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:

Is Math for Women?

At a River Poets reading at the public library in Bloomsburg, Pennsylvania on December 1, 2011, Carol Ann Heckman surprised me with her poem, "The Calculus Road Not Taken," presented below.  Not only is she a fine poet, but Carol Ann is curious about mathematics.  As a college student she was turned away by negative feedback from a math professor. But now she is reassessing her situation and ready to tackle calculus. Here she has fun with her calculus-deprived situation in lively verse:

The Calculus Road Not Taken   by Carol Ann Heckman  

               for JoAnne Growney

If I had only conquered
calculus
this wouldn't have
happened--the flood,
the earthquake, the
two hurricanes
in succession

Calculus (and calyculus)

For lots of years I have subscribed to A.Word.A.Day, founded by Anu Garg, and on 3 June 2013  -- offered in the category of "words that appear to be misspellings" -- the word that appeared in my email was calyculus (kuh-LIK-yuh-luhs), a noun designating a cup-shaped structure.  From this, of course, my thoughts turned to calculus and to poems on that subject.  Below I offer "UR-CALCULUS" by Jonathan Holden.  This Kansan poet has said that that his physicist father would write equations while sitting at the dining room table -- and "UR-CALCULUS" considers mathematics from a boy-riding-in-the-back-seat-of-a-car point of view.  

     UR-CALCULUS     by Jonathan Holden

               The child is the father of the man. 
                        -- W. W. Wordsworth

     Back then, "Calculus"
     was a scary college word,
     and yet we studied it
     from the back seat, we studied  
     the rates at which
     the roadside trees went striding 

Ghosts of Departed Quantities

     Years ago in calculus class I excitedly learned that an infinite number of terms may have a finite sum.  Manipulation of infinities seems somewhat routine to me now but my early ideas of calculus enlarged me a thousand-fold.  Algebra was a language, geometry was a world-view, and calculus was a big idea.  Like any big idea, even though it had been hundreds of years in formation, it met with resistance.  In 1764 Bishop George Berkeley attacked the logical foundations of the calculus that Isaac Newton had unified.  Here, from the online mathematics magazine plus,  is a description of the attack.

Midlife Calculus -- poems by Britt Kaufmann

     Today's featured poet, Britt Kaufmann, is not only a writer but also a graphic designer, a playwright, and "a lifelong reader and learner."  And a math tutor!  Out this month (from Press 53) is her mathy collection, Midlife Calculus -- a thoughtful and  fun-to-read collection that links math ideas to a variety of life's experiences.  

     Last February, I was introduced to Kaufmann's work when her book-title-poem, "Midlife Calculus," appeared in Scientific American.  I was delighted to also find her poem,  "Z-score of Zero" here in the April-May edition of MAA Focus and I was drawn to include it in this April, 2024 blog-posting.  Visit and enjoy!

     Midlife Calculus is available here.  And below are a couple of samples:    

Putting CALCULUS into a poem . . .

 Can our world be described using calculus?

     The poem-a-day offering this morning (6/21/21) from poets.org gives me new ideas about describing a problem-situation using some terms from mathematics.  I offer part of the poem below, followed by a link to the complete work.

from  Disintegrating Calculus Problem     by McKenzie Toma

A dramatic clue lodged in a rockface. Set in a shimmering sound belt slung around the grasses. Collections of numbers signify a large sum, a fatness that cannot be touched. Numbers are heart weight in script. Calculus means a small pebble pushed around maniacally. Binding affection, instead of fear, to largeness.  

Ideas are peeled into fours and pinned on the warm corners of earth to flap in a wind. Wind, the product of a swinging axe that splits the sums. This math flowers on the tender back of the knee.     . . . .

     McKenzie Toma's complete poem appears here (with other poem-a-day offerings at poets.org) and and here (along with several others of her poems).

Loving the difference quotient ... and more ...

     From Philadelphia poet-mathematician, Marion Cohen, a new collection  -- Closer to Dying (Word Tech, 2016).  When I received the book a few days ago and began to read I did, of course, seek out mathy poems.  Two of these are included below. In this first poem Cohen has some fun with the terms and symbols of introductory calculus.  In the second, she tells of an encounter of the sort that happens to many mathematicians  -- meeting someone who supposes that mathematicians do what calculators do. (This link leads to a collection of mathy poems (including ones by Cohen) at talkingwriting,com.)

from MIT Science-Poetry -- The Cal-Dif-Fluk Saga

     Recently I have enjoyed browsing a voluminous online 19th century Science-Poetry collection (Watchers of the Moon) hosted by MIT, gathered and edited by Norman Hugh Redington and Karen Rae Keck. Google led me to the site in a search for " poetry of calculus" and I found there found a fascinating item by J. M. Child:  The Cal-Dif-Fluk Saga (from The Monist: A Quarterly Magazine Devoted to the Philosophy of Science -- Open Court Publishing, 1917) and described as "a  pseudo-epic about the invention of calculus."  
     Child was a translator (from Latin into English) of the works of Isaac Barrow and Gottfried Leibniz and his poem presents the names of well-known mathematicians in clever scrambles:  Isa-Tonu is Newton, Zin-Bli is Leibniz, Isa-Roba is Barrow, Gen-Tan-Agg stands for Barrow's Gen-eral method of Tan-gents and of Agg-regates while Shun-Fluk and Cal-Dof refer to the methods of Newton and Leibniz.  One may, with a fair amount of work, enjoy this dramatization of warriors and weapons -- battles that were part of the development of calculus.  Here from the middle of the Saga (from Section 6 (of 17)), is a sample of Child's lines illustrating the struggles that calculus required.

Graffiti Calculus

     In my dreams I am an artist -- a cartoonist, perhaps, or a graffiti artist -- so skilled with lines and curves and so clever that my art gives pleasure AND delivers a punch.
     And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled Graffiti Calculus (CW Books, 2013).  I first met Willis in December, at Cafe Muse (where I will read next Monday, Feb 3 with Stephanie Strickland) and it was my pleasure also to hear her read again from that collection at the Joint Mathematics Meetings.  These poems by Willis give us, in sixty poetic chapters, the story of a mother seeking her son by following his graffiti tags through the city.  Here is a sample, sections 5 and 6: 

A poem-title that drew me in -- "Calculus I, II, III"

      A poetry event that I often enjoy is the posting by the Academy of American Poets of a poem-a-day -- today's poem is found here  and  information about the posting is found here at Poets.org.  my background in mathematics helped me to be especially pleased early this month (on 2/2) when the daily poem (written by poet and artist Brad Walrond) was entitled "Calculus I, II, III" -- and if offers reflection on different levels of learning.  Below I offer a few lines from the poem; the complete poem is available at this link.

from     Calculus I, II, and III    by Brad Walrond

      . . .    this calculus

     —how one body
     relates to another—

     that disturbs all the peace

     is the same as learning
     their one two threes       . . .

   Copyright © 2024 by Brad Walrond.   Read more here.

A poem of calculus (of ants on a worm)

Philip Wexler plays with the terminology of calculus in this poem:

     The Calculus of Ants on a Worm

     Swarming tiny
     bodies nibble
     away, no limits,

Mathy Limericks . . .

     One of the fun-to-visit poetry resources on the internet is the Omnificent English Dictionary in Limerick Form, a website resource that has for a goal the inclusion of at least one limerick for each meaning of each and every word in the English language.  Here is a link to an earlier mention of OEDILF in this blog and here, from the OEDILF site, are a pair of limericks about Calculus -- limericks that are currently awaiting dictionary approval.

          "Was it Newton or Leibniz?" I asked
          My professor. He smiled and then tasked
               Me to find more about
               My small calculus doubt.
          I researched and the truth was unmasked.     

Found: Elementary Calculus

Here is a poem by Saskatchewan poet Karen Solie.

       Found     by Karen Solie

       Elementary Calculus

                From    Elementary Calculus  A. Keith and W. J. Donaldson.
                          Glasgow:  Gibson, 1960.

       Speed (like distance)
       is a magnitude and has no
       direction; velocity (like displacement)

       has magnitude and direction.  

Mathematician of the Day

     On this date, May 16, in the year 1718, the talented Maria Agnesi was born.  A great source of historical information about mathematics and mathematicians is MacTutor, a math-history website maintained by the School of Mathematics and Statistics, University of St Andrews, Scotland.  One of the services that MacTutor provides is a list of names and information about mathematicians born on each day of the year.  For example, this link leads to the listing for May 16 -- and to lots of info about Agnesi.  Here, in a 7x7 syllable-square, is a brief sketch of  her life:

Maria Agnesi's life --

a complicated story --

wealthy and intelligent, 

in love with mathematics,

also very talented--

wrote a teaching text about 

differential calculus.

This 2018 Scientific American blog posting by Evelyn Lamb discusses a curve from calculus, often called (somewhat misleadingly) "the witch of Agnesi."   Previous mentions of Agnesi in this blog may be found at this link.

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.

Related rates -- in fiction and poetry

     During the Memorial Day weekend I had the opportunity to read Black Rice (WSI, 2013), a novella by Burmese-American poet, artist, activist -- and friend -- Kyi May Kaung; I strongly recommend this book to you.  (My 5-star review of Kaung's book is available here at amazon.com -- follow the link and scroll down.)
     Here, in this blog, we mention topics if and only if they relate to both mathematics and poetry.  Read on and you will see!
     Midway through Black Rice, the narrator (speaking of an overflowing stream) reveals a negative attitude toward mathematics -- a strategy often used to provoke readers to experience empathy:  "Ahhh, just like me."  Here are the Burmese soldier's words:

Dogs Know . . . Mathematics

     A mathematics/statistics education researcher who writes both poetry and song lyrics -- who writes these often and well -- is Lawrence "Larry" Lesser, professor at The University of Texas at El Paso.  A search of prior postings in this blog leads to a variety of Lesser's poems: here's a link.
   And here is another Lesser poem to enjoy  -- this one found along with lots more math-poetry in the Bridges 2016 Poetry Anthology, edited by Sarah Glaz (Tessellations Publishing, 2016).

   
       Dogs Know     by Larry Lesser

       A dog-eared College Mathematics Journal lies
       open to a paper called
       "Do dogs know calculus?"
       where the author's canine travels land
       and water to reach most quickly
       the ball thrown
       into Lake Michigan.  

A Mathy Celebration of National Poetry Month

     It is a delight to me to see math and science publications including poetry!  Today I am enjoying the work of North Carolina poet Britt Kaufmann -- Kaufmann works as a math tutor -- and her poem "Midnight Calculus" appeared in the February 2024 issue of Scientific American.  The accompanying bio mentioned that Kaufmann took her first calculus course at age 47.

     More recently, under the heading "In Celebration of National Poetry Month," MAA FOCUS, the Newsmagazine of the Mathematical Association of America. another Kaufmann poem appeared, "Z-score of Zero."   (A z-score measures exactly how many standard deviations above or below the mean a particular data-number is.)  Kaufmann gives us a thoughtful poetic reflection of math on life!  

If 1718 is a poem title . . .

If 1718 is a poem title, 

the poem should celebrate Marie Gaetana Agnesi (1718-1799)

author of the first book about both differential and integral calculus.

This post celebrates not only Agnesi (who was born 301 years ago today) but also present-day mathematician and writer Evelyn Lamb who produces lively and informative articles about STEM topics and people.  Go here to read Lamb's article about Agnesi for the Smithsonian Magazine on May 16, 2018 -- celebrating Agnesi's 300th birthday.

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 . . .