Is mathematics discovered or invented?

My neighbor, Glenn, is fond of asking math-folks that he meets the question "Is mathematics discovered or invented?" -- and when he asked the question of MAA lecturer William Dunham the response was one word, delivered with a smile, "Yes." The question of invention versus discovery -- which may apply to poetry or to mathematics  --  is thoughtfully considered in "Notes toward a Supreme Fiction" by Wallace Stevens (1879-1955); here are a few lines from that poem.

       from It Must Give Pleasure,  VII     by Wallace Stevens

     He imposes orders as he thinks of them,
     As the fox and the snake do. It is a brave affair.
     Next he builds capitols and in their corridors,    

Chaos and Order -- Stevens

An article by Jeff Gordinier, "For Wallace Stevens, Hartford as Muse," in the Travel Section of last Sunday's NY Times gives a gentle introduction to one of my favorite poets; the article also provoked me to escape for an hour into a rereading of selections from my copy of The Collected Poems (Vintage Books, 1990). Poems by Stevens (1879-1955) celebrate ideas and are, like pieces of mathematics, suggestive of a variety of situations. (Work by Stevens was featured in these earlier blog postings: 15 December 2010 (from "The Snow Man"), 4 May 2011 ("The Anecdote of the Jar"), and  13 May 2011 (from "Six Significant Landscapes"). Here, reconciling opposites, are two of the five sections of Stevens' "Connoisseur of Chaos" -- also from The Collected Poems.

Chaos Over the Hors d'Oeuvres

Some systems of equations can produce vast changes in output with only small changes in input.  Or not.  This sensitivitiy to initial conditions is a key characteristic of chaos.  As happens not infrequently in mathematics, the term chaos also carries larger-world meanings additional to the correct ones -- indeed, the phenomena studied in chaos theory are not haphazardly disordered but are complex.  Very very complex.  Judy Neri's poem addresses this topic. 

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: