EDGES -- as well as VERTICES -- are IMPORTANT!

G. H. Hardy (1877-1947) was a prominent English mathematician, well-known to mathematicians for his achievements in analysis and number theory -- and for his mentorship of the Indian mathematician, Srinivasa Ramanajuan.  For most people outside of mathematics, Hardy is better known for his 1940 expository essay, A Mathematician's Apology; here are Hardy's opening sentences:

Math Communicators also are important

A posting early this month featured the noted Indian mathematician Ramanujan (1887-1920) who was mentored by the British mathematician G. H. Hardy (1877-1947).  In addition to his important achievements in number theory and mathematical analysis, Hardy is well-known for his book, A Mathematician's Apology (Cambridge Univ. Press, 1969).  Here are its opening lines:

Hardy's words seem to echo a phrase I heard long ago --  "if you can't do, teach" -- a phrase that belittles teachers and other communicators.  But now, in the 21st century, this attitude seems to be changing  and perhaps it will continue that we give attention to the work of artists and teachers and writers who share mathematical connections.   Math is important -- SHARE it!

A diamond's beauty                               
          depends on reflection                 
                    of outside light.    

TEACHERS are important ... enlarge Hardy's view!

     One of the classics written about mathematics is G. H. Hardy's 1940 book-essay, A Mathematician's Apology -- a treatise that gives valued insights into the nature of mathematics, its beauty, and the roles of mathematicians.   But today I want to urge us all to enlarge Hardy's view (shown in the box below) which offers scorn for those who talk ABOUT mathematics instead of creating it.  Our teachers and the others who spread mathematics out into the world ALSO are vital.

    Let us use geometry as Edwin Markham does -- and include

in the important world of mathematics those persons who communicate about that world.

          Outwitted     by Edwin Markham (1852-1940)

          He drew a circle that shut me out--
               Heretic, rebel, a thing to flout.
          But Love and I had the wit to win:
               We drew a circle that took him in!

Connecting mathematics to a larger world . . .

     I begin with words from a former student -- a postal worker who had retired early and went back to school to become a primary-school teacher:

                    I will teach
                    mathematics
                    by punctuality
                    and perfect attendance.

     In 1959, a Rede Lecture by C. P. Snow (1905-1980)  famously identified two separate cultures  -- the scientists and the humanists -- and these days what is often termed the STEM to STEAM movement is attempting to humanize the sciences by emphasizing the necessity of the arts in scientific study.  

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 . . .   

Linking mathematics to the rest . . .

Today my obtuse anger is rightly directed toward G. H. Hardy (1877-1947) and to the followers who have accepted his view --  in his 1940 treatise, A Mathematician's Apology -- that explaining and appreciating mathematics is work for second-rate minds.  Despite his worthy achievements in number theory and analysis and his nurturing of Ramanujan, Hardy's words should not stand forth and belittle those who teach and explain and forge connections between mathematics and all the rest.
     An wonderful and ongoing source of integration of mathematics with the arts is the Journal of Humanistic Mathematics -- and I invite you to go to the current issue and browse there OR go to this link for more than thirty pages of mathematical Haiku.

The Man Who Knew Infinity

     A few days ago I followed a broken link on the Poetry Foundation website and the site offered me this cryptic quatrain by American poet J. V. Cunningham (1911-1985) -- it is the final stanza of a poem I have posted here.

       Error is boundless.
       Nor hope nor doubt,
       Though both be groundless,
       Will average out.
               – J.V. Cunningham, from “Meditation on Statistical Method”

     Often on my mind these recent days has been the film I saw last week -- "The Man Who Knew Infinity" -- and I invite you to follow these links to poetry concerning its central characters, mathematicians Srinivasa Ramanujan (1887-1920) and G. H. Hardy (1877-1947).

Two cultures

The opening poem of Uneasy Relations by mathematician-poet Michael Bartholomew-Biggs is concerned with similarities and differences between mathematical and poetic cultures -- a topic of immense interest also to me and one that I too try to address in my verse.  I wonder --  HOW can I show non-mathematicians that good mathematics is poetry??!!  And, moreover, how can I (mostly a mathematician) write (as advocated by Wallace Stevens and agreed with by other poets) of things rather than (as mathematics wants) of ideas.  OR, may one make poetry of ideas?

   Two Cultures     by Michael Bartholomew-Biggs

   Graves claimed there isn't
   much money in poetry:
   and none vice-versa.

   The first part stays true
   if we replace poetry
   by mathematics. 

Srinivasa Ramanujan

One of the most intriguing tales in the modern history of mathematics involves Indian-born mathematician and genius Srinivasa Ramanujan (1887-1920) who traveled to England to work with G H Hardy (1877-1947).  Poet Jonathan Holden, who writes often of matters mathematical, offers this portrait of the Indian prodigy: 

Mathematicians are NOT entitled to arrogance

Godfrey Harold “G. H.” Hardy (1877 – 1947) was an English mathematician known for his achievements in number theory and mathematical analysis. One of Hardy's lasting contributions is his 1940 essay, ;A Mathematician's Apology, which offers his self-portrait of the mind of a working mathematician. Here, written in lines and stanzas -- as a found poem -- is the opening paragraph of Hardy's essay: