Mathematics: "A Growing Organism"... "A Connected Web"

This Sunday's Reflection:

"Mathematics is a living and growing organism; within it are intricate and delicate structures of strong aesthetic appeal.  It offers opportunities for surprise as unexpected vistas open the mind to new lines of thought...
"Mathematics was created by all manner of people. There were religious bigots and atheists, political reactionaries and wild revolutionaries, snobs and egalitarians; some were people of great charm, some odious. If there is any common denominator, it is a driving curiosity, a desire to understand, a need to build, even if the structures be abstract. Admirably suited though mathematics is to modelling the real world, it can be developed totally without dependence on anything outside itself. Parts of it are simply mind creations, owing nothing to the physical world. It is a playground for the mind...

"Regrettably, many of us have never been allowed to see what mathematics is. It has been obscured by pointless emphasis on routines rather than ideas. This failure to distinguish what is important has led many people to see mathematics as a collection of totally arbitrary rules which have to be learnt by rote, and performed with the exactness and precision of a religious rite. Ask a person if there is much to be remembered in mathematics; if they speak of an overwhelming mass of material, their education in this area has been counter-productive; not merely neutral. Mathematics, properly seen, is a connected web; grasp at one piece and all the surrounding region comes to mind."

-- Laurie Buxton from the Introduction to  "Mathematics For Everyone" (1984)