What is beauty? Is mathematics beautiful?

     My thoughts have been turned to the beauty of mathematics by stumbling onto a very fine article, "Beauty Bare: The Sonnet Form, Geometry and Aesthetics," by Matthew Chiasson and Janine Rogers -- published in 2009 in the Journal of Literature and Science and available online here.
      The article opens with this quote from A Mathematician's Apology (see p. 14) by G. H. Hardy:       Beauty is the first test:  there is no permanent place 
                                                   in the world for ugly mathematics.

Today I'm puzzling over what "beauty" means . . .   

Some of the Magic of THREE

The Universe in Verse -- an Earth-Day celebration of Science and Poetry

A NYC event on April 23 -- learn more here!

     In her brain-pickings website, Maria Popova offers myriad links between science and poetry -- and one of the poems she has, to my delight, reminded me of is "Renascence" by Edna St. Vincent Millay (1892-1950).  Here is the first stanza:

 from    Renascence   by Edna St. Vincent Millay

          All I could see from where I stood
          Was three long mountains and a wood;
          I turned and looked another way,
          And saw three islands in a bay.
          So with my eyes I traced the line
          Of the horizon, thin and fine,
          Straight around till I was come
          Back to where I’d started from;
          And all I saw from where I stood
          Was three long mountains and a wood.
              . . .

Millay goes on to speak of flat and wide, of spheres and Infinity . . .. a story related to the poems is available here and the entire poem is found here at PoetryFoundation.org.

World Poetry Day -- Celebrate favorites!

     Down, down, down into the darkness of the grave
     Gently they go, the beautiful, the tender, the kind; 

     Quietly they go, the intelligent, the witty, the brave.

     I know. But I do not approve. And I am not resigned.

                      From "Dirge without Music" by Edna St Vincent Millay; offered by Hermann Weyl

                      in a Memorial Address for Amalie "Emmy" Noether on April 26, 1935 at Bryn Mawr College.

Earth Day -- April 22, 2015

Consider today the thoughtful words of this sonnet by Edna St. Vincent Millay (1892-1950):

     Read history: so learn your place in Time
     And go to sleep: all this was done before;
     We do it better, fouling every shore;
     We disinfect, we do not probe, the crime.
     Our engines plunge into the seas, they climb
     Above our atmosphere: we grow not more
     Profound as we approach the ocean's floor;
     Our flight is lofty, it is not sublime.
     Yet long ago this Earth by struggling men
     Was scuffed, was scraped by mouths that bubbled mud;
     And will be so again, and yet again;
     Until we trace our poison to its bud
     And root, and there uproot it: until then,
     Earth will be warmed each winter by man's blood.

These lines are found on my shelf in Collected Sonnets (Revised and Expanded Edition) by Edna St. Vincent Millay (Harper & Row, 1988).  AND, recall the arithmetic of a sonnet:  14 lines (or breaths) and 5 iambs (or heartbeats) per line. 

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.