Beauty in Mathematics

      A few days ago I found poetic words (offered below) by G. H. Hardy (1877-1947) posted on X by @TheMathFlow  -- I enjoyed not only the poem but also an exploration of various MathFlow postings -- which offer lots of delightful bits of mathematics.   (Visit @TheMathFlow and enjoy!)

Mathematics -- not isolated STARS but COMMUNITY

     In his 1940 book-length essay, A Mathematician's Apology, eminent British mathematician G. H Hardy minimizes the importance of those who communicate mathematics to those outside the research community   ... the book's opening paragraph is show below . . . it concludes with "Exposition, criticism, appreciation. is work for second rate minds."

The complete essay is available online here

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.