Musing on such problems as are the magic squares is fascinating to
thinkers of a mathematical turn of mind. We take delight in discovering
a harmony that abides as an intrinsic quality in the forms of our
thought. The problems of the magic squares are playful puzzles, invented
as it seems for mere pastime and sport. But there is a deeper problem
underlying all these little riddles, and this deeper problem is of a
sweeping significance. It is the philosophical problem of the world-order.
The formal sciences are creations of the mind. We build the sciences of
mathematics, geometry, and algebra with our conception of pure forms
which are abstract ideas. And the same order that prevails in these
mental constructions permeates the universe, so that an old philosopher,
overwhelmed with the grandeur of law, imagined he heard its rhythm in a
cosmic harmony of the spheres.