Recently, and perhaps always, opposites have interested me. For example, the complementary and sometimes conflicting nuggets of advice contained in "Pinch a penny, waste a pound" and "It is best to prepare for the days of necessity." And in "Kindness effects more than severity" and "Spare the rod, spoil the child." Maybe what I like best is the challenge of synthesizing opposite truths.
Mathematics contains many pairs of entities that are, each in some different sense, opposites:
2 and -2 2 and 1/2
horizontal and vertical differentiation and integration
And there are some arbitrary subdivisions that often are treated as if they are disconnected opposites:
pure vs. applied (creating mathematics vs. solving problems)
teaching and learning, creating vs. teaching, arts and sciences
In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :