How many grains of sand?

Recently one of my friends used "all the grains of sand" as an example of an infinite set "because it is impossible to count them all" and -- even as I rejected his answer -- I wondered how many of my other friends might agree with it.  In the following poem, mathematician Pedro Poitevin considers a similar question as he reflects on the countability of the birds in the night sky.

       Divertimentum Ornithologicum      by Pedro Poitevin

                              After Jorge Luis Borges's Argumentum Ornithologicum.

       A synchrony of wings across the sky
       is quavering its feathered beats of flight.
       Their number is too high to count -- I try 

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 . . .  

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: 

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.

A Lemma by Constance Reid

Constance Reid (1918-2010), died on October 14.  Sister of a mathematician (Julia Robinson), Reid wrote first about life in World War II factories that supported the war effort and then, later, several biographies (including one of her sister) and other books about mathematics.  Kenneth Rexroth's poem "A Lemma by Constance Reid" (offered below) is based on material appearing in Reid's popular book From Zero to Infinity:  What Makes Numbers Interesting (Thomas Y Crowell, 1955).  Reid is known for the enthusiasm and clarity with which she presented mathematical ideas--seeking to attract and to satisfy non-mathematical readers. 

Is mathematics discovered -- or invented?

The issue of whether mathematics is invented or discovered is posed often.  Less frequently, queries as to where poetry falls in these categories. Perhaps individual answers to these questions depend on how each of us, from the inside, views the workings of the mind.   Here we have, from poet (and math teacher) Amy Uyematsu,"The Invention of Mathematics."  

Reflections on the Transfinite

     Georg Cantor (1845-1918), a German mathematician, first dared to think the counter-intuitive notion that not all infinite sets have the same size--and then he proved it:  The set of all real numbers (including all of the decimal numbers representable on the number line) cannot be matched in a one-to-one pairing with the set of counting (or natural) numbers -- 1,2,3,4, . . . .   Sets whose elements can be matched one-to-one with the counting numbers are termed "countable" -- and Cantor's result showed that the set of all real numbers is uncountable.
     Cantor developed an extensive theory of transfinite numbers -- and poet (as well as philosopher and professor) Emily Grosholz reflects on these in a poem: