who earned his living as a scientist and is a writer in his retirement.  His webpage offers a variety of his creations--many of them permeated with mathematics.

Mathematics in poetry by Nichita Stanescu

     Though formerly a math professor, my recent teaching has involved poetry--and I have been fortunate to spend several summer months at Scoala Andrei Muresanu in Deva, Romania, teaching poetry and conversational English.       

In the same family -- a poet and a mathematician

When a poet and a mathematician are members of the same family, understandings result.  Ohio poet Cathryn Essinger is a twin of a mathematician and writes about this relationship.  Here are opening stanzas of two of her poems.

David Blackwell (1919 - 2010) -- and Game Theory

     David Blackwell, the first black scholar to be admitted to the National Academy of Sciences, a probabilist and statistician, died early this month. His NY Times and Washington Post obituaries tell of his many contributions. Blackwell's career connects to poetry through his interest in the Theory of Games.  He was co-author with Meyer Girshick of Theory of Games and Statistical Decisions, 1954, one of the early treatises on game theory.  

Ray Bobo's mathematical poem

Ray Bobo, a retired Georgetown mathematics professor, has written a love poem with mathematical symbols.  And, for those of us who might be unsure how to interpret the mathematics, Bobo has provided a parallel column with an English-language  interpretation of his mathematics.  Enjoy! 

Poetry-application of The Fundamental Theorem of Arithmetic

Destructive effects of human greed and neglect on the earth's natural environment are echoed hauntingly in the repetitions within "We Are the Final Ones" -- a dirge-like poem I've constructed using the Fundamental Theorem of Arithmetic.  (For those unfamiliar with the theorem, brief explanation is included in paragraphs that follow the poem):

Jordie Albiston -- structure behind the writing

       I love sonnets and the one below by Jordie Albiston is a favorite of mine.
     Albiston is an Australian poet with a sense of orchestration learned from music.  Her collection, The Sonnet According to 'M' recently won the New South Wales literary award.  In her words: 

Poetry-and-Math -- Interdisciplinary Courses

     On July 1 my posting considered math-poetry anthologies and began with a reference to Against Infinity, the discovery of which was a catalyst for my own inclusion of poetry in my mathematics classrooms.  Other mathematicians and writers have gone further and developed interdisciplinary courses--such courses are the topic for this posting. 
     I begin with a small item from Against Infinity, this one a "Found Poem" by Elaine Romaine (found in the math textbook Calclulus on Manifolds by Michael Spivak):

Digital poetry -- Stephanie Strickland et al

Stephanie Strickland writes with mastery of numbers, as we see in her poem below.  But numbers are only the beginning of her work.  A director of the Electronic Poetry Association and author of "Born Digital," Strickland is one of the leaders in the development of new types of poems that are constructed using animation and rearrangements and other visual and aural communications made possible by computers and the internet.

Poetry with Mathematics -- Anthologies

More than thirty years ago at a mathematics conference book exhibit I stumbled upon Against Infinity:  An Anthology of Contemporary Mathematical Poetry, edited by Ernest Robson and Jet Wimp.  This collection, now out of print, became a resource for my mathematics courses--an opportunity for students to see the links between mathematics and the surrounding world.   One of my early loves was "Arithmetic Lesson:  Infinity" by Linda Pastan.  Found also in Carnival Evening, the poem opens with these these lines:

Mathematics, like poetry, is ART

Doing mathematics is often misunderstood as primarily computation--an error that seems equivalent to seeing poetry writing as primarily a spelling exercise. 

Poetry with mathematical symbols

On the internet and elsewhere a variety of viewpoints are expressed about the criteria poetry should satisfy to be "mathematical." Today I want to introduce samples and links for three writers:   Bob Grumman (Florida), Gregory Vincent St Thomasino (New York), and Kaz Maslanka (California).  Grumman and Maslanka write poems with a strong visual element and, as the blogs and comments for all three testify, they differ in their views of what may be properly called "mathematical" poetry..

Three poems with the word "axiom"

Poems that contain  "number" are numerous; those with "axiom" are less easily found.  Here are 3 of them -- by 19th century American poet, Emily Dickinson (1830-1886), by Canadian poet and fiction writer, Margaret Atwood (b 1939), and by a poet from Virginia, Lesley Wheeler, whose work I recently have come to know.  I particularly enjoy Lesley's poems about parenthood--because they ring true and also because when I was a parent of young children I was not finding time to write.

Send your math-poems to QUARC

Canadian journal seeks submissions from poets or fiction writers whose work makes use of metaphors from the sciences or engages scientific themes.  Deadline: September 1, 2010.

Girls and Mathematics

In Indiana, Pennsylvania, my senior high school advanced math teacher was Laura Church--a Barnard College graduate and a flamboyant silver-haired woman who never let any of us suppose that girls could not do mathematics. In college my science scholarship kept me from fleeing mathematics to study literature when I was the only girl in my classes.

Square comment on shoe styles

     Recently I have returned to Silver Spring from a trip to Latvia, traveling with a friend who was born there.  My effort to find poetry with mathematics there was stymied by the fact that little Latvian literature has been translated into English.   
     The Latvian capital, Riga, is a charming city--and its cobblestone streets do not deter women from wearing elegant tall-heeled shoes.  The sight of them reminded me of a little poem I wrote a few years ago--a square poem--which comments on this stylish sort of shoe (in which I've never been able to walk). 

Celebrate Martin Gardner (1914-2010)

Martin Gardner described his relationship to poetry as that of "occasional versifier" -- he is the author, for example, of:

     π goes on and on
     And e is just as cursed
     I wonder, how does π begin
     When its digits are reversed?

Discovering the Secret

In this Robert Frost couplet, “The Secret Sits,”  the poet may not have intended to speak of mathematics but his lines sing true for mathematical discovery.

We dance round in a ring and suppose,
But the Secret sits in the middle and knows.

from The Witness Tree.

Glances at Infinity

Counter-intuitive notions are among my favorite parts of mathematics and, in considerations of infinity, these are numerous.  Recalling Zeno's paradox, we capture the infinite finitely in this summation:

     1 + 1/2 + 1/4 + 1/2³ + . . . + 1/2ⁿ +   . . .    =  1

Sense and Nonsense

     Nonsense verse has a prominent place in the poetry that mathematicians enjoy. Perhaps this is so because mathematical discovery itself has a playful aspect--playing, as it were, with non-sense in an effort to tease the sense out of it.      Lewis Carroll, author of  both mathematics and literature, often has his characters offer speeches that are a clever mix of sense and nonsense. For example, we have these two stanzas from "Fit the Fifth" of The Hunting of the Snark, the words of the Butcher, explaining to the Beaver why 2 + 1 = 3.

Poems starring mathematicians - 6 (Mandelbrot)

More familiar than the name Benoit Mandelbrot are images, like the one to the left, of the fractal that bears his name.  Born in Poland (1924) and educated in France, Mandelbrot moved to the US in 1958 to join the research staff at IBM. A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole, a property called self-similarity. 

The epitome -- Euler's Identity

Mathematics is a visual language.  As with poetry, placement on the page is a key ingredient of meaning.  Here is one of my favorite visual poems, "The Transcendence of Euler's Formula," by Neil Hennessy, a Canadian poet and computer scientist.  For additional math-poetry from Neil, follow the link.

          epitome
          epitome
          epitome
          epi+ome
          epItome
          _____________
          epit0me

Margaret Cavendish (1623-73) -- The Circle of the Brain cannot be Squared

Margaret Cavendish (1623-73) was a writer who published under her own name at a time when most women published anonymously.  Her writing addressed a number of topics, including gender equity and scientific method.

Mathematical 'grooks' from Piet Hein

Piet Hein (Denmark, 1905-1996) was many-faceted--by times a philosopher, mathematician, designer, scientist, inventor of games and poet. He also created a new poetic form that he called 'grook' ("gruk" in Danish). Hein wrote over 10,000 grooks, most in Danish or English, published in more than 60 books. Some say that the name is short for 'GRin & sUK' ("laugh & sigh", in Danish).  Here are samples, with links to more:

Poems starring mathematicians - 5

In my own library this next poem is found (untitled) in Collected Sonnets by Edna St Vincent Millay (1892-1950),  but it also is found online at various sites. The first line of the sonnet, which announces Euclid as its subject, is well-known to most mathematicians; enjoy here all fourteeen lines.

A Numerical Poem (Fibonacci)

Consider the following poem involving the Fibonacci numbers:
 

        1/89 = .0        +

                  .01        +

                  .001        +

                  .0002        +

                  .00003        +             

                  .000005        +

                  .0000008        +

                  .00000013        +

                  .000000021        +

                  .0000000034        +

                  .00000000055        +

                  .000000000089        +

                  .0000000000144        +

                  .  ...

Poems starring mathematicians - 4

Each of today's poems is in the voice of a student who looks back.  First, from Carol Dorf, a poem to the author of a book--written as a fan-letter, "Dear Ivar."   And then, for his hero (a special Grammar School teacher) by Czech poet and scientist Miroslav Holub (1923-98), "The Fraction Line."

       Dear Ivar,

       I read your book on the unexpected.

       Like most poets, I opposed mathematics

       when I was young, seeing it as the converse

       to feeling. The previous statement is false.

Poems starring mathematicians - 3

Today's poems illustrate the satirical humor and rhyme that frequently inhabit poems by mathematicians. (Previous postings of poems about mathematicians include March 23, April 14, and April 15.)

I Even Know of a Mathematician      by John L Drost

        “I even know of a mathematician who slept with his wife only
                   on prime-numbered days…” Graham said.
                            ―Paul Hoffman, The Man Who Loved Only Numbers

Poems of Calculus

In her thoughtful poem "Calculus" mathematician-poet Sarah Glaz writes of sharing with her students some of their subject's history--a drama enacted by two different sorts of mathematician.  Here are Glaz' opening lines:

A Square for Earth Day

Greetings on EARTH DAY.  Earth's inhabitants today pay a price not only for our own careless habits but also for earlier ignorance about the fragility of our world. (As Garrett Hardin has said, "There is no away to throw to.")  The April 20 edition of  the Washington Post had an AP article about the risks of trash to wildlife in the Atlantic that provoked me to write the following square poem.

April -- Poetry, Math, and Boxing

April continues—both as National Poetry Month and as Mathematics Awareness Month (with theme math and sports).  As in the April 9 posting on baseball, in this post I also blend these interests with a math-and-sports poem--this one celebrates boxer Sugar Ray Robinson.

Poems with Fibonacci number patterns

In 21st century poetry, there are a variety of non-rhyming forms--and several of them have derived from the Fibonacci numbers.*  The Danish poet, Inger Christensen (1935-2009), wrote a book-length poem, alphabet (New Directions, 2000) in which the numbers of lines in stanzas followed the sequence of Fibonacci numbers.  "Fibonacci," shown below, by Judith Baumel is a shorter example of this form.

Poems starring mathematicians - 2

Published a century later than William Benjamin Smith's "The Merman and the Seraph" (see April 14 posting) we have Crossing the Equal Sign (Plain View Press, 2007)--a poetry collection by Marion Deutsche Cohen.  Cohen lives in Philadelphia and teaches mathematics at Arcadia University where she has used her literary interests to develop a new course, "Truth and Beauty: Mathematics in Literature."  I have chosen several excerpts from Cohen's collection that offer internal snapshots of  her sort of mathematician:

Poems starring mathematicians - 1

This is the first in a series of postings involving poems in which the principal subject is a mathematician.

     In “The Ideal Mathematician,” an essay in The Mathematical Experience, authors Philip Davis, Reuben Hersh, and Elena Marchisotto endeavor to describe the most mathematician-like mathematician:  He rests his faith on rigorous proof ...  He is labeled by his field, by how much he publishes . . .   He finds it difficult to establish meaningful conversation with that large portion of humanity that has never heard of [his research topic] ...  His writing follows an unbreakable convention:  to conceal any sign that the author or the intended reader is a human being ....

Poetry and Mathematics -- Similarities

HOW are mathematics and poetry similar?

Often-quoted in mathematical circles are words from mathematician Karl Weierstrass (1815-97): “It is true that a mathematician, who is not somewhat of a poet, will never be a perfect mathematician.”    And from physicist Albert Einstein (1879-1955):  "Pure mathematics is, in its way, the poetry of logical ideas." More recently, from Lipman Bers (1914-1993): “  . . . mathematics is very much like poetry . . . what makes a good poem—a great poem—is that there is a large amount of thought expressed in very few words."

April: along with baseball we celebrate poetry and mathematics

Is it coincidence or design that

     April  is  National Poetry Month
            
           and

   April  is  Mathematics Awareness Month
          (This year's theme is  "mathematics and sports")

In my own reading, baseball is the sport for which I have found the most poetry.

Braided lines form a PANTOUM

The pantoum is derived from a Malaysian form of interlocking four-line stanzas in which lines 2 and 4 of one stanza are used as lines 1 and 3 of the next. The lines may be of any length, and the poem can go on for an indefinite number of stanzas; it may be completed with a final stanza that uses lines 1 and 3 of the first stanza as lines 4 and 2 of the last, closing the circle of the poem.  As with recursion, each stanza provides an impetus for the next.

John Donne's numbers

       Perhaps best known for the religious themes in his poetry, John Donne (1572-1631) also wrote many love poems. Although the mathematics here includes only numbers, they are well-used to strengthen both the intensity and the precision of the work.

The Primrose  by John Donne

Miroslav Holub, poet and scientist

Miroslav Holub (1923-1998), Czech poet and immunologist who excelled in both endeavors, is one of my favorite poets.  He combines scientific exactitude with empathy and absurdity.  Here are samples:

The Corporal Who Killed Archimedes

With one bold stroke

he killed the circle, tangent

and point of intersection

in infinity.

"Mathematical" Limericks

A dozen, a gross, and a score
Plus three times the square root of four
     Divided by seven
     Plus five times eleven
Is nine squared and not a bit more.

W. H. Auden's Kingdom of Number

Some poetry is termed "mathematical" because mathematical terminology is included in the text of the poem, often to vivid effect. Such is the case in this poem by W H Auden, in which it is also the case that most lines have 11 syllables.

Queneau and the Oulipo

Raymond Queneau was one of the leaders of a group of ten--primarily writers and mathematicians, primarily French--who founded a group, "Ouvroir de Littérature Potentielle" ("Workshop of Potential Literature"), that eventually became known as the Oulipo. Queneau described potential literature as "the search for new forms and structures that may be used by writers in any way they see fit."

Howard Nemerov's mathematical imagery

GETTING IT RIGHT IN LANGUAGE -- Poets and mathematicians alike are concerned with precise statement. Two-time US Poet Laureate Howard Nemerov (1920-1991) characterized poetry in a way that many mathematicians would likewise characterize their subject: POETRY is getting something right in language. Nemerov often used mathematical imagery in his poems. Here is a sample.

Poetry of Logical Ideas

When the NY Times failed to publish an obituary following the death of noted algebraist Amalie "Emmy" Noether, Albert Einstein corrected the omission with a letter to the editor (noting Noether's accomplishments) published on May 5, 1935. In addition to his praise for one of the most accomplished mathematicians of all time, Einstein said this of mathematics: "Pure mathematics is, in its way, the poetry of logical ideas." In the 1960s, as I climbed into the male-dominated world of mathematics, Emmy Noether was one of my heroes. Many years later I wrote this poem.