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

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.

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: 

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.   

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). 

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. 

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.   

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.

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: 

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.

Voices in a Geometry Classroom

I have been invited to return next week (October 20 at 7 PM) to Bloomsburg University, where I taught mathematics for lots of years, for a poetry reading.  Preparation for the reading (which celebrates my new book, Red Has No Reason) drew my thinking back to my teaching days at Bloom and to "Geometry Demonstration," a poem about the arguments in my head as I faced a particularly challenging class of geometry students.  Here it is.

Squares of Climate Concern

The square (with as many lines as syllables per line) is a poetry-form that has existed  for centuries and is now enjoying a revival.  Here are three small squares that come from my concerns for the precarious imbalances we humans have created within our natural environment. 

      There is no                           
      place to throw                     
      that's away.                          

Nursing--and other vital applications of counting

     Although counting is one of the basic activities of mathematics, its importance also extends to the highest mathematical levels.  We count the solutions to systems of equations, the crossings in a diagram of a knot, the intersections of surfaces in multi-dimensional space, the necessary repititions in a circuit covering the edges of a graph. Counting likewise imposes order on some of life's difficult and non-mathematical tasks.  In Veneta Masson's poem, "Arithmetic of Nurses," we have a vivid picture of the careful alertness required of those who cares for ill patients.
     Following Masson's poem, is "Things to Count On," one of my own poems of counting--a prose poem describing the way that numbers order the life of a frugal farmer and his family, working to make ends meet in Pennsylvania in the middle of the 20th century. 

Grasping at TIME

Different persons experience time differently -- as illustrated by the few lines included below (part II of  "Time" from my new collection, Red Has No Reason).  This musing is followed by the beautifully precise "Four Quartz Crystal Clocks" by  Marianne Moore (1887-1972).

From "Red Has No Reason" -- a poem about the nature of mathematics

My new poetry book, Red Has No Reason, is now available (from Plain View Press or amazon.com).  Several of the poems mention math--and one of them comments on the nature of mathematics.  Ideas for "A Taste of Mathematics" (below) came from a mathematics conference in San Antonio, TX (January 1993) where it was announced that the billionth digit in the decimal expansion of  π  is 9.  Recently an amazing  new calculation record of 5 trillion digits (claimed by Alexander J. Yee and Shigeru Kondo) has been announced.

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):

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:

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.

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.