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!

The opening paragraph of A Mathematician's Apology  (G. H. Hardy, 1940)
The entire essay is available online here.